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Analyzing the Potential of Space Elevator Technology for

Sustainable Asteroid Mining

Joseph M. Bate1, Noor Yousuf 2, Josiah Rothwell 3

Space Elevator Research Leadership Team, Department of Mechanical and Aerospace Engineering, Colorado

Springs, CO, 80918

Lynnane George 4

University of Colorado Colorado Springs, Department of Mechanical and Aerospace Engineering, Colorado

Springs, CO, 80918

This study explores the feasibility and economic advantages of space elevator technology

in space travel and asteroid mining. Originating from an ambitious visionary in the 1960s,

the space elevator offers benefits including extended launch windows and increased launch

frequency while reducing costs in comparison to traditional chemical rocket propulsion [1].

The main asteroid belt harbors valuable materials such as platinum, cobalt, and water. The

primary focus of our analysis is on the logistics of constructing a Ceres based space

elevator, with the intention of harvesting the natural resources of Ceres and other nearby

asteroids. This study will examine the intricacies of space elevator technology with an

emphasis on two-body dynamics, space elevator system design, and mining operations.

Furthermore, this study analyzes Earth-asteroid orbital dynamics by systematically

comparing these parameters with traditional rocket-based systems. This in-depth

comparison provides valuable insights into the sustainability and economic viability of

large-scale asteroid mining facilitated by space elevator technology. This study contributes

to the growing body of knowledge surrounding space exploration and resource utilization,

thus paving the way for future endeavors contemplating long-term, large-scale asteroid

mining.

1Undergraduate Student, Department of Physics and Energy, AIAA Student Member.

2Undergraduate Student, Department of Mechanical and Aerospace Engineering, AIAA Student Member.

3Undergraduate Student, Department of Mechanical and Aerospace Engineering, AIAA Student Member.

4Senior Instructor, Department of Mechanical and Aerospace Engineering, Associate Fellow, AIAA Member.

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2024 Regional Student Conferences

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Copyright © 2024 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

AIAA Regional Student Conferences

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I. Nomenclature

Var.

Definition

Var.

Definition

Ceres geosynchronous

orbit radius measured from

Ceres center

1191.62 km

Taper Ratio

R

Ceres radius

469.7 km

T

Force per unit area in cable

GPa

Ceres’s rotational angular

velocity

Mass density of elevator

tether material

G

Newton’s universal

gravitational constant

characteristic length of

elevator cable material

km

Ceres gravitational

constant (GM)

Ceres orbital velocity about

the Sun

g

acceleration due to gravity

at Ceres’s surface

mass of elevator cable

kg

h

length of tether beyond

geostationary orbit

1108.18 km

mass of counterweight

kg

length of tapered tether

from Ceres surface

1830.3 km

mass of tether climber

kg

H

distance from top of free-

standing tower to Ceres

center

2300 km

upward force due to the

portion of the tower above

dr

N

Sun mass

downward force due to the

portion of the tower below

dr

N

M

Ceres mass

kg

upwards centrifugal force

on the element dr

N

A

cross-sectional area of

tapered tether

W

downward force due to the

weight of the element

N

cross-sectional area of

tapered tether at Ceres

surface and counterweight

distance of a point on the

tether from Ceres’s center

km

cross-sectional area of

tapered tether at

geosynchronous orbit

dr

small element of tower

length

km

P

orbital period of Ceres

9.07417 hr

AU

Astronomical Unit

km

II. Background

The issues plaguing traditional interplanetary travel can be characterized by the immense fuel

requirements, as breaking free from Earth’s gravity is a high energy endeavor. This results in extremely high costs

and restricted payload capacity. In addressing this problem, an intuitive solution is to launch spacecrafts directly

from a large radius such that they escape the planetoid’s sphere of influence with minimal additional fuel required.

This can be achieved by placing a spacecraft in synchronous orbit and connecting a tether between the spacecraft

and the surface of the planetoid. The blueprint for an Earth based space elevator has been laid out in The Space

Elevator, a work published by Dr. Bradley C. Edwards and supported by NASA Institute for Advanced Concepts

(NIAC) [2]. This work not only outlines the operational obstacles and the associated solutions involved with

operating a space elevator, but it also proposes key strategies for successful tether system deployment. Our team

utilized components of this blueprint to design a new system for application on the dwarf planet Ceres. The space

elevator is designed to achieve reduced fuel requirements while maintaining reasonable time of flight values.

The construction of a space elevator consists of three main components: the anchor, the tether, and the

counterweight. PK Aravind derived the method for calculating the characteristics of an Earth based space elevator

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in his paper The Physics of a Space Elevator [3]. These methods are readily adapted to the analysis of a space

elevator located on Ceres. The anchor must be sufficiently strong to withstand the centrifugal force imposed by the

connected orbiting counterweight, and the counterweight must be sufficiently massive to keep the system in tension.

Thus, the tether must be able to withstand the large forces created by this equilibrium relationship so a sufficiently

strong material must be chosen for this application. With the advent of carbon nanotube technology, the

conceptualization of space elevators has ventured from sci-fi literature to real-world considerations. Carbon

nanotubes have been tested to have a uniaxial tensile strength up to 130 GPa [3]. This extremely high tensile

strength allows for the construction of a much smaller, and therefore realistic, tether.

To install this tether a spacecraft, also referred to as the Apex Anchor, containing a thin spooled cable must

be released into a stationary parking orbit. Once in a stable orbit, this spacecraft will deploy an initial strand of

tether downwards toward the planetary body [2]. This tether strand will be connected to the anchor point, and an

initial tether climber will ascend the thin cable. This initial climber will carry and attach nanotube strings along

with epoxy to strengthen the existing cable. This epoxy will create a finite difference in the material characteristics

of the cable, but this difference is accounted for using the small-scale cable design as proposed in Edwards paper.

Once the cable is sufficiently strong, it can be regularly used to launch payloads from above synchronous orbit to

interplanetary destinations.

This paper takes that concept and explores the application of this technology on dwarf planet Ceres as a

means of establishing mining operations. Data collected from the Gamma Ray and Neutron Detector (GRaND), an

instrument on board NASA’s Dawn probe, reveals a high distribution of hydrogen under the surface of Ceres.

Remarkably, these materials can be accessed at depths as shallow as one meter [3]. From this discovery, it can be

inferred that water is present on the surface of Ceres. Modern advancements in water electrolysis allow for in-situ

fuel refinement [4]. The location of Ceres is also ideal as it is in the main asteroid belt and will allow access to

nearby asteroids that contain valuable resources such as nickel, cobalt, and platinum. Using space elevator

technology will increase the rate at which we can return resources back to Earth while reducing cost over time, thus

demonstrating the economic value in its construction.

III. Methods

A. Space Elevator Components

1. Anchor

An anchoring system is an integral component of an operational space elevator as the success of the system hinges

on its stability. Ceres is classified as a carbonaceous chondrite and its surface composition is primarily made up of

iron-rich clay [4]. The surface material falls into the low end of the Moh’s hardness scale, ranging from 2 – 3.5, which

makes it nominal for installing as an anchoring system [5]. The anchor points must be able to withstand a vertical

force of 278.77 N which was calculated using the centrifugal force of the system in Section B. There are already

asteroid landing technologies in development that have been designed and tested to withstand up to 500N [3].

2. Tether

The tether is a daunting design challenge; however, a feasible

design is proposed which could be readily produced for application

on Ceres. Carbon nanotubes are currently only grown to a matter

of centimeters in length. To account for this, the nanotubes are

spun into continuous threads, which are woven into the tether [2].

This design allows the tether to maintain its strength and account

for the short sections of carbon nanotubes.

Additionally, Ceres mass is seven percent that of Earth. Using the

mass and orbital characteristics it can be calculated that the

acceleration due to gravity on Ceres’s surface is nearly two orders

of magnitude lower than that of Earth (See Section B). This means

that the overall force on the elevator is reduced and therefore the

necessary mass of the elevator is reduced. This proves beneficial

as it allows for less material required for construction, thus reducing

the total cost while utilizing materials that are currently in

Fig 1: Hoytether Proposed Tether Design [1]

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production. Two materials were identified as candidates for the tether design: Dyneema, also known as ultra-high

molecular weight polyethylene (UHMWPE) and carbon nanotubes. When comparing the two in terms of tensile

strength, it was found that while Dyneema was sufficient in strength, it exhibited excessive creep strain rate over time.

This means that the use of pure Dyneema in a space elevator would lead to a progressive loss of structural integrity in

the woven structure. Conversely, carbon nanotubes displayed a significantly higher tensile strength and demonstrated

negligible creep. Therefore, out of the materials currently in production carbon nanotubes are the most suitable choice.

3. Counterweight

The design of the space elevator relies on creating tension in the tether through the presence of the counterweight

in Ceres synchronous orbit (CSO). This counterweight creates tension because it is at a height higher than critical

radius, which is the location from which a payload must be released to escape the planetoid’s sphere of influence.

Therefore, for the system to be operational, the tether must extend beyond the CSO, which is approximately 1,192

km from the center of the dwarf planet. The length of the elevator is defined by a multitude of characteristics and

relationships including, but not limited to, material constraints, mass constraints, and cost limitations. One such

definitive relationship exists between the length of the tether cable and the mass of the counterweight. PK Aravind

postulated that to decrease the length of the tether and still maintain balance in the system, one must implement a

more massive counterweight [3]. Another key relationship exists between the length of the tether and , the

maximum distance a payload can travel upon release. By comparing the minimum orbit intersection distance

between Ceres and Earth, an ideal value for can be established. By basing the value on the to the minimum

intersection distance, the fuel required to decrease velocity upon arrival is minimized.

B. Space Elevator Tether Analysis

1. Quantifying the characteristics of a space elevator

In developing the theoretical values for the design components of a space elevator on Ceres, establishing the dwarf

planet’s orbital constants is crucial. By calculating both the synchronous orbital radius and the angular velocity, the

optimal dimensions of a Ceres space elevator can be defined. Ceres’s orbital angular velocity is calculated using

Appendix Eq. (A) where P=9.07417 hours is the synodic body rotation period of Ceres. The orbital angular velocity

of Ceres is found to be

.

The intention of a space elevator on any planetoid is to deliver payloads to an interplanetary destination with minimal

additional fuel required. The critical distance from the center of Ceres that a payload must be released from on the

tether to escape Ceres’s sphere of influence can be calculated using Appendix Eq. (B) where

represents µ, Ceres gravitational parameter [3][6]. This establishes a minimum height for the space elevator, resulting

in a conclusion that the apex anchor must extend higher than =1501.60 km for a payload to escape the gravitational

pull of Ceres.

2. Calculating the Maximum Achievable Launch Distance

The concepts of PK Ararvind’s Earth based space elevator analysis are readily applied to the orbital properties of

Ceres. To calculate the maximum distance a payload launched from the top of the tether can travel, angular momentum

and energy conservation equations are utilized under a set of assumptions. First, it is assumed that the tether’s rotation

occurs in the orbital plane of Ceres equator, which is not accurate but will suffice for this analysis. Upon release the

payload will travel away from Ceres along an elliptical path around the Sun. By releasing the payload when the tether’s

angular velocity is parallel to Ceres’s orbital velocity, the craft’s velocity relative to the Sun at release will be as large

as possible; in this case the perihelion point in the payload’s orbit is at the release point and the aphelion is a great

distance away, opposite the Sun. If the opposite is assumed and the payload is released when the tether’s velocity is

opposite to Ceres’s orbital velocity, then aphelion is at the release point and perihelion is at a much smaller distance

from the Sun. By releasing the payload opposite to Ceres’s orbital velocity, voyages to inner planets can be made.

To create a function that outputs maximum outward possible travel distance for a payload, it is assumed that the

orbital velocity of Ceres and the angular velocity of the spacecraft are parallel to each other upon release. Here

represents the orbital velocity of Ceres, H represents the distance from the center of Ceres to the end of the tether, and

represents the velocity of the spacecraft when it is released from the end of the tether. This results in a

direct summation of the two velocities ( such that maximum transfer velocity is achieved on release. Let

be the average distance between Ceres and the Sun and the perihelion distance of the payload’s elliptical orbit around

the Sun. The previous assumption neglects a small correction due to the finite length of the tether, however this can

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be accounted for during orbital transfer.

To create a set of comparable equations, Aravind represented as the aphelion distance of the craft from the Sun

and as its aphelion velocity. The laws of conservation of angular momentum and energy yield the equations

(1)

AND

(2)

where m and Ms are the mass of the spacecraft and sun respectively. Here is the average distance

between Ceres and the Sun,

is Ceres’s orbital velocity about the Sun, and

is

Newton’s gravitational constant [6]. The potential energy of the spacecraft in Ceres’s gravitational field is dwarfed by

the term

and has therefore been omitted. By eliminating from Eq. (1) and Eq. (2) we find that

satisfies the resulting quadratic equation. By using to solve the quadratic, the only relevant solution is

(3)

This equation outputs , the maximum distance in kilometers to be traveled from the space elevator as a function of

H, the distance from the upper end of the tether to the center of Ceres in kilometers. The symbol in Eq. (3) allows

for the output of distance towards or away from the Sun (i.e. by inputting , represents the travel distance

away from the Sun, and vice versa). This equation assumes coplanar transfer orbits, which will be accounted for via

generating thrust to correct the trajectory.

By creating a MATLAB code to iterate through the H values of this function at an interval of 100 km, a table of the

associated values was created. The average distance from Ceres to Earth is 1.58322 Atomic Units (AU) [7]. A

minimum value of 2.4 AU is established by using a safety margin of 1.5 for the distance a payload must travel to

reach the Earth. An H value of 2300 km was selected based on this factor of safety, the necessary counterweight mass,

and the overall reduction of system cost. As H is measured with respect to the center of Ceres, the tether will only be

about 1831 km long. Using the length of the tether and some orbital constants, the corresponding dimensions of the

tether are evaluated.

3. Tether Taper Ratio

A free-standing tower is characterized by the weight of the tower being counteracted by the centrifugal force

acting on it . This means that the tension force in both halves of the tower must also be equal [3].

In equilibrium these four values will sum to zero ( [3]. This idea of a free-standing tower is

ideal when considering the construction of a space elevator as it keeps the system in balance at such extreme lengths.

A cylindrical tower is ideal from a manufacturing perspective, however a tapered ribbon design is optimal

for this application. The taper is designed to increase exponentially to synchronous orbit, then decrease exponentially

to the counterweight. The taper allows for the constant distribution of tension T throughout the entire area of the cable.

To develop a tether with a factor of safety of 2, the chosen value for T is one half of the maximum tensile strength of

the chosen material. By analyzing this relationship in reference to , a small, tapered element of the tower, explicit

equations for cross-sectional area, cable length, cable mass, and counterweight mass can be derived.

A value for , the cross-sectional area at either end of the tether, must be established as a parameter to define the

rest of the tether. is determined by equating the effective mass of the tether climber at ground level to the

tension force due to the cable at the same point, which is represented by

(4)

where R=469.7 km is the radius of Ceres and

represents the acceleration due to gravity

on Ceres’s surface [3]. is isolated in this equation to explicitly solve for the cross-sectional area of the tether on

Ceres. The gravity on Ceres is nearly two orders of magnitude lower than that of Earth. As such, a much lower tether

climber mass, can be chosen on Ceres and still support the same effective weight. By comparing the ratio of

gravitational forces on Earth and Ceres to the necessary climber mass, a lower bound of 377 kg was established for

A tether climber mass of was chosen to account for design considerations and minimize tether costs.

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This tether construction allows for the forces acting on the tether to sum to zero at synchronous orbit. As such, it is

essential to define a value for , the radius at Ceres’s synchronous orbit, using Appendix Eq. (C). The resulting value

for the radius of CSO with respect to the center of the planetoid is To define the cross-sectional

area along any point of the tether, TdA is used to represent the relationship between the tensions. To simplify our stress

calculations TdA establishes a maximum tension at any point along the length of the cable. Here represents the

difference in areas between the upper and lower section of the cable. Explicit equations for W and are also

implemented into the equilibrium equation. An equation for cross-sectional area of the tether

is found by integrating the resulting equation with respect to dr. This equation is represented as

(5)

In Eq. (5), represents the density of the cable [3]. Exact values for and can be chosen based on the

characteristics of the material in question. By setting [3] as the cross-sectional area of the tether at

stationary height, a taper ratio for the tether is defined

(6)

where

represents the characteristic length of the material and Ag represents the cross-sectional area of the

tether at stationary height.

4. Mass Calculations

To find , the necessary mass of the counterweight is equated to the sum of Ceres’s gravitational pull on the

counterweight and the inward force of the elevator cable to the outward centrifugal force acting on it [3]. This

equilibrium equation is written as

(7)

The right side of the above equation represents the outward centrifugal force acting on the cable. By isolating and

solving for this term it is possible to determine the necessary strength of the anchor. This value was evaluated and

stated in Section III. By substituting the value of from Eq. (5) into Eq. (7) and solving for , the mass

of the counterweight, can be calculated using

(8)

The associated mass of the elevator can be calculated by integrating Eq. (5) numerically using Eq. (9). This results

in the integration equation

(9)

5. Material Selection

Dyneema has been theorized to have a wide variety of uses in tethered spacecrafts along with a moderately high

tensile strength. The strength to density ratio of carbon nanotubes makes them an ideal choice for high stress

applications such as a space elevator [2]. The associated properties of these materials are listed in the table below,

along with the resulting characteristics of a space elevator constructed using them. It is impossible to construct a space

elevator out of purely carbon nanotubes because each individual tube is only a few centimeters in length [2]. Dr.

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Edwards proposed solution to this will result in a slightly weaker design; However, this will not pose as a criticality

to mission viability. To prove this, the necessary design parameters for a space elevator constructed out of Dyneema

were evaluated. For reference, the tensile strength of Dyneema is about 27 times lower than that of carbon nanotubes.

The resulting data proved that the space elevator on Ceres could be constructed out of a much weaker material than

carbon nanotubes and still yield completely feasible design characteristics. Therefore, an epoxy/nanotube composite

is an ideal and feasible material to use in constructing the Ceres based space elevator.

Table 1: Calculated Design Characteristics of a Ceres Based Space Elevator

Symbol/Unit

Dyneema

Carbon Nanotubes

Tether Length (constant)

Tether Density (constant)

Tension in Tether (constant)

Characteristic Length of Tether

Cross Sectional Area of Tether at

Ceres and Apex Anchor

Taper Ratio of Tether

Mass of Counterweight

Mass of Tether

Maximum Travel Distance

Towards Earth

(AU)

2.4533

2.4533

Maximum Travel Distance Away

From Earth

(AU)

2.9845

2.9845

IV. Future Work

A. Trajectory

Lambert’s problem is an evolution of a Hohmann transfer as both algorithms calculate spacecraft trajectory.

However, Lambert’s problem, also known as a two-point orbital boundary value problem, allows for elliptical transfers

between two orbits of differing inclinations. A Lambert approach is utilized in establishing an optimized trajectory

between a Ceres space elevator and Earth. Through the implementation of the Gooding(1990) procedure, high

precision porkchop plots illustrating ideal departure and arrival dates were generated. Gooding’s algorithm facilitates

the reconstruction of velocity vectors in a computationally conservative manner without compromising accuracy.

Lambert’s problem ascertains the lowest possible characteristic energies (C3) in correspondence with the Julian dates.

[8]

B. Earth to Ceres Transfers

The efficiency of Earth to Ceres transfers can be calculated using porkchop plots. These plots show contour

intervals depicting varying levels of C3 depending on time of flight (TOF) and release locations. These values are

calculated by solving Lambert’s problem using python and plotting the edited results. To analyze the efficiency of the

space elevator two porkchop plots depicting different transfer methods can be compared. When comparing space

elevator plots to those of rocket propulsion it was found that the space elevator exhibited reasonable C3 values and

extended launch windows from two weeks to six months [9]. Fuel efficiency may be traded for a shorter time of flight

if this is a critical factor in mission design. Thus, space elevators allow for both reduced time of flight and extended

launch windows [9].

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C. Ceres Transfers to Nearby Asteroids

The proximity of Ceres to nearby asteroids makes it an excellent station for future asteroid mining endeavors.

Additionally, the proximity of Ceres to Jupiter makes interplanetary exploration a distinct possibility. Jupiter’s

extensive mass will allow for a gravity assist to deliver a payload an increased distance. The feasibility of an

asteroid based space elevator has been theoretically proven, and therefore it is proposed that it be extrapolated to

other asteroids in the future to harvest valuable materials. Asteroids, sometimes referred to as dwarf planets, are

predominantly located in the belt situated between Mars and Jupiter. Since the discovery of Ceres, the ephemeris

data of thousands of asteroids have been consequentially categorized. The distribution of asteroids, which catalogs

1796 asteroids, shows Ceres situated in an area of overabundance without entering the critical path of nearby

asteroids. This means that transfers to nearby asteroids is possible without critical risk of the asteroids damaging the

space elevator. Trajectories from Ceres to other locations in the belt require attitude determination and control to

account for the minor planet’s orbits.

D. Cost Analysis

A Ceres space elevator cost analysis can be conducted through the categorization of three primary cost drivers. These

drivers being: the tether, the counterweight satellite, and the anchor connecting the tether to Ceres surface. Mining

equipment and operational costs will require a separate analysis for an accurate estimate. Further analysis of the

telerobotic systems would also need to be conducted. The following monetary considerations are performed regarding

two main mission phases. The first phase will be a rocket containing the ground anchor, and the second rocket phase

will contain the counterweight satellite. Tether and apex anchor configuration expenses are categorized as One Time

Costs (OTC). The tether will initially be contained in this satellite and projected towards Ceres surface.

Cost estimations were determined through comparison to pre-established technology. SpaceX’s Falcon 9 Heavy

rocket was taken into consideration for payload delivery as it has a high mass capacity over long travel distances. This

rocket costs approximately 97 million dollars per launch and has already been utilized in multiple missions [10][11].

To provide sufficient fuel for interplanetary travel, chemical payload propellants such as hydrazine must contribute

to 25% of the payload’s overall wet mass. The dry mass of the initial payload, the ground anchor, will be approximately

3400 kg. This is the approximate weight of the Philae lander, which performed a similar anchoring mission. The dry

mass of the secondary payload, which is the apex anchor, is 3296.53 kg; Therefore, the total combined wet mass of

these systems is approximately 8730.66 kg. This constitutes 1674.13 kg being allocated to hydrazine propellent, which

is valued at $196.2/kg [12][13].

The carbon nanotubes used in constructing the Ceres space elevator tether are valued at $300/gram; therefore, for a

projected tether mass of ~19.88 kg, tether expenses are appraised at $5,964,240[14]. The conclusive cost of the apex

anchor was determined by correlating the mass and budget of NASA’s Dawn mission to that of the Ceres space

elevator. The Dawn spacecraft’s launch mass is a factor of 3.4 times less than that of the Apex Anchor [15]. In

determining the projected price of the Apex Anchor, the total cost of the Dawn mission was then multiplied by 3.4,

thus resulting in an approximate anchor cost of $1,516,400,000.].

Table 2: Ceres Space Elevator Cost Analysis

Ceres Space Elevator Mining Operation Costs (USD) For the Initialization of 11-Phases

Launch Vehicle and Propellent Expenses

Launch Vehicle:

$194,000,000

Chemical Payload Hydrazine:

$328,465

Tether and Apex Anchor Configuration Expenses

Carbon nanotube Tether (OTC):

~ $5,964,240

Apex Anchor (OTC):

~ $1,516,400,000

Ceres Base-Anchor (OTC):

~3,500,000,000

Total Costs:

$5,246,692,705

E. Equipment

There are a multitude of proposed methods to mine asteroids. These include boring, scraping, heating and more.

Strategies like boring and drilling require significant reaction forces and raise a large amount of dust, which damages

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mechanical components. The conditions of Ceres are conducive to microwave radiation mining, which involves

heating soil in a vertically angled pipe using microwave radiation. This pipe will be installed via a small drill which

will create an initial hole for the pipe to be inserted. The soil density is very low on Ceres, which will make inserting

the mining rod into the ground a feasible operation [4]. The anchor described earlier will provide as a reaction force

in the drilling of the boring holes. Microwave radiation will be sent into the soil which will excite and vaporize the

soil’s water content and cause it to evaporate up the tube. This water vapor will then reach a cold trap where it is

condensed to water. This water will either be refined via an in-situ water refinery, or will be shipped to Earth to be

refined in Earth’s synchronous orbit.

VI. Conclusion

As humans continue into the next great frontier, it is vital to come up with innovative solutions to daunting

technological challenges. The space elevator technology is one such solution which offers an alternative to traditional

methods of interstellar travel. By utilizing the angular rotation of a celestial body the fuel costs and associated time of

flight values can be greatly reduced. This system lends itself to use in harvesting the valuable contents of an asteroid

for ready delivery to Earth. By using the physics relationships of two orbiting bodies the associated characteristics of

a Ceres based space elevator have been established. These are more than reasonable system requirements which would

maintain a low cost in realm of space travel. This is made possible by new developments in materials engineering and

chemical processing. Harvesting the water from the asteroid Ceres is a lucrative endeavor. The benefits of the space

elevator have been proven through the programming-based analysis of two-body orbital dynamics resulting in reduced

energy consumption and time of flight. For the advancement of humans, it is imperative that we look skyward for our

next endeavors in expansion and exploration.

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VII. Appendix

Value [10]

Equations

Value [10]

Equations

[A]

Orbital

Angular

Velocity

[1]

Conservation

of Angular

Momentum

[B]

Critical Radius

[2]

Conservation

of Energy

[C]

Radius at

Synchronous

Orbit

[F]

Combination

Equation – (1)

& (2)

[D]

Modified

Space Elevator

Force

Equilibrium

Equation (1)

[3]

Travel

Distance of

Payload

[E]

Modified

Space Elevator

Force

Equilibrium

Equation (2)

[7]

Counterweight

Equilibrium

Equation

[5]

Tether Cross-

Sectional Area

Function

[8]

Mass of

Counterweight

[4]

Cross Sectional

Area of Tether

at Surface

[9]

Mass of Tether

[6]

Taper Ratio of

Tether

Acknowledgments

The authors would like to thank Dr. George for her expertise and knowledge of interplanetary trajectories and

Jon Gabbard for his technical guidance. We would additionally like to thank Dr. Bradley Edwards for his

substantial research in space elevator technologies, as well as Autumn Reed, David Schoenberger, Rob Whitley,

and Samarth Patel for their contributions.

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References

1. Artsutanov, Y., “Kosmos na Elektrovoze,” Lvov, Vol. 158, No. 455, 1967.

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Downloaded by Lynnane George on July 25, 2024 | http://arc.aiaa.org | DOI: 10.2514/6.2024-85461