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A constellation design for orbiting solar reflectors to enhance terrestrial solar energy

April 2024
Acta Astronautica 217(12)

DOI:10.1016/j.actaastro.2024.01.031

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Delft University of Technology

Orbiting solar reflectors (OSRs) are flat, thin and lightweight reflective structures that are proposed to enhance terrestrial solar energy generation by illuminating large terrestrial solar power plants locally around dawn/dusk and during night hours. The incorporation of OSRs into terrestrial energy systems may offset the daylight-only limitation of terrestrial solar energy. However, the quantity of solar energy delivered to the Earth’s surface remains low due to short duration of orbital passes and the low density of the reflected solar power due to large slant ranges. To compensate for these, this paper proposes a constellation of multiple reflectors in low-Earth orbit for scalable enhancement of the quantity of energy delivered. Circular near-polar orbits of 1000 km altitude in the terminator region are considered in a Walker-type constellation for a preliminary analysis. Starting from a simplified approach, the equations of Walker constellations describing the distribution of the reflectors are first modified by introducing a phasing parameter to ensure repeating pass geometry over solar power farms. This approach allows for a single groundtrack optimisation to define the constellation, which was carried out by a genetic algorithm for single and two reflectors per orbit with an objective function defined as the total quantity of energy delivered per day, to existing and hypothetical solar power projects around the Earth. When full-scale constellations are considered with a number of reflectors, the quantity of solar energy delivered is substantial in the broader context of global terrestrial solar energy generation.

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74th International Astronautical Congress, Baku, Azerbaijan, 2-6 October 2023.

reserved.

IAC–23–C1,IPB,4,x77299

A constellation design for orbiting solar reflectors to enhance

terrestrial solar energy

Onur C¸ elik∗, Colin R. McInnes

Space and Exploration Technology Group, James Watt School of Engineering, University of Glasgow,

Glasgow G12 8QQ, Scotland, United Kingdom

Orbiting solar reﬂectors (OSRs) are ﬂat, thin and lightweight reﬂective structures that are proposed to

enhance terrestrial solar energy generation by illuminating large terrestrial solar power plants locally around

dawn/dusk and during night hours. The incorporation of OSRs into terrestrial energy systems may oﬀset

the daylight-only limitation of terrestrial solar energy. However, the quantity of solar energy delivered to the

Earth’s surface remains low due to short duration of orbital passes and the low density of the reﬂected solar

power due to large slant ranges. To compensate for these, this paper proposes a constellation of multiple

reﬂectors in low-Earth orbit for scalable enhancement of the quantity of energy delivered. Circular near-

polar orbits of 1000 km altitude in the terminator region are considered in a Walker-type constellation for a

preliminary analysis. Starting from a simpliﬁed approach, the equations of Walker constellations describing

the distribution of the reﬂectors are ﬁrst modiﬁed by introducing a phasing parameter to ensure repeating

pass-geometry over solar power farms. This approach allows for a single groundtrack optimisation to deﬁne

the constellation, which was carried out by a genetic algorithm for single and two reﬂectors per orbit with an

objective function deﬁned as the total quantity of energy delivered per day, to existing and hypothetical solar

power projects around the Earth. When full-scale constellations are considered with a number of reﬂectors,

the quantity of solar energy delivered is substantial in the broader context of global terrestrial solar energy

generation.

1. Introduction

Orbiting solar reﬂectors are large, thin and ultra-

lightweight reﬂector structures in orbit, proposed to

illuminate the Earth for a variety of applications.

The earliest proposals are before the modern space

era and included the illumination of cities and loca-

tions such as airports at night [1]. The later pro-

posals in the 1970s and 1980s extended those appli-

cations to terrestrial solar energy generation by il-

luminating ultra-large utility-scale solar power farms

at night, enhancing agriculture and street illumina-

tion [2, 3, 4]. Global demand for clean energy due to

climate change, decreasing launch costs due to com-

mercialisation and other advancements in space tech-

nologies such as in-orbit assembly and manufacturing

have attracted renewed interest in the concept of or-

biting solar reﬂectors in the 21st century [5].

‡This manuscript is based on the manuscript presented at

International Astronautical Congress, 74, Baku, Azerbaijan,

2-6 October 2023. Paper no. IAC-23,C1,IPB,4,x77299. Copy-

right by the authors.

∗Corresponding author

Email addresses:

Onur.Celik@glasgow.ac.uk (O. C¸ elik),

Colin.McInnes@glasgow.ac.uk (C. R. McInnes)

The most important limitation of terrestrial solar

energy generation is its restriction to daylight hours,

which, despite the Sun as a practically endless source

of energy, limits the electricity generation from solar

power farms to a much lower level than their actual

capacity. To that end, a reﬂector in orbit, placed

in orbits that are both visible to the Sun and to

the solar power farm, could extend the operational

hours by illuminating the farm locally, thereby en-

hancing its utility [5]. The concept of orbiting solar

reﬂectors has therefore been studied for the 21st cen-

tury energy demands and requirements by leveraging

the advancements in space technology. Fraas and co-

authors have studied this concept primarily for the

enhancement of solar energy [6, 7, 8, 9] but also for

municipal street lighting [10]. Among more recent

studies, Bonetti & McInnes presented a two-reﬂector

constellation in a so-called anti-heliotropic orbit to

deliver solar energy to three ultra-large hypothetical

solar power farms in equatorial regions [11]. Viale et

al. instead presented a reference architecture study

for near-term applications with a ﬁve-reﬂector system

in Sun-synchronous orbits, delivering solar energy to

13 existing and under-development solar power farms

around the Earth [12]. The authors also presented a

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technology roadmap for the employment of the con-

cept of orbiting solar reﬂectors [13]. Other propos-

als of OSRs include a dual reﬂector system with a

Sun-facing parabolic reﬂector and a small, agile and

steerable reﬂector in orbits displaced on either side

of the terminator line to further enhance the energy

delivery [14]. Orbiting solar reﬂectors are also consid-

ered in lieu of battery technology for terrestrial solar

energy [15].

The quantity of energy delivered from orbiting so-

lar reﬂectors is scalable by the number and size of the

reﬂectors [16, 13]. Single reﬂectors may be increased

in size to enhance the quantity of solar energy deliv-

ered, which would increase solar power density on the

ground but it would not extend the daily operational

hours. Instead, a number of reﬂectors may be consid-

ered in a constellation that could provide continuous,

scalable and predictable solar energy input to a solar

power farm. Ehricke’s (1979) Powersoletta constella-

tions envisaged a very large number of reﬂectors in a

constellation to provide electricity to the entire Earth

by only solar energy [3]. On the other hand, Canady

& Allen (1982) considered a four-reﬂector constella-

tion to illuminate several major cities in the United

States [4]. Frass (2012, 2013) constellations consisted

of 18 satellites in a single dawn/dusk orbit at 1000 km

altitude, servicing some 40 hypothetical solar power

farms on its groundtrack [6, 7]. Bonetti & McInnes

(2019) employed a much larger altitude elliptical or-

bit and a ﬂower constellation pattern [17] for a two-

reﬂector constellation to deliver solar energy to hypo-

thetical large equatorial solar power farms [11]. Viale

et al. (2023) reference architecture study may also be

considered a form of constellation with ﬁve reﬂectors

in a closely spaced train motion in a single, 24-hour

repeating ground track dawn-dusk Sun-synchronous

orbit, whose ground track is “anchored” to an ex-

isting solar power farm project [12]. However, none

of these studies consider optimal constellations that

consider solar power farms that are existing or un-

der development with realistic models of solar energy

delivery and provide detailed insights into individual

passes.

Constellations of orbiting solar reﬂectors may need

to satisfy several requirements. For a truly global so-

lar energy delivery at dawn and dusk hours, orbits of

near-polar inclinations placed at near-terminator re-

gions are more desirable. Especially Sun-synchronous

orbits provide natural Sun-tracking ability by exploit-

ing Earth’s oblateness [5]. But widely used constella-

tion geometries such as Walker constellation [18] and

more generalised Flower constellations [17] distribute

orbit planes around the Earth equally and not spe-

ciﬁc regions. Moreover, continuous and scalable en-

ergy delivery requires reﬂectors to be placed in orbits

in such a way to follow the same pass geometry over

solar power farms. This requires the distribution of

orbit planes and the reﬂectors on them to be synchro-

nised with the Earth’s rotation in the presence of the

Earth’s oblateness, which may also be deﬁned by a

phase angle between them to be controllable. Arnas

& Casanova (2020) tackles a similar problem by using

the analytical expressions of Flower and Walker con-

stellations, though they only consider constellations

equally distributed globally and use time instead of

a phase angle [19]. Considering the existing, under

development and hypothetical farms with an objec-

tive to maximise the daily quantity of solar energy

delivered globally, the constellation design problem

becomes an optimisation problem of a new kind. The

constellations with repeating pass geometries would,

in fact, make this problem an optimisation problem

of a single reﬂector’s groundtrack where the distribu-

tion of others in the orbit plane and mean anomaly

would provide the same pass geometry for a scalable

expansion.

This paper therefore presents an optimal constel-

lation design for orbiting solar reﬂectors to enhance

terrestrial solar energy generation. A Walker constel-

lation pattern is considered with polar and near-polar

Sun-synchronous circular orbits at 1000 km altitude.

First, starting from a simpliﬁed approach of multiple

reﬂectors in a single orbit and non-rotating Earth,

the scalability aspects are discussed in relation to the

phase angle between reﬂectors. This phase angle is

later used to modify the analytical distribution of re-

ﬂectors in a Walker constellation pattern to synchro-

nise successive orbit planes with Earth’s rotation in

the presence of Earth’s oblateness perturbation to en-

sure the same pass geometry for all reﬂectors in the

constellation. The groundtrack optimisation of the

initial reﬂector satellite is then carried out by using a

genetic algorithm with an objective function deﬁned

as the maximum daily energy delivery. The optimi-

sation function includes a realistic model of reﬂected

solar energy delivery [20]. A single-reﬂector and two-

reﬂector conﬁgurations are considered in the optimi-

sation by delivering solar energy to existing and hypo-

thetical solar power farms. Detailed investigations of

individual solutions are oﬀered and discussed compar-

atively with other works. 5, 10 and 20-reﬂector con-

stellations are presented and discussed in the wider

context of enhancing terrestrial solar energy.

This paper is structured as follows: In the next sec-

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tion, the model for reﬂected solar energy delivery will

be summarised. In Sec. 3, the approach for constel-

lation design will be introduced. The optimisation

problem will be discussed in Sec. 4 and the results of

the optimisation will be discussed in Sec. 5. Section

6 will expand on the implications of the results for re-

ﬂector constellation and, ﬁnally, conclusions will be

presented in Sec. 7.

2. Reﬂected solar energy delivery from space

The power delivered by a reﬂector in orbit to the

surface of the Earth can be written as follows [16]:

PSP F =χ(t)I0

Aim(t)AS P F cos ψ(t)

2(1)

where I0is the solar constant which is assumed to fol-

low an inverse-square law with the distance from the

Sun and equal to 1.37 GWkm−2at the mean distance

between the Earth and the Sun, i.e. 1 Astronomical

Unit (AU). AM,ASP F ,Aim are the areas of the re-

ﬂector, solar power farm and the projected image of

the Sun (i.e., illuminated region) on the ground. AM

and ASP F have ﬁxed areas, but Aim is an elliptical

area whose size is a time-dependent function that can

be written as [20]:

Aim(t) = πa(t)b(t) = π[d(t) tan (α/2)]2

sin ϵ(t)(2)

where ddenotes the magnitude of the slant range

vector measured from the topocentric-horizon refer-

ence frame (THF) of the ground target such as a solar

power farm and αdenotes the angle subtended by the

Sun, approximately 0.0093 rad at 1 AU. ϵdenotes the

elevation angle measured from the local horizontal,

deﬁned again in the topocentric frame of the ground

target and is given by [20]:

ϵ(t) = arcsin zT HF (t)

d(t)(3)

where zT HF is the z-axis component of the slant

range vector and given in Ref. [20]. The details of

the derivation of Eqs. 2 and 3 will not be provided in

this paper for conciseness, but in a recent paper C¸ elik

& McInnes presented detailed analytical derivations

as a function of orbital elements for both as a three-

dimensional vector model by including the Earth’s

rotation and the Earth’s oblateness perturbation for

applications to Sun-synchronous orbits [20]. A sim-

pliﬁed scalar model is also presented for polar orbits

in C¸elik & McInnes [16].

Of the other terms in Eq. 1, the time-dependent

atmospheric transmission eﬃciency, χ(t) is provided

with the following empirical relationship [21]:

χ(t)=0.1283 + 0.7559e−0.3878 sec(π/2−ϵ(t)) (4)

Finally, ψ(t) is the incidence angle, measured as the

angle between the incoming and outgoing sunlight.

ψ(t) is also a time-dependent function where the in-

coming sunlight is dependent on the Sun vector and

the outgoing sunlight is dependent on the reﬂector’s

position with respect to the solar power farm. A per-

fect pointing for the reﬂector is assumed as the eﬀect

of pointing errors in the quantity of energy delivered

is considered minimal with an appropriate attitude

control system design [22].

Therefore, the quantity of the energy delivered, E

to the surface can be calculated by integrating Eq. 1

over a desired duration, such that:

E=Zt

PSP F dτ(5)

where tis time. tis typically the pass duration over

a solar power farm, Tpass. In the three-dimensional

reﬂected solar energy delivery model presented by

C¸ elik & McInnes, Tpass is found by generating the

zT HF and dproﬁles semi-analytically in the topocen-

tric frame of a given solar power farm for a given time

span and ﬁnding the time points where ϵbecomes

0 deg and 180 deg, where the diﬀerence between them

is equal to Tpass [20]. In more simpliﬁed approaches

where the Earth is non-rotating, Tpass can be found

in a more straightforward way by ﬁnding the cone

angle, measured as the angle between the Earth and

orbit radii vectors extending from the centre of the

Earth to the point where the local horizontal plane

of the solar farm intersects with the orbit. This ap-

proach will ﬁrst be used in the preliminary design of

the constellations presented next.

3. Constellation design

3.1 Simpliﬁed approach

The simpliﬁed approach aims to understand how

the geometry of the constellation reﬂectors aﬀects the

reﬂected sunlight delivery. For this preliminary anal-

ysis, it is assumed that the Earth is non-rotating and

the reﬂectors are separated by a phase angle ϕin one

orbit, as shown in Fig. 1.

According to Fig. 1, the cone angle deﬁnes the an-

gle between the line that extends from the Earth’s

center to the solar power farm and the line that ex-

tends from the Earth’s center to the intersection point

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reserved.

Fig. 1: Schematics of a simpliﬁed constellation de-

sign approach with multiple satellites in one orbit

around a non-rotating Earth.

of the orbit and the local horizontal plane can be ex-

pressed as:

β= arccos RE

RE+h(6)

According to this, the maximum number of reﬂectors

in view can be written as:

Nmax

view =ceil 2β

ϕ(7)

where ceil() denotes the ceiling function that out-

puts the nearest equal or greater integer value. The

next reﬂector satellite would appear in view after

some time tn+1 that can be expressed as:

tn+1 =ϕ

ωo

(8)

where ωois the orbit angular speed, deﬁned as ωo=

2π

Twith Tdenoted as orbit period:

T= 2πs(RE+h)3

µ(9)

with µas the gravitational parameter, i.e., µ=

398 600 km3s−2.

If there is more than one satellite separated by a

phase angle ϕ, the pass duration, Tpass , can be ex-

tended by some ∆Text:

∆Text =Tpassϕ

2β=βT

2β=T ϕ

2π(10)

The reﬂected sunlight from successive reﬂectors

would also overlap for a duration Tover :

Tover =Tpass(β−ϕ)

β=βT

(β−ϕ)

β=T(β−ϕ)

(11)

As the Earth is assumed non-rotating and the reﬂec-

tor spacecraft are in the same orbit, their pass geom-

etry and energy delivery properties would in principle

be the same, such that the quantity of total energy

delivered by a single reﬂector can be linearly scaled

with the number of reﬂectors as:

Etot =NE (12)

This scalability oﬀers the advantage of analysing the

problem with a few parameters and for a single satel-

lite but it is evidently oversimpliﬁed. Generalising

this to a more realistic case with Earth rotation will

require a more detailed constellation analysis, which

is tackled in the next subsection.

3.2 Repeating pass geometries with modiﬁed Walker

constellations

The basic idea presented in the previous section

will be generalised to a more realistic case of rotating

Earth, which would mean that the reﬂector spacecraft

will no longer be in the same orbit but in separate or-

bit planes, arranged such that the pass geometry of

each spacecraft is the same. To analyse the details of

the problem, ﬁrst Walker constellations will be con-

sidered [18]. Walker constellations are one of the most

common orbit constellations [18], widely used for ap-

plications such as navigation [23]. The satellites in

Walker constellations would possess the same orbit

radius, eccentricity and inclination, and would be dis-

tributed in the right ascension of the ascending node

(RAAN) and mean anomaly space equally for a given

number of orbits and satellites and a phasing param-

eter [18]. The state-space form of this distribution

can be expressed as follows [18]:

No0

NpNsoΩmn −Ω11

Mmn −M11= 2πm−1

n−1(13)

where Nodenotes the number of orbits, Nso denotes

the number of satellites per orbit, Npdenotes a phas-

ing parameter that takes integer values in the range

Np∈[0 No-1]. Note that the phasing parameter Np

is diﬀerent than the phase angle ϕ. Ω and Mare

RAAN and mean anomaly, respectively, and mand

nare the indices of orbits and satellites, respectively.

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Ω and Mcan also be rewritten as [18]:

Ωmn = Ω11 +2π

(m−1) (14a)

Mmn =M11 +2π

Nso

(n−1) −Np

Nso

∆Ω (14b)

where ∆Ω = Ωmn −Ω11. The general form of the

Walker constellation given in Eq. 14 distributes the

orbit planes equally around the Earth by 2π/Noterm.

On the one hand, this is not useful for orbiting solar

reﬂector applications, as the primary aim is to deliver

solar energy at dawn/dusk around the terminator re-

gion. On the other hand, it is also not clear what

other angle can replace 2πin Eq. 14a. As the aim

of the reﬂector constellations is to ensure the same

geometry across all reﬂectors, the separation between

the orbit planes will be set accordingly. If the Earth’s

rotation is taken into account, the subsequent reﬂec-

tor’s orbit needs to be synchronised with this rotation

to ensure the same geometry, such that:

∆Ω = ωEtn+1 =ωE

ωo

ϕ(15)

where ωEis the Earth’s rotation rate, ωE= 7.272 ×

10−5rad/sec. However, if the Earth’s oblateness is

taken into account, the orbit plane of all reﬂectors

will also precesses due to this perturbation. In this

paper, the Earth’s oblateness up to the second order

(i.e., J2= 1082.63×10−3) is considered, whose impact

on RAAN can be expressed as the rate of change [24]:

ΩJ2=−3

2J2√µR2

(RE+h)7/2cos i(16)

where iis the orbit inclination. Therefore, the preces-

sion in the orbit plane of the subsequent spacecraft

by considering the J2eﬀect can be expressed as:

∆ΩJ2=−˙

ΩJ2tn+1 =−˙

ΩJ2

ωo

(17)

It is worth noting that the orbit angular rate will

also be altered as a result of the Earth’s oblateness,

due to the change in the orbit period, which can be

expressed as:

TJ2=T"1−3

2J2

(RE+h)2−3

4J24−5 sin2iR2

(RE+h)2#

(18)

Finally, combining Eqs. 15 and 17 would yield the

angular separation between orbit planes, such that:

∆Ω = ωE−˙

ΩJ2

ωo,J2!ϕ(19)

where ωo,J2is the J2altered orbit angular rate and is

equal to ωo,J2= 2π/TJ2. Then, if the 2πterm at the

right-hand side of Eq. 14a is redeﬁned as some angle

ηΩ, it can be found as:

ηΩ= ωE−˙

ΩJ2

ωo,J2!ϕNo(20)

If, for example, a constellation is considered with six

orbit planes and ϕ= 15 deg separation between them,

ηΩwould become 6.58 deg in which the orbit planes

would be equally distributed in this range.

In a case where the orbit is unperturbed, an ini-

tial shift in mean anomaly Mby ϕwould ensure that

subsequent reﬂectors would follow the same pass ge-

ometry. However, the Earth’s oblateness also rotates

the orbit itself (i.e., shifts the start/end point of the

orbit), such that [24]:

ωJ2=−3

2J2√µR2

(RE+h)7/25

2sin2i−2(21)

where ωdenotes the argument of pericentre. Then

the shift in ωcan be described as:

∆ω=−˙

ωJ2tn+1 =−˙

ωJ2

ωo,J2

ϕ(22)

∆ωcan now be combined with the unperturbed

mean anomaly shift M−ϕand orbit plane separation

∆Ω in Eq. 19 to describe the distribution of reﬂec-

tors in a constellation of morbit planes with a single

reﬂector in each orbit:

Ωm= Ω11 + ωE−˙

ΩJ2

ωo,J2!ϕ(m−1) (23a)

Mm=M11 −1 + ˙

ωJ2

ωo,J2ϕ(m−1) (23b)

The parameter nis not in the set of equations as there

is one reﬂector per orbit, which is due to the second

term in the right-hand side of Eq. 14b becoming zero

for a single reﬂector per orbit. Table 1 shows how

the separation between orbit planes ∆Ω and mean

anomaly values ∆M, alongside associated pass du-

ration extension from Eq. 10, for three diﬀerent ϕ

values.

The eﬀect of the Earth’s oblateness perturbation is

relatively small but still needs to be added in order

to account for their eﬀect on the evolution of constel-

lations. The values are approximately linearly scaled

with the angular separation ϕ. Closely spaced con-

stellations could extend the pass duration only for a

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Table 1: Some examples of the relationship between

ϕ, ∆Ω, ∆Mand extension of pass duration ∆Text

ϕ[deg] ∆Ω [deg] ∆M[deg] ∆Text [min]

5 0.37 4.99 1.44

15 1.10 14.98 4.32

30 2.19 29.98 8.65

few minutes but can be extended by increasing the

separation between them. These aspects will be fur-

ther discussed later in the design of the reﬂector con-

stellations later.

Equation 23b can be expanded to include more

satellites per orbit by including the same term in Eq.

14b by replacing 2πterm with some angle ηMfor

further customisation of the constellation:

Ωmn = Ω11 + ωE−˙

ΩJ2

ωo,J2!ϕ(m−1) (24a)

Mmn =M11 +ηM

Nso

(n−1) −1 + ˙

ωJ2

ωo,J2ϕ(m−1)

(24b)

The description of the constellation orbits in Eqs.

23 and 24 ensures that the reﬂectors will exhibit the

same pass geometry as they pass over a solar power

farm. Even if there is more than one reﬂector per or-

bit, the second reﬂector in the subsequent orbit would

also follow the same geometry as the second reﬂector

in the previous orbit plane. This will be used to in-

vestigate dawn/dusk clusters of constellation reﬂec-

tors later. To demonstrate the same pass geometry

among all reﬂectors, a constellation of six reﬂectors

in six orbit planes at 1000 km altitude is analysed to

observe the elevation proﬁle (in distance) from the lo-

cal horizontal plane of a hypothetical equatorial solar

power farm. The elevation proﬁle is given in Fig. 2.

Figure 2 already shows the closely spaced passes

over the solar power farms that reach up to the same

height. However, Fig. 2(b) in particular shows a

close-up of passes that happen approximately after

12 hours. The close-up ﬁgure shows how all six re-

ﬂectors reach up to the same height, where the error

between them is found to be at the sub-meter level,

therefore it can be conﬁrmed that the pass geometry

will be the same for all reﬂector spacecraft. The ad-

vantage of the same pass geometry is that, it would be

no longer necessary to consider all reﬂector satellites

in all orbit planes in the constellation optimisation,

but the ﬁrst reﬂector’s orbit. The orbits and mean

anomaly values of the rest of the reﬂector satellites

can then distributed according to Eqs. 23 and 24 and

(a) All-day view

(b) Zoomed-in view at approximately 12th hour

Fig. 2: The elevation proﬁle of a constellation reﬂec-

tors in six orbit planes, distributed according to

Eqs. 23

the result can be generalised. But care must still be

taken to set the optimisation problem to ensure the

range of orbits is appropriately placed in the termina-

tor region to avoid conditions such as eclipses. This

will be discussed next.

4. Groundtrack optimisation

The optimisation problem tackled in this paper in-

corporates the energy delivery process and the place-

ment of the orbit in the orbital element space. A

single 1000 km circular orbit is considered through-

out, but both polar and Sun-synchronous variants

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reserved.

are considered. The optimisation parameters are or-

bit RAAN and initial Greenwich meridian and the

objective function is the quantity of total energy

generated per day. The details of the optimisa-

tion process will be explained later. For both polar

and Sun-synchronous orbits, two optimisation cases

are investigated. The ﬁrst is a single reﬂector in

the aforementioned orbit, initially at mean anomaly

M= 0 deg. The second case is a two-reﬂector conﬁg-

uration, both in the same orbit with 180 deg apart in

mean anomaly, i.e., M11 = 0 deg and M12 = 180 deg.

The latter case aims at a dawn/dusk cluster of orbits

when expanded with multiple orbit planes to create a

constellation. Recall that the setting of the constella-

tion problem in Eqs. 23 and 24 ensure that reﬂectors

in subsequent orbits would follow the same pass ge-

ometry over the solar power farms as the reﬂectors in

the ﬁrst orbit. Before the details of the optimisation

process is presented, ﬁrst the selection of the solar

power farms will be summarised.

4.1 Solar power farms

Solar power farms (SPF) in this paper are se-

lected from some of the largest operational and

under-development projects with nameplate capacity

greater than 500 MW as of 2020, ﬁrst summarised in

Viale et al. (2023) [12] and updated to the current

known capacity and land size values in this paper. In

addition, this paper also considers a number of hy-

pothetical solar power farms. The potential beneﬁts

of additional solar power farms that are strategically

placed near the groundtrack of a selected reﬂector

orbit and high-insolation regions were previously dis-

cussed in Viale et al. (2023) in enhancing the terres-

trial solar energy generation [12]. In this paper, this

will be considered alongside existing solar power farm

projects to assess that enhancement. The SPF con-

sidered in this paper are presented alongside a yearly

mean insolation map (covering 1990-2004) in Fig. 3.

Figure 3 shows how the existing SPF projects are

placed in favourably insolated geographical locations.

For hypothetical farms, a similar approach is taken,

but longitudes of hypothetical SPF are also chosen

by considering the longitudinal shift of the ground

track on the surface of the Earth after each orbit.

Considering eastward Earth rotation at a rate of ωE

and westward rotation due to the J2eﬀect, ˙

ΩJ2,

the orbit ground track would shift approximately

(ωE−˙

ΩJ2)TJ2. As will be outlined in the next

section, the orbit altitude will be 1000 km, which

means that the westward groundtrack shift for a Sun-

synchronous orbit and polar orbit at this altitude

would be 26.7 deg and 26.3 deg, respectively. There-

fore, the longitudinal separation between two consec-

utive hypothetical SPFs is considered to be 26.7 deg

as SSOs are more relevant for orbiting solar reﬂec-

tor applications and considering the small diﬀerence

between the values. Latitudinal placement is more

related to nearby existing SPF, insolation properties,

proximity to land and generally attempting to avoid

an orbit groundtrack passing over multiple farms at

the same time (or in quick succession) to ensure dis-

tinctive passes and the maximal use of all SPFs. The

locations of the SPF are listed in Table 2.

Table 2: Selected solar power farms in this paper [12].

The land size and capacity information are up-

dated to the latest values available.

# Solar power farm Capacity Land size Coord.

(SPF) (lat., lon)

[MWh] [km2] [deg, deg]

Existing solar power farm projects

1 Bhadla 2700 160 27.5, 71.9

2 Pavagada 2050 53 14.7, 77.2

3 Benban 1650 37 24.7, 32.8

4 Tengger 1547 43 37.6, 105.04

5 Noor Abu Dhabi 1177 8 24.6, 55.4

6 Datong 1070 N/A 40.7, 113.1

7 Kurnool 1000 24 16.15, 78.4

8 Longyangxia 850 14 36.9, 100.5

9 Villanueva 828 24 26.3, -102.9

10 Solar Star I&II 747 13 35.8, -118.15

11 Topaz 550 19 34.4, -115.2

12 Sun Cable 6000 105 -17.29, 133.5

Hypothetical solar power farms

13 SPF-13 - 78.5 35, 89.45

14 SPF-14 - 78.5 24.73, 6.42

15 SPF-15 - 78.5 24.73, -19.91

16 SPF-16 - 78.5 -5, -32

17 SPF-17 - 78.5 0,-128

18 SPF-18 - 78.5 0, -154

19 SPF-19 - 78.5 -24, 150

20 SPF-20 - 78.5 -24, 118

The existing solar farm projects are dominantly in

the northern hemisphere, with a number of large SPF

in India, China, and USA together with single farms

in UAE and Egypt. Among the large projects con-

sidered, the Sun Cable SPF project is the only one in

the southern hemisphere, which is currently under de-

velopment and may potentially be one of the largest

SPF in the world with a nameplate capacity of 6 GW.

Among the hypothetical SPF, two each are placed in

North Africa, Australia and the equatorial regions of

the Paciﬁc and one each in western China and the

eastern tip of Brasil. The most geographically re-

mote SPF are in the Paciﬁc (SPF-17 and SPF-18)

and oﬀshore, but they are also in very high insolation

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reserved.

Fig. 3: Existing and hypothetical solar power farms on global yearly mean insolation map 1990-2004 (The

insolation map is freely available at https://www.soda-pro.com/maps/maps-for-free (Accessed March

3, 2022).

regions, which may be considered to provide electric-

ity to Paciﬁc island countries or Hawaii if a higher

latitude is considered. Two hypothetical SPF in Aus-

tralia (SPF-19 and SPF-20) are at the two edges of

the country, while the existing project Sun Cable is at

the north, potentially providing electricity all around

the country. One of two farms in North Africa (SPF-

15) and the one in Brasil (SPF-16) are oﬀshore due to

longitudinal separation, although both are still very

close to land. The one selected in western China

(SPF-13) is likely in a high-altitude region, but so-

lar energy experiences less atmospheric transmission

losses in high altitudes [21], which may be preferable

from that perspective. The selection of hypothetical

SPF also increases the number of opportunities all

around the globe, particularly in the southern hemi-

sphere. Ultimately the optimisation of groundtracks

will demonstrate their eﬀectiveness, whose process is

outlined in the next subsection.

4.2 Optimisation process

The optimisation process is as follows: First, for

given orbit parameters, the orbit pass geometry is

calculated for 24 hours in terms of its elevation angle

for each of the solar power farms presented in Table 2.

This check is performed by using analytical elevation

formulations presented in Eq. 3 and in Ref. [20]. If

the maximum elevation angle is greater than 60 deg at

any point during the day, these instances are recorded

and the pass duration is calculated for that pass. It

is expected that such a pass could occur twice per

day per reﬂector at the maximum, at dawn and dusk

each. If no pass over the selected solar power farm

reach a maximum elevation angle greater than 60 deg,

then that solar power farm is considered not serviced

by the reﬂector on the given orbit.

For the passes that satisfy the 60 deg requirement,

the quantity of energy delivered is calculated. This

follows the procedures discussed in C¸elik & McInnes

(2022, 2023) with the equations presented in Sec. 2

and includes Earth rotation and oblateness, geomet-

ric and atmospheric losses in the energy delivery pro-

cess [16, 20].

This procedure is performed for all reﬂectors (if

there is more than one) and for all solar power farms.

Finally, the quantity of total energy delivered per day

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reserved.

is calculated. The procedure of calculating the opti-

mised orbit is presented in Fig. 4.

Fig. 4: Diagram of the optimisation process. OE

and GMT denote orbital elements and Greenwich

mean time respectively.

One limitation of this approach is the existence

of solar power farms that are located very close to

each other. The examples include Bhadla (SPF-1),

Pavagada (SPF-2) and Kurnool (SPF-7) farms in In-

dia or Villanueva (SPF-9), Solar Star I/II (SPF-10)

and Topaz (SPF-11) farms in Mexico and the United

States. It was observed that often the same orbit

groundtrack passes over both of those targets satis-

fying the 60 deg requirement, hence the quantity of

energy delivery is overcalculated within the optimi-

sation function. This is not necessarily a problem,

however, as one of those overlapping passes will in-

deed provide the highest quantity of energy delivered,

which is considered while the others are removed as

infeasible in the post-processing.

As noted earlier, the objective is to maximise the

total quantity of energy delivered per day, and the

two optimisation parameters are the right ascension

of the ascending node of the orbit, Ω and the initial

Greenwich meridian, θG,0. The latter parameter ap-

pears relatively arbitrary as it only determines when

the orbit starts during a day, but it will be shown that

there are multiple optima available in the problem

based on diﬀerent Ω-θG,0combinations. The range of

Ω is selected based on the eclipse considerations and a

range extending by βon either side of the terminator

line deﬁned at π/2 from the x-axis in the ECI frame.

The upper limit of Ω is also reduced by an angle of

ηΩ, such that if the optimised Ω is found in this up-

per limit, it would still be possible to place the rest of

the constellation reﬂectors without any eclipses. To

that end, it is necessary to determine the number of

orbit planes, No, before the optimisation to calculate

ηΩwith Eq. 20 to set the upper limit of Ω. In this

paper, No= 10 is selected. As for θG,0, the range is

selected between −45 deg and 30 deg measured from

the x-axis in the ECI frame or approximately 9:00

am-2:00 pm GMT. The upper limit is kept at 30 deg

to avoid Ω being pushed to the upper limit during

the optimisation process. The other parameters in-

cluding the orbital elements used in the optimisation

are presented in Table 3.

Table 3: Parameters of the optimisation problem

Orbital parameters

Altitude [km] 1000

Eccentricity [-] 0

Inclination [deg] 90 (Polar), 99.5 (SSO)

Reﬂector parameters

Diameter [km] 1

Reﬂectivity [-] 1

Solar power farms

Diameter [km] 10

Location Table 2

Optimisation parameters

Objective function -Etot

Variables [deg] Ω∈[90 −β, 90 + β−ηΩ]

θG,0∈[−45,30]

The single-objective optimisation is performed us-

ing a genetic algorithm [25] and implemented in MAT-

LAB through its ga() function.∗The genetic algo-

rithm relies on evolutionary principles and aims to

reach the best result (or global optimum) via stochas-

tically generated populations through their crossovers

and mutations. It is widely used in constellation op-

timisation problems where the best distribution of

satellites minimising an objective function is not ap-

parent or trivial. In the problem here, even though

the optimisation does not contain many reﬂectors,

the pass geometry over the listed solar power farms

and the associated quantity of energy deliverable to

those cannot be found trivially. In the absence of this

information, the genetic algorithm becomes a suitable

choice. As for diﬀerent options available for ga() in

MATLAB, initial parameter space is created based on

a uniform distribution with scattered crossover and

∗Available at https://uk.mathworks.com/help/gads/ga.

html, Accessed August 29, 2023.

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stochastic uniform selection of parents at each step.

For the mutations, an adaptive feasible mutation op-

tion is selected, which generates random search direc-

tions and is adaptive to the success of each genera-

tion. The function and constraint tolerances are 10−6

and 10−3, respectively. The rest of the options are

used as default in ga() in MATLAB. By using the pro-

cedures and tools explained in this section, ground-

track optimisation is performed, and whose results

are presented in the next section.

5. Optimised orbits and their properties

The orbit optimisation is performed for polar and

Sun-synchronous orbits, which are also near polar at

99.5 deg inclination, as presented in Table 3. Consid-

ering the stochastic nature of the set of initial con-

ditions and generated populations in the genetic al-

gorithm, each groundtrack optimisation is performed

10 times and the results are post-processed to ob-

tain the total quantity of energy delivered in each

case. Then, the orbit is selected not only based on

its highest quantity of energy delivered but also its

Ω value. These aspects will be discussed in the next

subsections together with the results.

5.1 Polar orbits

5.1.1 Single reﬂector

The optimisation results of the polar orbits are pre-

sented in Table 4.

Table 4: Polar orbit results. Solution with asterisks

is selected for further investigation

#θG,0ΩEtot Etot,pp

[deg] [deg] [MWh] [MWh]

1 14.45 85.98 453.1 334.2

2 -6.81 64.73 454.3 334.7

3 22.88 94.42 452.6 333.7

4 17.54 89.08 452.9 333.9

5 11.26 82.80 453.3 334.3

6 14.02 85.56 453.1 334

7 28.36 99.91 452.3 333.3

8 2.34 73.88 453.8 334.7

9* 15.90 87.45 453.0 334

10 3.22 74.76 453.7 334.6

The results show the existence of multiple local op-

tima depending on diﬀerent θG,0−Ω pairs, with the

total quantity of energy (unprocessed) ranging be-

tween 452.3 and 454.3 MWh. As the Earth’s rota-

tion is included in the problem, it may be reasonable

to ﬁnd such close results with adjustments in θG,0

and Ω. The highest Etot values in this range is at

Ω = 64.73 deg, close to the lower bound of the opti-

misation range, 59.82 deg. The push in the solution

towards this edge may be explained by the geometry

of the energy delivery in polar orbits. As a simpliﬁed

case, if a non-rotating Earth is assumed, a reﬂector

satellite passing over a solar power farm would have

a ﬁxed angle of incidence with respect to the Sun, as

shown in Fig. 5.

Fig. 5: Variation in energy delivery in polar orbits as

a result of the change in right ascension of the as-

cending node (Ω) of the orbit. For a non-rotating

Earth, the angle of incidence ψwould be near con-

stant and related to Ω by a cosine relationship.

This means that the quantity of the solar energy

delivered to the night side of the Earth would be

greater than that of day side.

It can be seen in Fig. 5 that the angle with respect

to the Sun increases as the satellite on the day side

and decreases on the night side. The implication of

this is that according to Eq. 1 the quantity of power

delivered at any instant would be increased on the

night side and decreased on the day side. For the so-

lution with the highest quantity of energy delivered,

Ω is closest to the lower bound of the optimisation

problem, suggesting that more passes are encountered

on the night side when the incidence angle is smaller.

Some of the other solutions in Table 4 with higher

Etot also have lower Ω values, e.g. Solution #8 and

#10. Conversely, if this reasoning holds, then Ω val-

ues closer to upper bound should result in lower Etot

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reserved.

values, which what is seen, for example, in Solution

#3 or #7. However, it should be noted that this best

solution is only slightly higher in the ﬁnal Etot com-

pared to the rest of the solutions. This increase ulti-

mately becomes more marginal when the results are

post-processed to remove overlapping passes of close-

by solar power farms. The post-processed quantity

of total energy delivered per day, Etot,pp, varies only

by 1.4 MWh, between 333.3 MWh and 334.7 MWh.

It was found that the sequence of passes is the same

in all solutions. However, instead of simply selecting

the highest Etot,pp, an orbit closer to the terminator

line (i.e., Ω = 90 deg) is also considered, and Solution

#9 is selected for further in-depth investigation. The

ground track of this orbit is presented in Fig. 6.

This orbit groundtrack shows multiple near-

overhead passes that deliver the highest quantity of

energy. These appear to be populated around the so-

lar power farms in North America, but other passes

also exist in China, India and Australia. Figure 7

depicts the daily distribution of these passes.

In Fig. 7, the horizontal axis shows the elapsed

time since the beginning of the propagation whereas

the vertical axis shows the elevation from the

topocentric horizon frame of the solar power farm

in degrees. The spike-like appearance of the data is

due to the short duration of passes (∼17 min) com-

pared to the 24-hour simulation time. All solar power

farms listed in Table 2 are visible to the reﬂector dur-

ing a day, but due to the close proximity of some of

the solar power farms, some passes overlap. These

are apparent particularly between SPF-10 and SPF-

11. The former is more favourable in the ﬁrst in-

stance whereas the latter is more favourable approx-

imately half a day later. Indeed the second pass is

almost overhead with maximum elevation reaching

nearly 90 deg. The other overlapping passes are less

apparent but between SPF-6 and SPF-4, and SPF-7

and SPF-2 where the geometry is more favourable for

SPF-6 and SPF-7 in these cases. When such overlap-

ping passes occur, the one with the higher quantity

of energy delivered in post-processing is selected as

more than one solar power farm cannot be serviced.

Detailed schedule of the passes are provided in Table

Ultimately a total of 10 distinct passes can be

achieved with SPF-6 visited twice. Five of those

are with a maximum elevation greater than 80 deg,

which is one more than previously achieved with Sun-

synchronous orbits in Viale et al. (2022) [12]. The

total quantity of energy delivered to these farms is

334 MWh, which is also approximately 18% higher

Table 5: Polar orbit results

SPF # Tpass [min] ϵmax [deg] E[MWh]

1 16.77 74.6 32.7

10 17.56 84.9 34.8

12 17.54 77.9 33.9

6 17.45 71.3 32.0

7 17.50 68.5 30.4

11 17.56 89.3 34.9

5 17.56 87.4 34.9

3 17.46 69.0 31.0

6 17.57 86.6 34.8

9 17.56 84.3 34.6

Total 334.0

than previous results [12], improving the viability of

orbiting solar reﬂectors.

5.1.2 Dawn/dusk reﬂectors

The second investigation with polar orbits is a case

of two reﬂectors in one orbit, one placed at M11 =

0 deg and the other placed at M12 = 180 deg. This

is essentially a basic constellation on a single orbit,

selected to service both dawn and dusk times. Again

the optimisation is performed 10 times to consider

the stochastic nature of the genetic algorithm. The

results are presented in Table 6

Table 6: Polar orbit dawn/dusk results. The solution

with the asterisks is selected for further investiga-

tion.

#θG,0ΩEtot E11 E12 Etot,pp

[deg] [deg] [MWh] [MWh] [MWh] [MWh]

1 -28.87 94.77 744 295 269.2 564.2

2 -28.43 106.88 742.8 261.2 301.4 562.6

3 -9.44 94.65 742.9 261.3 301.8 563.1

4 7.33 63.52 743 261.7 301.6 563.3

5 -38.10 85.79 745.6 268.1 265.3 533.4

6 -25.16 81.80 742.8 261.2 301.6 562.8

7 28.17 114.61 745 297.1 267.1 564.2

8 -17.89 61.01 746 268.6 265.5 534.1

9* 5.78 95.37 744.5 296.3 268.2 564.5

10 -9.95 67.43 746.1 268.8 265.5 534.3

Table 6 also includes the post-processed results of

individual reﬂectors, E11 and E12. The total quantity

of energy delivery has increased due to two reﬂectors,

but the quantity of energy delivered per reﬂector is

eﬀectively decreased. On average, Etot per reﬂector

is approximately 372 MWh before post-processing,

which decreases to approximately 282 MWh after

post-processing. This diﬀerence may be explained

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Fig. 6: 24-hour groundtrack of the selected optimal polar orbit

Fig. 7: Elevation proﬁle of passes in the selected op-

timal polar orbit. Single reﬂector case.

by the proportion of solar power farms in the eastern

and western hemispheres of the Earth. Of the exist-

ing largest solar power farms in Table 3, only three

are in the western hemisphere. Therefore, it is possi-

ble that one reﬂector has always fewer opportunities

to deliver energy, whereas the passes of the other may

overlap with multiple farms, of which only one can be

chosen.

When individual reﬂectors are considered, it ap-

pears that there are several diﬀerent solution combi-

nations that lead to approximately the same result.

For example, for Solutions #1 and #9, the ﬁrst reﬂec-

tor delivers more energy (E11 > E12), for Solutions

#2, #3, #4 and #6 the second reﬂector delivers more

(E12 > E11) and there are two other solutions where

the energy delivery is similar for both reﬂectors (So-

lutions #5 and #10), which in total deliver the least

quantity of energy. These diﬀerent solution struc-

tures also result in diﬀerent sequences of solar power

farm visits. Within similar solutions, the orbit place-

ment also diﬀers with diﬀerent θG,0−Ω pairs.

Again, given the similarity between most of the

solutions in terms of Etot,pp, Solution #9 is selected

for further investigation due to its proximity to the

terminator line. Only the elevation angle properties

of the individual reﬂectors will be shown in Fig. 8 for

conciseness.

The arguments made about the solutions obtained

and the proportion of solar farms in the eastern and

western hemispheres of the Earth may be more ap-

parent in Fig. 8. First reﬂector (M11 = 0 deg) has

only three passes that exceed a maximum elevation

of 80 deg and one of them only slightly exceeds that

point. No elevation is greater than 85 deg. There

are also several overlapping passes towards the end

of the day, which decreases the overall total quan-

tity. On the other hand, the second reﬂector has only

four passes that exceed the 80 deg mark (three greater

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(a) First reﬂector

(b) Second reﬂector

Fig. 8: Elevation proﬁle of passes in the selected op-

timal polar orbit. Dawn/dusk case.

than 85 deg), but does not visit any solar power farm

until the 7th hour of its operation. Ultimately, how-

ever, the ﬁrst reﬂector visits more targets and delivers

more energy between the two. The total number of

distinct visits is equal to 17, of which 9 is achieved by

the ﬁrst reﬂector and 8 for the second, individually

delivering 296.3 MWh and 268.2 MWh, respectively.

This is less than what a single reﬂector can achieve

(10 per day) as discussed in the previous subsection.

The single reﬂectors then demonstrate superior per-

formance compared to the two-reﬂector dawn/dusk

conﬁguration in one orbit for the polar orbit case.

This discussion can be extended to Sun-synchronous

orbits, which are more relevant for orbiting solar re-

ﬂector applications.

5.2 Sun-synchronous orbit

5.2.1 Single reﬂector

Sun-synchronous orbits (SSO) would provide a

more favourable choice for solar reﬂector applica-

tions [12] as the orbit plane tracks the Sun’s direction

through the perturbation due to the Earth’s oblate-

ness. Considering this, the optimisation is performed

with the parameters in Table 3 for 10 times and the

results in Table 7 are obtained.

Table 7: SSO optimisation results. The solution with

asterisks is used for further investigation

#θG,0ΩEtot Etot,pp

[deg] [deg] [MWh] [MWh]

1 17.31 82.04 537.1 363.4

2* 27.59 92.32 537.0 363.5

3 26.02 90.75 537.0 363.3

4 16.01 80.74 537.1 363.4

5 -1.59 63.14 537.3 362.6

6 9.85 74.58 537.2 363.3

7 18.53 83.26 537.1 363.5

8 8.96 73.69 537.2 363.4

9 0.19 64.92 537.3 362.7

10 -2.09 62.63 537.3 363.4

The SSO results demonstrated a more uniform so-

lution that does not diﬀer much in terms of Etot (the

maximum diﬀerence is 0.3 MWh), but again multiple

local optima are available. Due to the inclined orbits

and the pertubation due to Earth’s oblateness, the

incidence angle is not constant and the arguments

about the incidence angle (see Fig. 5) discussed for

polar orbits appear less prevalent to explain the sim-

ilarity in Etot throughout the given range of lower

and upper bounds. The post-processed results show

slightly more variation (0.9 MWh) but the variation

is still less than the polar orbit case. Therefore, so-

lution #2 is selected for further investigation. The

ground track of this orbit is presented in Fig. 9.

An immediate qualitative comparison can be made

between SSO in Fig. 9 and polar orbit groundtracks

in Fig. 6, where the SSO groundtrack visits more

solar power farms and of which more appear to be

close to overhead. Indeed, it appears that nearly all

solar power farms have close-by groundtracks, except

Sun Cable (SPF-12), which may still be visible albeit

with a maximum elevation lower than that of required

in this paper, i.e., ϵmax ≥60 deg. The elevation angle

for all passes can be seen in Fig. 10.

Indeed Fig. 10 shows 9 passes with ϵmax >80 deg

(5 over 85deg), which is almost double that of the

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Fig. 9: 24-hour groundtrack of the selected optimal Sun-synchronous orbit

Fig. 10: Elevation proﬁle of passes in the selected

optimal Sun-synchronous orbit. Single reﬂector

case.

polar orbits. However, there is almost an exact over-

lap between SPF-7 and SPF-2 around the 12th hour

mark, where the passes demonstrate almost the same

elevation properties, although, in the end, SPF-7 ex-

hibits better opportunity in terms of the quantity of

energy delivered. Therefore, only 8 passes are avail-

able with ϵmax >80 deg. In total, 11 distinct passes

satisfy the ϵmax ≥60 deg requirement and a total of

363.5 MWh of energy is delivered. This is more than

the polar orbit case in the previous subsection, al-

though the diﬀerence is approximately one pass more

on average with the additional pass over SPF-1 be-

ing at low elevation. However, as noted earlier SSO

provides more favourable properties over yearly op-

erations.

Table 8: SSO results

SPF # Tpass [min] ϵmax [deg] E[MWh]

5 16.11 70.6 31.4

10 17.35 86.0 34.3

3 17.36 86.5 34.3

6 17.33 81.7 33.9

9 17.25 69.1 30.7

7 17.34 87.3 34.4

5 17.32 80.5 33.8

8 17.37 85.1 34.2

7 17.33 83.3 34.2

1 17.12 64.0 27.9

9 17.35 88.8 34.4

Total 363.5

When compared with the reference architecture

study presented by Viale et al. [12], the optimal SSO

in this paper presents a signiﬁcant improvement in

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reserved.

daily operations. Despite using a smaller reﬂector

(1 km diameter in this paper vs. 1.016 km eﬀective

diameter in Ref. [12]) and a higher altitude (which

reduces the solar power density), the quantity of en-

ergy delivered per day is increased by approximately

28% (363.5 MWh in this paper vs. 283.84 MWh in

Ref. [12]). The diﬀerence between this paper and

Viale et al. (2023) [12] is that the orbit selection

in the latter was motivated by anchoring the ground-

track to a particular solar power farm (SPF-12 in this

paper), whereas in this paper the selection is moti-

vated to maximise the daily energy delivery globally.

The SSO analysis can also be extended to the

dawn/dusk two-reﬂector case, which is discussed

next.

5.2.2 Dawn/dusk reﬂectors

The optimisation results of the two-reﬂector case

in SSO are presented in Table 9.

Table 9: SSO dawn/dusk results

#θG,0ΩEtot E11 E12 Etot,pp

[deg] [deg] [MWh] [MWh] [MWh] [MWh]

1 -5.07 77.4 730.2 228.1 285.2 513.3

2 -15.14 70.22 757.3 225 325.4 550.4

3 18.0 64.52 758.5 226.6 325 551.6

4 -27.61 95.14 756.8 224.4 325.3 549.7

5 -2.13 76.73 757.7 224.4 325.3 549.7

6* -10.13 95.44 757.4 224.4 325.4 549.8

7 -31.85 101.35 756.7 224.3 325.7 550

8 24.75 77.20 758.7 224.4 325.2 549.6

9 -35.47 69.87 756.6 224.3 325.3 549.6

10 16.46 77.06 758.4 224.4 325.1 549.5

The quantity of total energy delivered by the two

reﬂectors in SSO is higher than that of the same case

in polar orbits (except Solution #1 in Table 9) be-

fore post-processing. But this may be a misleading

result as the post-processed results indeed show a de-

crease below the values achieved by polar orbits, ex-

cept polar orbit Solutions #5 and #8. The overall

decrease in the two-reﬂector cases in both SSO and

polar orbits may be explained by the disproportionate

distribution of solar power farms in the eastern and

western hemispheres of the Earth, but the decrease

in SSO as compared to polar orbits is not directly

evident. A possible explanation could come from the

single reﬂector results in Fig. 10. Indeed the pass

geometries, in general, are much better with ϵmax

exceeding 80 deg for several solar power farms. But

there are also more overlapping passes with similar

elevation proﬁles, such as between SPF-10 and SPF-

11 or SPF-7 and SPF-2, in which the latter overlaps

twice in a day, as shown in Fig. 10. These are not dis-

tinguished during the optimisation process, therefore

the value of the objective function is maximised by

these overlaps, even though the actual result will be

lower. But if the overlapping passes are of the same

high quality, then the decrease will also be greater

when these overlaps are removed. This may be a po-

tential explanation for the initially higher Etot but

ﬁnally lower Etot,pp values in the SSO case as com-

pared to polar orbits. Nevertheless, it should also

be noted that the diﬀerence between the SSO and

polar orbit cases is only approximately 15 MWh at

the maximum, which is less than one overhead pass

equivalent quantity of energy, i.e., approximately 35

MWh from earlier analyses [16, 20].

For all the solutions presented in Table 9, the sec-

ond reﬂector always delivers more energy (i.e. E12 >

E11) and all but one solution (solution #1) is dif-

ferent in terms of the visit sequence of solar power

farms. Therefore among similar solutions, Solution

#6 is selected for further investigation and the eleva-

tion proﬁles of both reﬂectors are presented in Fig.

11.

Reﬂector #1 has only three passes that exceed

80 deg elevation, but there are a number of passes

that overlap, which supports the argument made

above. The very ﬁrst pass has SPF-1, SPF-7 and

SPF-2 overlapping, where SPF-1 provides the high-

est elevation. SPF-2 (ϵmax = 75 deg) and SPF-7

(ϵmax = 66deg) need to be removed in this case but

each delivers 31.5 MWh and 28 MWh, respectively.

Similarly, the SPF-11 pass overlaps with the SPF-10

pass, where the latter’s signiﬁcant contribution (31.3

MWh) is also removed. The same occurs for the sec-

ond reﬂector as well, where overlapping SPF-7 and

SPF-2 passes both exhibit ϵmax >80 deg and remov-

ing SPF-2 results in a signiﬁcant loss (34 MWh) in

ﬁnal deliverable energy.

It appears that the proximity of some of the so-

lar power farms has considerable eﬀect on the to-

tal quantity of deliverable energy in both single and

dawn/dusk reﬂector cases. Some of this may be over-

come by strategically located solar power farms and

the orbits servicing them, which will be analysed

next.

5.3 Orbits optimised with hypothetical solar power

farms

The same orbit optimisation is performed with the

inclusion of hypothetical solar power farms as addi-

tional targets. Recall that the locations of solar power

farms are primarily selected in highly insolated re-

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reserved.

(a) First reﬂector

(b) Second reﬂector

Fig. 11: Elevation proﬁle of passes in the selected op-

timal Sun-synchronous orbit. Dawn/dusk case.

gions (see Fig. 3) with the longitudinal diﬀerences

between them equal to the orbit groundtrack shift for

a 1000-km altitude SSO. These criteria are informed

from both the selected orbit and the day-time solar

energy potential of these regions, allowing an over-

all increase in both day and nighttime utility of solar

energy.

Given the inferior performance of dawn/dusk re-

ﬂector systems in general, the optimisation was only

performed for single reﬂectors in polar and Sun-

synchronous orbits. Again, ten diﬀerent optimisa-

tions were performed for both cases, but it was ob-

served that the ﬁnal results are similar and the pass

sequences are the same for all solutions, therefore a

detailed investigation of the solution structure will

not be presented. Orbit groundtracks and a break-

down of the passes will be discussed instead. The

selected solutions are presented in Table 10. Among

them, the ﬁrst groundtrack results are presented for

polar orbits in Fig. 12 below.

Table 10: The selected optimal solutions for further

investigation

Orbit θG,0ΩEtot Etot,pp

[deg] [deg] [MWh] [MWh]

Polar 14.16 88.01 621.3 534.5

SSO 24.03 89.51 859.9 588.4

As aimed at and expected, the number of passes

during the day increases with a signiﬁcant number of

near-overhead passes. The hypothetical solar power

farms in North Africa, Australia, Brasil and China

have all been targeted. The SPFs in the Paciﬁc have

not been targeted in the optimisation with polar or-

bits for near-overhead passes. Figure 13 below shows

the details of the elevation proﬁles of all passes.

Among all 20 existing and hypothetical SPFs, 16 of

them are available for energy delivery, though some

of the passes either overlap or are too close to each

other to service them all. Ten of them achieve max-

imum elevation greater than 80 deg. Again SPF-10

and SPF-11 have overlapping passes, where SPF-10 is

selected as it provides better geometry. Other notable

passes include SPF-1 that reaches ϵmax >89 deg and

SPF-13 reaches ϵmax >85 deg. Table 11 shows the

breakdown of the passes and the quantity of energy

delivered in each pass.

A total of 16 passes are available in a day that

reaches higher than 60 deg elevation in a day. At

the orbit altitude chosen (1000 km), a reﬂector would

complete 13.7 orbits in a day, which means that some

passes are in the same orbit. From Figs. 12 and 13

and Table 11, it appears that for example SPF-13

and SPF-11, and SPF-1 and SPF-10 share the same

orbit on the opposite sides of the Earth. An earlier

study showed that these may still be achievable as

on average 6 min is suﬃcient for the reﬂector to re-

orient itself for the next pass [12]. The quantity of

energy delivered is greater than 34 MWh for the ma-

jority of the passes with the minimum being 28 MWh

(SPF-19) and the total quantity of energy per day is

534.4 MWh. Compared to the quantity in the single

reﬂector case with existing SPF in the previous sub-

section (Etot = 334 MWh), this is a 60% increase in

the quantity of energy delivered for 67% increase in

the number of SPF (from 12 to 20). The nearly lin-

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reserved.

Fig. 12: 24-hour groundtrack of the selected optimal polar orbit with hypothetical farms

Fig. 13: Elevation proﬁle of passes in the selected op-

timal polar orbit with hypothetical SPF included.

ear increase in the quantity of energy delivered ben-

eﬁts from the strategic selection of locations of solar

power farms. In comparison to the reference archi-

tecture study by Viale et al. [12], this represents an

88% increase in the quantity of energy that can be

potentially delivered per day.

The next investigation will be for Sun-synchronous

orbits with hypothetical solar power farms. The orbit

Table 11: Polar orbit pass sequence results

SPF # Tpass [min] ϵmax [deg] E[MWh]

1 16.15 89.4 34.9

10 17.36 81.4 34.3

16 17.35 83.6 34.6

12 17.34 86.0 34.7

6 17.35 83.6 34.7

13 17.34 65.8 29.3

11 17.33 76.8 33.5

5 17.25 72.4 32.2

3 17.35 83.7 34.7

14 17.21 83.7 34.7

15 17.35 83.6 34.7

19 17.34 64.0 28.0

20 17.20 79.5 34.1

6 17.21 80.5 34.3

13 17.34 86.8 34.8

9 17.36 69.8 31.0

Total 534.4

groundtrack is shown in Fig. 14.

Qualitatively, Fig. 14 shows a much better use of

solar power farms by the SSO. All listed SPF appear

to have a part of groundtrack passing nearby, once or

twice a day. Some passes again overlap where more

favourable ones are chosen. The elevation proﬁles for

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reserved.

Fig. 14: 24-hour groundtrack of the selected optimal SSO with hypothetical farms

all passes are shown in Fig. 15.

Fig. 15: Elevation proﬁle of passes in the selected op-

timal Sun-synchronous orbit with SPFs included.

Figure 15 shows that all passes except Sun Ca-

ble SPF (SPF-12) are available. Considering mul-

tiple passes over certain SPF, the total number of

passes in a day is equal to 24, which is greater than

the number of existing and hypothetical SPF listed

(20). However, ultimately 18 distinct passes are fea-

sible when considering the overlaps and very closely

spaced sequences. Again, 18 passes mean that some

passes are in the same orbit at the opposite sites of

the Earth. 11 of those passes have ϵmax >85 deg,

meaning the passes are near-overhead with a near-

maximum quantity of energy delivery. Among the

existing solar power farms, SPF-3, SPF-5, SPF-7 and

SPF-9 and among the hypothetical farms, SPF-14 are

visited twice a day. Table 12 shows the breakdown

of all passes with associated details on pass duration,

elevation and quantity of energy delivered.

As mentioned, there are several near-overhead

passes in the SSO case, which result in greater than

34 MWh energy delivered with the highest being 34.5

MWh. The total quantity of energy delivered per

day is equal to 588.4 MWh. Compared to the po-

lar orbit case in this subsection, the SSO provides

approximately two additional near-overhead equiva-

lent quantities of solar energy delivery. In comparison

with the SSO case with the existing SPF in the pre-

vious subsection, the increase is approximately 62%

(from 363.5 MWh to 588.4 MWh), again representing

an approximately linear increase with the number of

solar power farms (approx. 67%). Compared to Viale

et al. [12], the quantity of energy delivered is more

than doubled (from 283.4 MWh [12] to 588.4). It is

also worth noting that, by increasing the number of

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reserved.

Table 12: SSO pass sequence results

SPF # Tpass [min] ϵmax [deg] E[MWh]

5 16.15 66.3 29.2

10 17.36 89.6 34.4

3 17.35 88.6 34.3

18 17.34 89.4 34.5

14 17.35 88.1 34.4

15 17.34 87.6 34.4

19 17.33 74.0 32.8

20 17.25 69.5 30.5

6 17.35 85.6 34.3

9 17.21 64.9 28.5

7 17.35 87.5 34.4

5 17.34 85.3 34.3

3 17.20 63.9 27.9

14 17.21 64.4 28.1

16 17.34 86.3 34.3

8 17.36 89.3 34.4

7 17.32 78.3 33.4

9 17.36 86.4 34.3

Total 588.4

solar power farms, the duty cycle of reﬂectors will also

increase. The pass duration of a single reﬂector is 17.3

min on average. The total daily operation time with

18 passes would be approximately 5.2 hours which is

approximately 21.6% of a day. By including several

low-elevation passes, Viale et al. enhanced the duty

cycle from approximately 5% to 15% with a total of

13 passes [12]. Therefore, even though the duty cycle

in this paper has been increased only by 5% com-

pared to Viale et al. [12], the energy delivered has

been increased by more than 100% with additional

and high-elevation passes. It is also noteworthy that

the duty cycle in this paper is lower (13%) compared

to Ref. [12] when existing farms are considered due

to a smaller number of passes (11 in this paper vs.

13 in Ref. [12]). But ultimately the total quantity

of energy delivered is higher due to higher elevation

passes. Before further discussion, the results of opti-

misation can be summarised in Table 13 below.

The results in Table 13 could potentially be in-

creased further with the optimisation of new SPF lo-

cations for a chosen orbit to ensure that hypothet-

ical SPFs do not overlap with existing SPF or en-

able twice-daily passes. For the latter, for example,

Fig. 14 shows favourable locations where ground-

track passes over the same location twice a day in

North Africa or Australia, where some of the chosen

hypothetical farms are located closely. Their loca-

Table 13: Summary of optimised orbits, number of

distinct passes in a day and the quantity of en-

ergy delivered provided for existing and hypo-

thetical SPF for comparison

SPF Case Orbit No. of passes Etot [MWh]

Existing (12)

Single Polar 10 334

SSO 11 363.5

Two-reﬂector Polar 17 (9 + 8) 564.5

SSO 17 (7 + 10) 549.8

All (20)

Single Polar 16 534.4

SSO 18 588.4

tion can be optimised in conjunction with orbit op-

timisation to achieve higher energy delivery. For ex-

ample, if SPF-14 ([latitude, longitude] = [24.73 deg,

6.42 deg]) is located at a slightly higher latitude at

the intersection point the quantity of energy deliv-

ered could be increased approximately by about 6.4

MWh per day. Similarly, if SPF-19 and SPF-20 are

located favourably at the intersection, the total quan-

tity of energy delivered to those farms could be ap-

proximately 138 MWh (34.5 MWh x 2 passes x 2

SPF) per day, instead of the current 63.3 MWh, or

at least increase by 5.7 MWh to 69 MWh. Then,

the total could reach approximately 600 MWh and

could even increase to 635 MWh per day. Then the

additional quantity of energy would be increased by

approximately 75% (from 363.5 MWh to 635 MWh),

higher than the increase in the number of SPF (67%)

or approximately reach the same level at 65% (from

363.5 MWh to 600 MWh). The strategic placement of

new solar power farms could also decrease the number

of overlapping passes or increase the distinct passes,

potentially increasing the energy delivery further. A

ﬁnal note can also be made for dawn/dusk reﬂectors,

which demonstrated inferior performance per reﬂec-

tor on average. The reasoning was found to be the

disproportionate distribution of SPFs in the eastern

and western hemispheres of the Earth in this case.

With the hypothetical farms, the ratio of the number

of SPF between the eastern and western hemispheres

increases from 0.33 (3 vs 9) to 0.54 (7 vs 13), which

may improve the results of the dawn/dusk reﬂector

case as well. Ultimately, however, orbiting reﬂector

constellations will be aimed at increasing the quan-

tity of energy delivered further.

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6. Constellations of Orbiting Solar Reﬂectors

The results of a single orbit presented in the pre-

vious section can now be extended to a constellation.

Here, a relatively small number of reﬂectors will be

considered for a Sun-synchronous orbit constellation.

Single reﬂectors will be considered for 5, 10 and 20

orbit planes and the results will be discussed for both

existing and hypothetical SPF cases. Recall from Sec.

4 that the constellation orbits are circular and have

the same orbital elements except for the right ascen-

sion of the ascending node, Ω. Also recall from the

mathematical derivations in Sec. 3 that the appro-

priate selection of the RAAN diﬀerence between the

orbit planes, ∆Ω and mean anomaly ∆Mbetween

subsequent reﬂector orbits will provide the same pass

geometry in terms of elevation. Hence the pass du-

ration and the quantity of energy delivered would be

scaled by the number of reﬂectors according to Eq.

10 for pass duration and linearly for the quantity of

energy as Etot,N =NEtot. The placement of orbit

planes and the extension of pass duration requires a

phase angle, ϕ, to be deﬁned for the constellation. ϕ

is selected to be 15 deg initially, but the implications

of a smaller and a larger value will also be discussed

later. According to this design choices, Table 14 sum-

marises the constellation properties for the selected

number of reﬂector satellites.

Table 14: The results of extended pass duration and

the quantity of energy delivered in diﬀerent con-

stellation options

N Tpass Etot Etot

(mean) (existing) (hypothetical)

[min] [MWh] [MWh]

5 34.5 1817.5 2942

10 56.0 3635 5884

20 98.9 7279 11768

Table 14 shows that with just 5 reﬂectors, the ex-

tension of operations at a solar power farm would ap-

proximately be doubled and could be over 1.5 hours

with 20 reﬂectors. With 5, 10 and 20 reﬂectors and

ϕ= 15 deg, the constellation would span a Ω range

of 4.40, 9.90 and 20.9 deg. If the leading reﬂector is

placed approximately at the terminator line, it would

provide suﬃcient angular range before the Earth’s

shadow on the reﬂector occurs. The maximum allow-

able range extends up to approximately β= 30.2 deg

from the terminator point for a 1000 km altitude or-

bit. The quantity of energy delivery linearly scales

with the number of reﬂectors and reaches nearly 12

GWh for a 20-reﬂector constellation with the inclu-

sion of hypothetical solar power farms. It is previ-

ously argued that if polar orbit RAAN is greater and

smaller than 90 deg, there would be enhanced energy

delivery at night due to the geometry with the Sun-

line, according to Fig. 5. This is not true for SSOs, or

at least the change is minuscule as previously demon-

strated in a fully numerical model in Viale et al. [12],

therefore the scalability would apply for the SSO case,

as the similarity in diﬀerent solutions in Table 7 also

demonstrate. Then, Figure 16 shows an example 10-

reﬂector constellation with the reﬂectors’ distribution

in orbit.

Fig. 16: Orbits and distribution of orbiting solar re-

ﬂectors with 10 reﬂectors and ϕ= 15 deg phase

angle between them. Each gray dot represents a

reﬂector and magenta circles represent orbits.

The lead reﬂector satellite in Fig. 16 is the SSO

solution in Table 10 with ∆Ω and ∆Mas given in

Table 1 for ϕ= 15 deg. In the y−zprojection of the

orbits, the equal and ϕ= 15 deg distribution can be

seen.

It is also of interest how the proﬁle of power deliv-

ered would appear with the separation between the

reﬂectors. This has implications on the duration, in-

tensity and uniformity of the power proﬁle desired

by the receiving solar power farm. The impact of the

separation angle ϕin this case will be discussed for

a 10-reﬂector constellation and ϕ= 5, 15 and 30 deg.

The assumption again is that the proﬁles are the same

thanks to the favourable placement of reﬂectors in the

constellation. Figure 17 shows these combined power

proﬁles together.

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reserved.

0 5 10 15 20 25 30

200

400

600

800

1000

1200

1400

(a) ϕ= 5 deg

0 10 20 30 40 50 60

100

200

300

400

500

600

(b) ϕ= 15 deg

0 20 40 60 80 100

100

200

300

400

500

Fig. 17: Combined power proﬁle of a 10-reﬂector constellation with phase angles 5, 15, 30 deg between the

reﬂectors. Individual power proﬁles are shown with coloured ﬁgures.

With the reﬂector constellation considered in Ta-

ble 14, where ϕ=15 deg, the power proﬁle varies sinu-

soidally after the second reﬂector appears for approx-

imately 40 min and the variation is bounded approxi-

mately between 380 and 550 MW. On the other hand,

if ϕis increased to 30 deg, the sinusoidal variation is

between 60 to 490 MW, meaning that the overlap is

not eﬀective, but the advantage of larger ϕis the ex-

tended pass duration of longer than 1.5 hours. It is

worth noting that if ϕ=30 deg or other larger num-

bers are selected, the Ω range may be greater than β

angle for this altitude, therefore initial Ω needs to be

smaller than 90 deg. Finally, if a smaller ϕvalue is se-

lected, such as ϕ= 5deg in Fig. 17a, then the power

proﬁle shows a much larger peak at 1400 MW, but the

total pass duration decreases down to approximately

30 min.

The power proﬁle could be adjusted according to

the energy demand or other terrestrial or space seg-

ment requirements by modifying the orbit RAAN

within the constellations. Changing the power pro-

ﬁle from Fig. 17b to Fig. 17a, or ϕ=15 deg to 5 deg

means that ∆Ω and ∆Mneed to be reduced from

1.10 deg to 0.37 deg and from 14.98 deg to 4.99 deg,

respectively. This may be achieved by solar radia-

tion pressure by utilising the reﬂectors as solar sails.

For a reﬂector of areal density of 18.8 g m−2in a cir-

cular orbit similar to this paper (at 884.6 km), the

authors found that 1 deg shift in Ω may be achieved

in approximately 10 days, if the reﬂector is Sun fac-

ing. The change in Ω is smaller here (approximately

0.7 deg), therefore a better performance may be ex-

pected.

Alternatively, the sinusoidal variations in Fig. 17b

and 17c can be made more uniform by using a large

number of smaller reﬂectors with smaller spacing be-

tween them. To demonstrate this, the power proﬁle

in Fig. 17b will be considered. To that end, the

area of a single 1 km diameter reﬂector is equal to 25

200-m diameter reﬂectors. Then, as the equivalent

of a 10-reﬂector constellation, there would be 250 re-

ﬂectors with a 200-m diameter each. Dividing the Ω

range for this constellation into 250 equal angles and

converting them into ϕthrough Eqs. 20 and 17 result

in a spacing of ϕ= 0.5413 deg between the reﬂectors.

Combining the power proﬁles of the smaller reﬂectors

would result in the power proﬁle in Fig. 18.

Fig. 18: Power proﬁle of 250 200-m diameter reﬂec-

tors in a constellation adopted from 10-reﬂector

constellation with ϕ= 15 deg. Individual proﬁles

are shown with coloured ﬁgures.

Figure 18 shows a square wave like, uniform power

delivery proﬁle. This provides approximately 445

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reserved.

MW power for approximately 40 min of nearly an

hour pass duration. A similar approach may also be

taken when ϕ=30 deg, but in that case, the uniform

maximum power delivered would be lower, but deliv-

ered in a longer duration. Using smaller reﬂectors in

this form in a constellation may provide several ad-

vantages. First, it may be preferable from the solar

power farm operation perspective where the reﬂec-

tors provide uniform constant power delivery for an

apriori known duration. Second, it may be preferable

from a space segment perspective, as smaller reﬂec-

tors have more manageable attitude control require-

ments [12] and may be easier to build and launch

than single monolithic reﬂectors of 1 km in diameter.

Some ﬁnal remarks could also be made about the

potential contribution of orbiting solar reﬂector con-

stellations to terrestrial electricity generation. En-

ergy generation can be quantiﬁed by the capacity

factor, which deﬁnes the ratio between the total elec-

tricity generated by that source and the total capac-

ity for a given time. Utility-scale solar power farms

currently have a global average capacity factor of ap-

proximately 0.17†, i.e., a solar power farm would gen-

erate electricity approximately 17% of its nameplate

capacity over a year. As a reference, the global aver-

age capacity factor is approximately 0.4 for wind and

more than 0.9 for nuclear energy in 2011-2013 [26].

The greatest inhibitor of the capacity factor for solar

energy is the daylight limitation.

The US average capacity factor is 0.25 in 2014-

2017 [27], which means that, for example, the 550

MW capacity Topaz solar power farm (SPF-11 in

Table 2) would generate approximately 3300 MWh

electricity per day on average. A 10-reﬂector con-

stellation would deliver 3635 MWh solar energy to

existing SPFs globally, from which, approximately

363.5 MWh electricity can be generated with a 20%

conversion and 50% land-coverage ratios, i.e., ap-

proximately equivalent to 11% of the actual daily

capacity of Topaz. The number can be doubled

for a 20-reﬂector constellation, providing an approx-

imately 22% increase and can be approximately lin-

early scaled. If hypothetical solar power farms are

included in this comparison, then a 20-reﬂector con-

stellation could generate electricity equivalent to 36%

of Topaz capacity with 1176.8 MWh. If looked at

globally, existing SPF capacity (except for SPF-12,

which is not yet operational) may be linearly scaled

to that of a 10-km diameter circular SPF area (i.e.,

†Available at https://www.

statista.com/statistics/799330/

global-solar- pv-installation- cost-per-kilowatt/,

Accessed August 29, 2023.

approximately 78.5 km) for a comparison. The SPF

with a larger area than 78.5 km2is not scaled down

but instead kept constant. Again, with a global aver-

age capacity factor assumption of 0.17, the electric-

ity generated in the existing SPF is approximately

equal to 181.02 GWh per day. A 20-reﬂector constel-

lation would then enhance the electricity generation

by about 0.4% globally with 728 MWh, at potentially

a fraction of the cost of all 11 SPFs combined [12].

Further enhancement can be achieved by increasing

the number of reﬂectors in the constellation. Orbit-

ing solar reﬂector constellations may then be seen as

analogous to additional solar power farms in space,

that provide near-constant daily solar energy deliv-

ery, i.e., a near-constant capacity factor throughout

the year, enhancing the existing terrestrial solar en-

ergy globally.

7. Conclusions

Constellations of orbiting solar reﬂectors could en-

hance terrestrial solar energy generation by provid-

ing additional illumination to solar power farms on

Earth. This speciﬁc application requires constella-

tion reﬂectors to be placed near the dawn/dusk ter-

minator region and to follow a similar pass geometry

for continuous, predictable and scalable solar energy

delivery. This paper therefore investigates constella-

tions that address these requirements and analyses

their properties.

First, the equations of Walker-type constellations

are modiﬁed in the presence of the Earth’s oblateness

perturbation such that successive reﬂectors repeat

the same elevation proﬁle over solar power farms.

Such a formulation also allows for optimising only

one orbit’s groundtrack and extrapolating its proper-

ties to the other reﬂectors in the constellation. Using

this favourable property, the genetic optimisation of

groundtracks of circular polar and Sun-synchronous

orbits (SSO) is performed with an objective function

deﬁned as the total quantity of energy delivered to

predeﬁned solar power farms on the Earth. The opti-

misation is performed for either a single reﬂector per

orbit or two-reﬂector (placed 180 deg apart) per orbit.

Among all cases, SSO and single reﬂector cases were

found to be superior. A constellation with 20 reﬂec-

tors could deliver a signiﬁcant quantity of solar en-

ergy to existing solar power farm projects, which may

be enhanced even further with strategically placed

new solar power farms. Constellations of orbiting

solar reﬂectors could then be seen as analogous to

additional solar power farm in space, distributing so-

lar energy globally rather than locally, enhancing the

Page 22 of 24

74th International Astronautical Congress, Baku, Azerbaijan, 2-6 October 2023.

reserved.

capacity of terrestrial solar energy.

This paper has only considered a single orbit al-

titude and a limited set of possible orbital conﬁgu-

rations, which, nevertheless, has demonstrated the

potential of solar reﬂector constellations to enhance

terrestrial solar energy generation. Alternative con-

stellation geometries could enhance this further for a

truly global clean energy generation by orbiting solar

reﬂectors.

Acknowledgments

This project has received funding from the Euro-

pean Research Council (ERC) under the European

Union’s Horizon 2020 research and innovation pro-

gramme (grant agreement No. 883730). CRM is also

supported by the Department of Science, Innovation

and Technology (DSIT) and the Royal Academy of

Engineering under the Chair in Emerging Technolo-

gies programme.

For the purpose of open access, the author(s) has

applied a Creative Commons Attribution (CC-BY)

licence to any Author Accepted Manuscript version

arising from this submission.

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A constellation design for orbiting solar reflectors to enhance terrestrial solar energy

Abstract

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