The Gravitational Spacecraft

The Gravitational Spacecraft

Fran De Aquino
Maranhao State University, Physics Department, S.Luis/MA, Brazil.
Copyright © 1997-2010 by Fran De Aquino. All Rights Reserved

There is an electromagnetic factor of correlation between gravitational mass and inertial mass,
which in specific electromagnetic conditions, can be reduced, made negative and increased in
numerical value. This means that gravitational forces can be reduced, inverted and intensified
by means of electromagnetic fields. Such control of the gravitational interaction can have a lot
of practical applications. For example, a new concept of spacecraft and aerospace flight arises
from the possibility of the electromagnetic control of the gravitational mass. The novel
spacecraft called Gravitational Spacecraft possibly will change the paradigm of space flight
and transportation in general. Here, its operation principles and flight possibilities, it will be
described. Also it will be shown that other devices based on gravity control, such as the
Gravitational Motor and the Quantum Transceivers, can be used in the spacecraft,
respectively, for Energy Generation and Telecommunications.


Key words: Gravity, Gravity Control, Quantum Devices.


CONTENTS

1. Introduction 02

2. Gravitational Shielding 02

3. Gravitational Motor: Free Energy 05

4. The Gravitational Spacecraft 06

5. The Imaginary Space-time 13

6. Past and Future 18

7. Instantaneous Interstellar Communications 20

8. Origin of Gravity and Genesis of Gravitational Energy 23

Appendix A 26
Appendix B 58
Appendix C 66
Appendix D 71
References 74

2
1. Introduction

The discovery of the correlation
between gravitational mass and inertial
mass [1] has shown that the gravity
can be reduced, nullified and inverted.
Starting from this discovery several
ways were proposed in order to obtain
experimentally the local gravity
control [2]. Consequently, new
concepts of spacecraft and aerospace
flight have arisen. This novel
spacecraft, called Gravitational
Spacecraft, can be equipped with other
devices also based on gravity control,
such as the Gravitational Motor and
the Quantum Transceiver that can be
used, respectively, for energy
generation and telecommunications.
Based on the theoretical background
which led to the gravity control, the
operation principles of the
Gravitational Spacecraft and of the
devices above mentioned, will be
described in this work.

2. Gravitational Shielding

The contemporary greatest
challenge of the Theoretical Physics
was to prove that, Gravity is a
quantum phenomenon. Since the
General Relativity describes gravity as
related to the curvature of the space-
time then, the quantization of the
gravity implies the quantization of the
proper space-time. Until the end of the
century XX, several attempts to
quantify gravity were accomplished.
However, all of them resulted fruitless
[3, 4].





In the beginning of this century,
it has been clearly noticed that there
was something unsatisfactory about
the whole notion of quantization and
that the quantization process had many
ambiguities. Then, a new approach has
been proposed starting from the
generalization of the action function*.
The result has been the derivation of a
theoretical background, which finally
led to the so-sought quantization of the
gravity and of the space-time.
Published under the title:
“Mathematical Foundations of the
Relativistic Theory of Quantum
GravityӠ, this theory predicts a
consistent unification of Gravity with
Electromagnetism. It shows that the
strong equivalence principle is
reaffirmed and, consequently
Einstein’s equations are preserved. In
fact, Einstein’s equations can be
deduced directly from the Relativistic
Theory of Quantum Gravity. This
shows, therefore, that the General
Relativity is a particularization of this
new theory, just as the Newton’s
theory is a particular case from the
General Relativity. Besides, it was
deduced from the new theory an
important correlation between the
gravitational mass and the inertial
mass, which shows that the
gravitational mass of a particle can be
decreased and even made negative,
independently of its inertial mass, i.e.,
while the gravitational mass is

* The formulation of the action in Classical Mechanics
extends to the Quantum Mechanics and it has been the
basis for the development of the Strings Theory.
† http://arxiv.org/abs/physics/0212033

3
progressively reduced, the inertial
mass does not vary. This is highly
relevant because it means that the
weight of a body can also be reduced
and even inverted in certain
circumstances, since Newton’s gravity
law defines the weight of a body as
the product of its gravitational mass
by the local gravity acceleration ,
i.e.,
P
gm g
( )1gmP g=

It arises from the mentioned law
that the gravity acceleration (or simply
the gravity) produced by a body with
gravitational mass is given by gM

( )22r
GM
g g=

The physical property of mass
has two distinct aspects: gravitational
mass mg and inertial mass mi. The
gravitational mass produces and
responds to gravitational fields. It
supplies the mass factors in Newton's
famous inverse-square law of
gravity ( )2rmGMF gg= . The inertial
mass is the mass factor in Newton's
2nd Law of Motion . These
two masses are not equivalent but
correlated by means of the following
factor [1]:
( amF i= )

( )31121
2
00 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛ Δ+−=
cm
p
m
m
ii
g

Where is the rest inertial mass and
is the variation in the particle’s
kinetic momentum; is the speed of
light.
0im
pΔ
c
This equation shows that only
for 0=Δp the gravitational mass is
equal to the inertial mass. Instances in
which pΔ is produced by
electromagnetic radiation, Eq. (3) can
be rewritten as follows:
( )41121
2
3
2
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛+−=
c
Dn
m
m
r
i
g
ρ

Where is the refraction index of the
particle; is the power density of the
electromagnetic radiation absorbed by
the particle; and
rn
D
ρ its density of
inertial mass.
It was shown [1] that there is an
additional effect of gravitational
shielding produced by a substance
whose gravitational mass was reduced
or made negative. This effect shows
that just above the substance the
gravity acceleration will be reduced
at the same proportion
1g
0ig mm=χ ,
i.e., , ( is the gravity
acceleration bellow the substance).
gg χ=1 g
Equation (4) shows, for
example, that, in the case of a gas at
ultra-low pressure (very low density of
inertial mass), the gravitational mass
of the gas can be strongly reduced or
made negative by means of the
incidence of electromagnetic radiation
with power density relatively low.
Thus, it is possible to use this
effect in order to produce gravitational
shieldings and, thus, to control the
local gravity.
The Gravity Control Cells
(GCC) shown in the article “Gravity
Control by means of Electromagnetic

4

Field through Gas or Plasma at Ultra-
Low Pressure”‡, are devices designed
on the basis, of this effect, and usually
are chambers containing gas or plasma
at ultra-low pressure. Therefore, when
an oscillating electromagnetic field is
applied upon the gas its gravitational
mass will be reduced and,
consequently, the gravity above the
mentioned GCC will also be reduced
at the same proportion.
It was also shown that it is
possible to make a gravitational
shielding even with the chamber filled
with Air at one atmosphere. In this
case, the electric conductivity of the
air must be strongly increased in order
to reduce the intensity of the
electromagnetic field or the power
density of the applied radiation.
This is easily obtained by
ionizing the air in the local where we
want to build the gravitational
shielding. There are several manners
of ionizing the air. One of them is by
means of ionizing radiation produced
by a radioactive source of low
intensity, for example, by using the
radioactive element Americium (Am-
241). The Americium is widely used
as air ionizer in smoke detectors.
Inside the detectors, there is just a little
amount of americium 241 (about of
1/5000 grams) in the form of AmO

2.
Its cost is very low (about of US$
1500 per gram). The dominant
radiation is composed of alpha
particles. Alpha particles cannot cross
a paper sheet and are also blocked by
some centimeters of air. The
Americium used in the smoke

‡ http://arxiv.org/abs/physics/0701091

detectors can only be dangerous if
inhaled.
The Relativistic Theory of
Quantum Gravity also shows the
existence of a generalized equation for
the inertial forces which has the
following form
( )5aMF gi =

This expression means a new law for
the Inertia. Further on, it will be
shown that it incorporates the Mach’s
principle to Gravitation theory [5].
Equation (3) tell us that the
gravitational mass is only equal to the
inertial mass when . Therefore,
we can easily conclude that only in
this particular situation the new
expression of reduces to
0=Δp
iF amF ii = ,
which is the expression for Newton's
2nd Law of Motion. Consequently,
this Newton’s law is just a particular
case from the new law expressed by
the Eq. (5), which clearly shows how
the local inertial forces are correlated
to the gravitational interaction of the
local system with the distribution of
cosmic masses (via ) and thus,
incorporates definitively the Mach’s
principle to the Gravity theory.
gm
The Mach’s principle postulates
that: “The local inertial forces would
be produced by the gravitational
interaction of the local system with the
distribution of cosmic masses”.
However, in spite of the several
attempts carried out, this principle had
not yet been incorporated to the
Gravitation theory. Also Einstein had
carried out several attempts. The ad
hoc introduction of the cosmological

5
term in his gravitation equations has
been one of these attempts.
With the advent of equation (5),
the origin of the inertia - that was
considered the most obscure point of
the particles’ theory and field theory –
becomes now evident.
In addition, this equation also
reveals that, if the gravitational mass
of a body is very close to zero or if
there is around the body a
gravitational shielding which reduces
closely down to zero the gravity
accelerations due to the rest of the
Universe, then the intensities of the
inertial forces that act on the body
become also very close to zero.
This conclusion is highly
relevant because it shows that, under
these conditions, the spacecraft could
describe, with great velocities, unusual
trajectories (such as curves in right
angles, abrupt inversion of direction,
etc.) without inertial impacts on the
occupants of the spacecraft.
Obviously, out of the above-
mentioned condition, the spacecraft
and the crew would be destroyed due
to the strong presence of the inertia.
When we make a sharp curve
with our car we are pushed towards a
direction contrary to that of the motion
of the car. This happens due to
existence of the inertial forces.
However, if our car is involved by a
gravitational shielding, which reduces
strongly the gravitational interaction of
the car (and everything that is inside
the car) with the rest of the Universe,
then in accordance with the Mach’s
principle, the local inertial forces
would also be strongly reduced and,
consequently, we would not feel
anything during the maneuvers of the
car.

3. Gravitational Motor: Free Energy

It is known that the energy of
the gravitational field of the Earth can
be converted into rotational kinetic
energy and electric energy. In fact, this
is exactly what takes place in
hydroelectric plants. However, the
construction these hydroelectric plants
have a high cost of construction and
can only be built, obviously, where
there are rivers.
The gravity control by means of
any of the processes mentioned in the
article: “Gravity Control by means of
Electromagnetic Field through Gas or
Plasma at Ultra-Low Pressure” allows
the inversion of the weight of any
body, practically at any place.
Consequently, the conversion of the
gravitational energy into rotational
mechanical energy can also be carried
out at any place.
In Fig. (1), we show a schematic
diagram of a Gravitational Motor. The
first Gravity Control Cell (GCC1)
changes the local gravity from
to
g
ngg −=′ , propelling the left side of
the rotor in a direction contrary to the
motion of the right side. The second
GCC changes the gravity back again to
i.e., from g ngg −=′ to , in such a
way that the gravitational change
occurs just on the region indicated in
Fig.1. Thus, a torque
g
T given by

( ) ( ) ( )[ ]
( ) grmn
rgmgmrFFT
g
gg
2
11
22
+=
=+′−=+′−=

6
Is applied on the rotor of gravitational
mass , making the rotor spin with
angular velocity
gm
ω .
The average power, , of the
motor is
P
ωTP = . However,
.Thus, we have rgg 2ω=+′−
( ) ( )61 3321 rgnmP i +=
Consider a cylindrical rotor of iron ( )3.7800 −= mKgρ with height ,
radius
mh 50.=
mRr 0545.03 == and inertial
mass . By adjusting
the GCC 1 in order to obtain
kghRmi 05.327
2 == ρπ
( ) ( ) ( ) 191 −=−== nmm airiairgairχ and, since
, then Eq. (6) gives 2.81.9 −= smg

HPKWwattsP 2942191019.2 5 ≅≅×≅

This shows that this small motor
can be used, for example, to substitute
the conventional motors used in the
cars. It can also be coupled to an
electric generator in order to produce
electric energy. The conversion of the
rotational mechanical energy into
electric energy is not a problem since
it is a problem technologically
resolved several decades ago. Electric
generators are usually produced by the
industries and they are commercially
available, so that it is enough to couple
a gravitational motor to an electric
generator for we obtaining electric
energy. In this case, just a gravitational
motor with the power above
mentioned it would be enough to
supply the need of electric energy of,
for example, at least 20 residences.
Finally, it can substitute the
conventional motors of the same
power, with the great advantage of not
needing of fuel for its operation. What
means that the gravitational motors
can produce energy practically free.
It is easy to see that gravitational
motors of this kind can be designed for
powers needs of just some watts up to
millions of kilowatts.
g
g’= -ng
Rotor
r
r
R
χar(2)= (χar(1))-1
χar(1)= -n = mg(ar)/mi(ar)
g’’=χair(2)g’ = g
g’=χair(1)g






GCC (2)














GCC (1)



g





Fig. 1 – Gravitational Motor - The first Gravity Control Cell
(GCC1) changes the local gravity from g to ngg −=′ , propelling
the left side of the rotor in contrary direction to the motion of the
right side. The second GCC changes the gravity back again to g i.e.,
from ngg −=′ to g , in such a way that the gravitational change
occurs just on the region shown in figure above.
4. The Gravitational Spacecraft

Consider a metallic sphere with
radius in the terrestrial atmosphere.
If the external surface of the sphere is
recovered with a radioactive substance
(for example, containing Americium
241) then the air in the space close to
the surface of the sphere will be
strongly ionized by the radiation
emitted from the radioactive element
and, consequently, the electric
conductivity of the air close to sphere
will become strongly increased.
sr

7
By applying to the sphere an
electric potential of low frequency ,
in order to produce an electric field
starting from the surface of the
sphere, then very close to the surface,
the intensity of the electric field will
be
rmsV
rmsE
srmsrms rVE = and, in agreement with
Eq. (4), the gravitational mass of the
Air in this region will be expressed by
( ) ( ) ( )7144121 024
43
2
0
airi
airs
rmsair
airg mr
V
fc
m
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎟⎟⎠
⎞⎜⎜⎝
⎛+−= ρπ
σμ
Therefore we will have
( )
( )
( )81
44
121
24
43
2
0
0 ⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎟⎟⎠
⎞
⎜⎜⎝
⎛+−==
airs
rmsair
airi
airg
air r
V
fcm
m
ρπ
σμχ
The gravity accelerations acting on the
sphere, due to the rest of the Universe
(See Fig. 2), will be given by

nigg iairi ,...,2,1==′ χ

Note that by varying or the
frequency , we can easily to reduce
and control
rmsV
f
airχ . Consequently, we can
also control the intensities of the
gravity accelerations in order to
produce a controllable gravitational
shielding around the sphere.
ig ′
Thus, the gravitational forces
acting on the sphere, due to the rest of
the Universe, will be given by ( )iairgiggi gMgMF χ=′=
where is the gravitational mass of
the sphere.
gM
The gravitational shielding
around of the sphere reduces both the
gravity accelerations acting on the
sphere, due to the rest of the Universe,
and the gravity acceleration produced
by the gravitational mass of the
own sphere. That is, if inside the
shielding the gravity produced by the
sphere is
gM
2rMGg g−= , then, out of the
shielding it becomes gg airχ=′ .Thus, ( ) ( ) 222 rGmrMGrMGg ggairgair −=−=−=′ χχ ,
where
gairg Mm χ=
Therefore, for the Universe out of the
shielding the gravitational mass of the
sphere is and not . In these
circumstances, the inertial forces
acting on the sphere, in agreement
with the new law for inertia, expressed
by Eq. (5), will be given by
gm gM
( )9igii amF =
Thus, these forces will be almost null
when becomes almost null by
means of the action of the gravitational
shielding. This means that, in these
circumstances, the sphere practically
loses its inertial properties. This effect
leads to a new concept of spacecraft
and aerospatial flight. The spherical
form of the spacecraft is just one form
that the Gravitational Spacecraft can
have, since the gravitational shielding
can also be obtained with other
formats.
gm
An important aspect to be
observed is that it is possible to control
the gravitational mass of the
spacecraft, , simply by
controlling the gravitational mass of a
body inside the spacecraft. For
instance, consider a parallel plate
capacitor inside the spacecraft. The
gravitational mass of the dielectric
between the plates of the capacitor can
be controlled by means of the ELF
electromagnetic field through it. Under
these circumstances, the total
gravitational mass of the spacecraft
will be given by
(spacecrafgM )

8


( ) ( )
( )1000 idielectrici
gspacecrafg
total
spacecrafg
mM
mMM
χ+=
=+=
where is the rest inertial mass of
the spacecraft(without the dielectric)
and is the rest inertial mass of the
dielectric;
0iM
0im
0igdielectric mm=χ , where
is the gravitational mass of the
dielectric. By decreasing the value of
gm
dielectricχ , the gravitational mass of the
spacecraft decreases. It was shown,
that the value of χ can be negative.
Thus, when 00 iidielectric mM−≅χ , the
gravitational mass of the spacecraft
gets very close to zero.
When 00 iidielectric mM−<χ , the gravitational
mass of the spacecraft becomes
negative.
Therefore, for an observer out
of the spacecraft, the gravitational
mass of the spacecraft is
( ) 00 idielectricispacecrafg mMM χ+= , and not
. 00 ii mM +
Another important aspect to be
observed is that we can control the
gravity inside the spacecraft, in order
to produce, for example, a gravity
acceleration equal to the Earth’s
gravity ( )2.81.9 −= smg . This will be
very useful in the case of space flight,
and can be easily obtained by putting
in the ceiling of the spacecraft the
system shown in Fig. 3. This system
has three GCC with nuclei of ionized
air (or air at low pressure). Above
these GCC there is a massive block
with mass . gM
































χair
M’g
r
Mg Erms
g1 = - G M’g / r2
g1’ = χair g1
S
Gravitational Shielding
Fig.2- The gravitational shielding reduces the gravity
accelerations ( g1’) acting on the sphere (due to the rest of the
Universe) and also reduces the gravity acceleration that the sphere
produces upon all the particles of the Universe (g’). For the
Universe, the gravitational mass of the sphere will be mg = χair Mg.
g’ = - χair g = - χair G Mg / r2 =

= - Gmg / r2

mg = χair Mg
g = - G Mg / r2
As we have shown [2], a
gravitational repulsion is established
between the mass and any positive
gravitational mass below the
mentioned system. This means that the
particles in this region will stay
subjected to a gravity acceleration ,
given by
gM
ba
( ) ( ) ( )11ˆ2
0
33 μχχ
r
M
Gga gairMairb −≅≅ rr
If the Air inside the GCCs is
sufficiently ionized, in such way that
, and if ,
, and
then the Eq.8 shows that inside the
GCCs we will have
13 .10 −≅ mSairσ Hzf 1=
3.1 −≅ mkgairρ KVVrms 10≅ cmd 1=
( )
( )
3
24
43
2
0
0
101
44
121 −≅
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎦
⎤
⎢⎢⎣
⎡
−⎟⎟⎠
⎞⎜⎜⎝
⎛+−==
air
rmsair
airi
airg
air d
V
fcm
m
ρπ
σμχ

9
























Fig.3 – If the Air inside the GCC is sufficiently
ionized, in such way that 13 .10 −≅ mSairσ and
if Hzf 1= ; cmd 1= ; 3.1 −≅ mkgairρ and KVVrms 10≅
then Eq. 8 shows that inside the CCGs we will have
310−≅airχ . Therefore, for kgMM ig 100≅≅ and
mro 1≅ the gravity acceleration inside the spacecraft
will be directed from the ceiling to the floor of the
spacecraft and its intensity will be 2.10 −≈ smab .
GCC 1
G CC3
GCC 2
Mg
FM
( ) ( ) μχχ ˆ
2
0
33
r
M
Gga gairMairb −≅≅ rr
ab
airχ
airχ
airχ
μ
Ceiling
Floor
r0
d
Therefore the equation (11) gives

( )1210
2
0
9
r
M
Ga gb +≈
For and (See
Fig.3), the gravity inside the spacecraft
will be directed from the ceiling to the
floor and its intensity will have the
following value
kgMM ig 100≅≅ mr 10 ≅
( )13.10 2−≈ smab
Therefore, an interstellar travel in a
gravitational spacecraft will be
particularly comfortable, since we can
travel during all the time subjected to
the gravity which we are accustomed
to here in the Earth.
We can also use the system
shown in Fig. 3 as a thruster in order
to propel the spacecraft. Note that the
gravitational repulsion that occurs
between the block with mass and
any particle after the GCCs does not
depend on of the place where the
system is working. Thus, this
Gravitational Thruster can propel the
gravitational spacecraft in any
direction. Moreover, it can work in the
terrestrial atmosphere as well as in the
cosmic space. In this case, the energy
that produces the propulsion is
obviously the gravitational energy,
which is always present in any point of
the Universe.
gM
The schematic diagram in Fig. 4
shows in details the operation of the
Gravitational Thruster. A gas of any
type injected into the chamber beyond
the GCCs acquires an acceleration
, as shown in Fig.4, the intensity of
which, as we have seen, is given by
gasa
( ) ( ) ( )142
0
33
r
M
Gga ggasMgasgas χχ −≅=
Thus, if inside of the GCCs,
then the equation above gives
910−≅gasχ
( )1510
2
0
27
r
M
Ga ggas +≅
For kgMM ig 10≅≅ , we have
. With this enormous
acceleration the particles of the gas
reach velocities close to the speed of
the light in just a few nanoseconds.
Thus, if the emission rate of the gas is
mr 10 ≅
217 .106.6 −×≅ smagas
hourlitresskgdtdmgas /4000/10
3 ≅≅ − , then
the trust produced by the gravitational
thruster will be

10
( )16105 N
dt
dm
c
dt
dm
vF gasgasgas ≅≅=



Gas


mg μ

Fm

Gas
GCC
1
Mg

FM
GCC
3
GCC
2 agas
Fig. 4 – Gravitational Thruster – Schematic diagram
showing the operation of the Gravitational Thruster. Note
that in the case of very strong airχ , for
example 910−≅airχ , the gravity accelerations upon the
boxes of the second and third GCCs become very strong.
Obviously, the walls of the mentioned boxes cannot to stand
the enormous pressures. However, it is possible to build a
similar system [2] with 3 or more GCCs, without material
boxes. Consider for example, a surface with several
radioactive sources (Am-241, for example). The alpha
particles emitted from the Am-241 cannot reach besides
10cm of air. Due to the trajectory of the alpha particles, three
or more successive layers of air, with different electrical
conductivities 1σ , 2σ and 3σ , will be established in the
ionized region. It is easy to see that the gravitational
shielding effect produced by these three layers is similar to
the effect produced by the 3 GCCs above.
r0

It is easy to see that the gravitational
thrusters are able to produce strong
trusts (similarly to the produced by the
powerful thrusters of the modern
aircrafts) just by consuming the
injected gas for its operation.
It is important to note that, if
is the thrust produced by the
gravitational thruster then, in
agreement with Eq. (5), the spacecraft
acquires an acceleration ,
expressed by the following equation
F
spacecrafta
( ) ( )
( )17
spacecraftioutspacecraftg
spacecraft M
F
M
F
a χ==
Where outχ , given by Eq. (8), is the
factor of gravitational shielding which
depends on the external medium
where the spacecraft is placed. By
adjusting the shielding for 01.0=outχ
and if then for a thrust
, the acceleration of the
spacecraft will be
KgM spacecraft
410=
NF 510≅
( )18.1000 2−= smaspacecraft
With this acceleration, in just at 1(one)
day, the velocity of the spacecraft will
be close to the speed of light.
However it is easy to see that outχ can
still be much more reduced and,
consequently, the thrust much more
increased so that it is possible to
increase up to 1 million times the
acceleration of the spacecraft.
It is important to note that, the
inertial effects upon the spacecraft will
be reduced by 01.0≅= igout MMχ . Then,
in spite of its effective acceleration to
be , the effects for the crew
of the spacecraft will be equivalents to
an acceleration of only
2.1000 −= sma

1.10 −≈=′ sma
M
M
a
i
g

This is the magnitude of the
acceleration on the passengers in a
contemporary commercial jet.
Then, it is noticed that the
gravitational spacecrafts can be
subjected to enormous accelerations
(or decelerations) without imposing
any harmful impacts whatsoever on
the spacecrafts or its crew.
We can also use the system
shown in Fig. 3, as a lifter, inclusively
within the spacecraft, in order to lift
peoples or things into the spacecraft as
shown in Fig. 5. Just using two GCCs,
the gravitational acceleration produced
below the GCCs will be

11
( ) ( ) ( )19ˆ2022 μχχ rMGga gairMairg −≅=r
Note that, in this case, if airχ is
negative, the acceleration ga
r will have
a direction contrary to the versor μˆ ,
i.e., the body will be attracted in the
direction of the GCCs, as shown in
Fig.5. In practice, this will occur when
the air inside the GCCs is sufficiently
ionized, in such a way that
. Thus, if the internal
thickness of the GCCs is now
13 .10 −≅ mSairσ
mmd 1=
and if ; and
, we will then have
. Therefore, for
Hzf 1= 3.1 −≅ mkgairρ
KVVrms 10≅
510−≅airχ kgMM ig 100≅≅
and, for example, the
gravitational acceleration acting on the
body will be . It is obvious
that this value can be easily increased
or decreased, simply by varying the
voltage . Thus, by means of this
Gravitational Lifter, we can lift or
lower persons or materials with great
versatility of operation.
mr 100 ≅
2.6.0 −≈ smab
rmsV
It was shown [1] that, when the
gravitational mass of a particle is
reduced into the range, to
, it becomes imaginary, i.e.,
its masses (gravitational and inertial)
becomes imaginary. Consequently, the
particle disappears from our ordinary
Universe, i.e., it becomes invisible for
us. This is therefore a manner of to
obtain the transitory invisibility of
persons, animals, spacecraft, etc.
However, the factor
iM1590.+
iM1590.−
( ) ( )imaginaryiimaginaryg MM=χ remains real
because

( )
( )
real
M
M
iM
iM
M
M
i
g
i
g
imaginaryi
imaginaryg ====χ
Thus, if the gravitational mass of
the particle is reduced by means of the
absorption of an amount of
electromagnetic energy U , for
example, then we have
( ) ⎭⎬⎫⎩⎨⎧ ⎥⎦⎤⎢⎣⎡ −+−== 1121 220cmUM
M
i
i
gχ
This shows that the energy U
continues acting on the particle turned
imaginary. In practice this means that
electromagnetic fields act on
imaginary particles. Therefore, the
internal electromagnetic field of a
GCC remains acting upon the particles
inside the GCC even when their
gravitational masses are in the range
iM1590.+ to iM1590.− , turning them
imaginaries. This is very important
because it means that the GCCs of a
gravitational spacecraft remain
working even when the spacecraft
becomes imaginary.
Under these conditions, the
gravity accelerations acting on the
imaginary spacecraft, due to the rest of
the Universe will be, as we have see,
given by
nigg ii ,...,2,1==′ χ
Where ( ) ( )imaginaryiimaginaryg MM=χ and
( ) 2iimaginarygii rGmg −= . Thus, the
gravitational forces acting on the
spacecraft will be given by

( )
( ) ( )( )( ) ( )20.22
2
igigigig
jimaginarygjimaginaryg
iimaginaryggi
rmGMriGmiM
rGmM
gMF
χχ
χ
+=−=
=−=
=′=

Note that these forces are real. By
calling that, the Mach’s principle says
that the inertial effects upon a particle
are consequence of the gravitational
interaction of the particle with the rest

12
of the Universe. Then we can conclude
that the inertial forces acting on the
spacecraft in imaginary state are also
real. Therefore, it can travel in the
imaginary space-time using the
gravitational thrusters.






















Fig.5 – The Gravitational Lifter – If the air inside the
GCCs is sufficiently ionized, in such way that
13 .10 −≅ mSairσ and the internal thickness of the
GCCs is now mmd 1= then, if Hzf 1= ;
3.1 −≅ mkgairρ and KVVrms 10≅ , we have
510−≅airχ . Therefore, for kgMM ig 100≅≅ and
mr 100 ≅ the gravity acceleration acting on the
body will be 2.6.0 −≈ smab .
GCC 1
GCC 2
Mg
( ) ( ) μχχ ˆ
2
22
b
g
airMairb r
M
Gga −≅≅ rr
ab
airχ
airχ
μ
rb
It was also shown [1] that
imaginary particles can have infinity
velocity in the imaginary space-time.
Therefore, this is also the upper limit
of velocity for the gravitational
spacecrafts traveling in the imaginary
space-time. On the other hand, the
travel in the imaginary space-time can
be very safe, because there will not be
any material body in the trajectory of
the spacecraft.
It is easy to show that the
gravitational forces between two thin
layers of air (with masses and
) around the spacecraft , are
expressed by
1gm
2gm
( ) ( )21ˆ
2
212
2112 μχ r
mm
GFF iiair−=−=
rr
Note that these forces can be strongly
increased by increasing the value of
airχ . In these circumstances, the air
around the spacecraft would be
strongly compressed upon the external
surface of the spacecraft creating an
atmosphere around it. This can be
particularly useful in order to
minimize the friction between the
spacecraft and the atmosphere of the
planet in the case of very high speed
movements of the spacecraft. With the
atmosphere around the spacecraft the
friction will occur between the
atmosphere of the spacecraft and the
atmosphere of the planet. In this way,
the friction will be minimum and the
spacecraft could travel at very high
speeds without overheating.
However, in order for this to occur,
it is necessary to put the gravitational
shielding in another position as shown
in Fig.2. Thus, the values of airBχ
and airAχ will be independent (See
Fig.6). Thus, while inside the
gravitational shielding, the value of
airBχ is put close to zero, in order to
strongly reduce the gravitational mass
of the spacecraft (inner part of the
shielding), the value of airAχ must be
reduced to about in order to
strongly increase the gravitational
attraction between the air molecules
around the spacecraft. Thus, by
810−

13
substituting intoEq.21, we
get
810−≅airAχ
( )22ˆ10
2
2116
2112 μr
mm
GFF ii−=−= rr
If, and
then Eq. 22 gives
kgmm airairii
8
2121 10VV
−≅≅=≅ ρρ
mr 310−=
( )2310 42112 NFF −−≅−= rr
These forces are much more intense
than the inter-atomic forces (the forces
that unite the atoms and molecules) the
intensities of which are of the order of
. Consequently, the air
around the spacecraft will be strongly
compressed upon the surface of the
spacecraft and thus will produce a
crust of air which will accompany the
spacecraft during its displacement and
will protect it from the friction with
the atmosphere of the planet.
N81010001 −×−



















Fig. 6 – Artificial atmosphere around the gravitational
spacecraft - while inside the gravitational shielding
the value of airBχ is putted close to zero, in order to
strongly reduces the gravitational mass of the
spacecraft (inner part of the shielding), the value of
airAχ must be reduced for about 810− in order to
strongly increase the gravitational attraction between
the air molecules around the spacecraft.
airBχ
airAχ
rmsE
Atmosphere
of the
Spacecraft
Gravitational Shielding
(GCC)
Gravitational
Spacecraft



5. The Imaginary Space-time

The speed of light in free space
is, as we know, about of 300.000 km/s.
The speeds of the fastest modern
airplanes of the present time do not
reach 2 km/s and the speed of rockets
do not surpass 20 km/s. This shows
how much our aircraft and rockets are
slow when compared with the speed of
light.
The star nearest to the Earth
(excluding the Sun obviously) is the
Alpha of Centaur, which is about of 4
light-years distant from the Earth
(Approximately 37.8 trillions of
kilometers). Traveling at a speed about
100 times greater than the maximum
speed of our faster spacecrafts, we
would take about 600 years to reach
Alpha of Centaur. Then imagine how
many years we would take to leave our
own galaxy. In fact, it is not difficult
to see that our spacecrafts are very
slow, even for travels in our own solar
system.
One of the fundamental
characteristics of the gravitational
spacecraft, as we already saw, is its
capability to acquire enormous
accelerations without submitting the
crew to any discomfort.
Impelled by gravitational
thrusters gravitational spacecrafts can
acquire accelerations until or
more. This means that these
spacecrafts can reach speeds very
close to the speed of light in just a few
seconds. These gigantic accelerations
can be unconceivable for a layman,
however they are common in our
Universe. For example, when we
submit an electron to an electric field
28 .10 −sm

14
of just it acquires an
acceleration , given by
mVolt /1
a
( )( ) 211
31
19
.10
1011.9
/1106.1 −
−
−
≅×
×== smmVC
m
eE
a
e


As we see, this acceleration is about
100 times greater than that acquired by
the gravitational spacecraft previously
mentioned.
By using the gravitational
shieldings it is possible to reduce the
inertial effects upon the spacecraft. As
we have shown, they are reduced by
the factor igout MM=χ . Thus, if the
inertial mass of the spacecraft is
and, by means of the
gravitational shielding effect the
gravitational mass of the spacecraft is
reduced to then , in spite
of the effective acceleration to be
gigantic, for example, , the
effects for the crew of the spacecraft
would be equivalents to an
acceleration of only
kgM i 000.10=
ig MM
810−≈
29 .10 −≈ sma
a′
( )( ) 298 .101010 −− ≈==′ sma
M
M
a
i
g
This acceleration is similar to that
which the passengers of a
contemporary commercial jet are
subjected.
Therefore the crew of the
gravitational spacecraft would be
comfortable while the spacecraft
would reach speeds close to the speed
of light in few seconds. However to
travel at such velocities in the
Universe may note be practical. Take
for example, Alpha of Centaur (4
light-years far from the Earth): a round
trip to it would last about eight years.
Trips beyond that star could take then
several decades, and this obviously is
impracticable. Besides, to travel at
such a speed would be very dangerous,
because a shock with other celestial
bodies would be inevitable. However,
as we showed [1] there is a possibility
of a spacecraft travel quickly far
beyond our galaxy without the risk of
being destroyed by a sudden shock
with some celestial body. The solution
is the gravitational spacecraft travel
through the Imaginary or Complex
Space-time.
It was shown [1] that it is
possible to carry out a transition to the
Imaginary space-time or Imaginary
Universe. It is enough that the body
has its gravitational mass reduced to a
value in the range of
to
iM1590.+
iM1590.− . In these circumstances,
the masses of the body (gravitational
and inertial) become imaginaries and,
so does the body. (Fig.7).
Consequently, the body disappears
from our ordinary space-time and
appears in the imaginary space-time.
In other words, it becomes invisible
for an observer at the real Universe.
Therefore, this is a way to get
temporary invisibility of human
beings, animals, spacecrafts, etc.
Thus, a spacecraft can leave our
Universe and appear in the Imaginary
Universe, where it can travel at any
speed since in the Imaginary Universe
there is no speed limit for the
gravitational spacecraft, as it occurs in
our Universe, where the particles
cannot surpass the light speed. In this
way, as the gravitational spacecraft is
propelled by the gravitational
thrusters, it can attain accelerations up
to , then after one day of trip
with this acceleration, it can
29 .10 −sm

15






transition
( −0.159 > mg > +0.159 )



1 light-year




dAB = 1 light-year





transition
( −0.159 < mg < +0.159 ) mg
Gravitational Spacecraft

Fig. 7 – Travel in the Imaginary Space-time.

ΔtAB =1 second
A
B
ΔtAB =1 year
photon
Vmax = ∞ Vmax = c
reach velocities (about 1
million times the speed of light). With
this velocity, after 1 month of trip the
spacecraft would have traveled
about . In order to have idea of
this distance, it is enough to remind
that the diameter of our Universe
(visible Universe) is of the order
of .
114 .10 −≈ smV
m2110
m2610
Due to the extremely low
density of the imaginary bodies, the
collision between them cannot have
the same consequences of the collision
between the dense real bodies.
Thus for a gravitational
spacecraft in imaginary state the
problem of the collision doesn't exist
in high-speed. Consequently, the
gravitational spacecraft can transit
freely in the imaginary Universe and,
in this way reach easily any point of
our real Universe once they can make
the transition back to our Universe by
only increasing the gravitational mass
of the spacecraft in such way that it
leaves the range of
to
iM1590.+
iM1590.− . Thus the spacecraft can
reappear in our Universe near its
target.
The return trip would be done in
similar way. That is to say, the
spacecraft would transit in the
imaginary Universe back to the
departure place where would reappear
in our Universe and it would make the
approach flight to the wanted point.
Thus, trips through our Universe that
would delay millions of years, at
speeds close to the speed of light,
could be done in just a few months in
the imaginary Universe.
What will an observer see when
in the imaginary space-time? It will
see light, bodies, planets, stars, etc.,
everything formed by imaginary
photons, imaginary atoms, imaginary
protons, imaginary neutrons and
imaginary electrons. That is to say,
the observer will find an Universe
similar to ours, just formed by
particles with imaginary masses. The
term imaginary adopted from the
Mathematics, as we already saw, gives
the false impression that these masses
do not exist. In order to avoid this
misunderstanding we researched the
true nature of that new mass type and
matter.
The existence of imaginary mass
associated to the neutrino is well-
known. Although its imaginary mass is
not physically observable, its square
is. This amount is found
experimentally to be negative.
Recently, it was shown [1] that quanta
of imaginary mass exist associated to
the photons, electrons, neutrons, and