DOW-UAP-D135, AAWSAP DIRD, Antigravity for Aerospace Applications, March 2010
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This document is a Defense Intelligence Reference Document (DIRD), a technical reference format used by the Defense Intelligence Agency (DIA) to capture baseline knowledge on a specific topic for later analytic use. DIRDs are best understood as reference and synthesis products rather than as original research. It is one of 38 DIRDs produced under the Advanced Aerospace Weapon System Applications Program (AAWSAP) between 2009 and 2011. Because AAWSAP’s scope permitted a broad range of supporting topics, not every DIRD in the series directly concerns aerospace systems or future threat assessment. The following summary reflects the DIRD’s scope and framing at the time of writing and should not be read as implying current validation of the concepts discussed. This DIRD surveys a range of proposed “antigravity,” or gravitational control, concepts for aerospace applications, drawing mainly from Newtonian gravity, general relativity, cosmology, and quantum field theory to hypothesize that gravity might someday be reduced, counteracted, or redirected as a means of propulsion. The report reviews mechanisms including ultra-dense matter, gravitomagnetic effects, relativistic moving masses, negative energy, dark or vacuum energy, and quantum vacuum or dispersion-force approaches, while presenting some of these ideas as theoretically permissible under extreme, idealized conditions within established physics. However, it notes that any practical implementation faces currently insurmountable engineering barriers, including astronomical energy requirements, currently unproven exotic matter conditions, kilometer-scale or otherwise unbuildable apparatuses, and highly immature experimental foundations. Although the report draws on broadly accepted theoretical concepts, its implication that those concepts might eventually yield viable “antigravity” propulsion systems deviates significantly from mainstream physics consensus.
[번역 실패: TooManyRequests] UNCLASSIFIED//1'8R: 81'fl@liltL I.I§& 8Ptb>f Defense Intelligence Reference Document Acquisition Threat Support 30 March 2010 !COD: 1 December 2009 DIA-08-1003-018 Antigravity for Aerospace Applications UNCLASSIFIED//FOR OFFl&IAL I.IS! 8HL I UNCLASSIFIED//F&R: GFFl61tl.L W&lii QtlL¥ Antigravity for Aerospace Applications Prepared by: Acquisition Support Division (DW0-3) Defense Warning Office Directorate for Analysis Defense Intelligence Agency Author: AAP Person 58 Administrative Note COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized. This product is one in a series of advanced technology reports produced in FY 2009 under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace Weapon System Applications (AAWSA) Program. Comments or questions pertaining to I this document should be addressed tolAAP Person 1 AAWSA Program Manager, Defense Intelligence Agency, ATTN: CLAR/DWO-3, Bldg 6000, Washington, DC 20340-5100. ii UNCLASSIFIED/f,J;QA GFJ;IGlifil W&& 8HLV UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ Contents Foreword.................................................................................................................v I. Introduction ....................................................................................................... 1 II. Concepts for Antigravity Within Newtonian Physics .......................................... 2 Negating Newtonian Gravity .............................................................................. 2 Energy Estimate for Newtonian Levitation ......................................................... 3 III. Concepts for Antigravity Within General Relativity .......................................... 4 Antigravity via Gravitomagnetic Forces.............................................................. 4 Historical Foundations ................................................................................... 4 Forward's Dipole Gravitational Field Generator.............................................. 4 Felber's Relativistic Antigravity Effect................................................................ 7 Negative Energy-Induced Antigravity ................................................................ 9 Examples of Exotic or "Negative" Energy Found in Nature ........................... 10 Toy Model Estimate for Negative Energy-Induced Antigravity...................... 10 Cosmological Antigravity.................................................................................. 13 Pressure as a Source of Gravity.................................................................... 13 Vacuum Energy of Einstein's Cosmological Constant.................................... 13 Dark Energy ................................................................................................. 15 Antigravity Propulsion Application of Dark/Vacuum Energy ........................ 17 IV. Quantum Antigravity Propulsion Concepts ..................................................... 17 Antigravity via Quantum Vacuum Zero-Point Fluctuation Force ....................... 19 Antigravity via Nonretarded Quantum Interatomic Dispersion Force ............... 21 V. Conclusion: The Way Forward .......................................................................... 24 Appendix A ........................................................................................................... 29 Static Radial Electric & Magnetic Fields ............................................................ 29 Squeezed Quantum Vacuum ............................................................................. 29 Gravitationally Squeezed Electromagnetic Zero-Point Fluctuations.................. 30 iii UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ Quantum Vacuum Field Stress: Negative Energy from the Casimir Effect ......... 31 Dynamical Casimir Effect: Moving Mirrors ........................................................ 32 References ........................................................................................................... 34 Figures Figure 1. Dipole Electric Field Generator ................................................................ 5 Figure 2. Diople Gravitational Field Generator........................................................ 6 Figure 3. Dipole Gravitational Field Generator: Inside-Out Whirling Dense [번역 실패: TooManyRequests] Matter Torus............................................................................................ 7 Figure 4. Illustration of the Casimir Effect........................................................... 31 Figure 5. Negative Energy Flux {Gold) Emanating From a Moving Mirror ............. 33 iv UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ Antigravity for Aerospace Applications Foreword Antigravity effects can be implemented by manipulating spacetime. This paper reviews several different theoretical approaches for exploring the possibility of controlling gravity by generating forces that counteract, or otherwise modify, gravity for the purpose of aerospace propulsion. Einstein's General Theory of Relativity is the theoretical framework guiding this study. The paper also reviews other antigravity approaches via the interaction of quantum theory with gravitation. And it explores the question of which method or technique is best suited for aerospace applications and evaluates the make-or-break issues that limit them. V UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ I. Introduction Gravity is the bane of aerospace transportation. The force of the Earth's gravitational field acts to pull all objects, whether in motion or at rest, downward towards the Earth's surface. Because aerospace transportation involves the motion of vehicles through the atmosphere and/or into space, propulsion engineers are always faced with the requirement that aerospace vehicles will have to carry enough propellant and associated tankage in order to provide enough propulsive thrust to overcome the downward pull of gravity and achieve rectilinear motion. Energy has to be expended by a propulsion system to overcome the force of gravity in addition to providing for rectilinear motion, and the majority of propulsive energy is dedicated to overcome gravity. The aerospace propulsion engineer is faced with two choices for the control of gravity in this regard: passive control and active control. Modern aerospace propulsion technology, which is based on accumulated scientific knowledge since recorded history, can only achieve the passive control of gravity whereby a given propulsion device must develop a thrust that will passively counteract the Earth's gravitational pull, lift a vehicle off the surface, and propel it through the air or into space. Newton's laws of motion and gravity require that the fuel fraction of any aerospace vehicle can never be less than that given by a simple function of the ratio of the vehicle's maximum speed to the speed of its rocket plume, jet, fan, or propeller wake. For example, this limit implies that a single-stage rocket that accelerates to escape velocity must be composed of more than 93 percent fuel. That is because a rocket must accelerate its working fluid from rest (relative to the rocket) up to its exhaust speed. Thus, exhaust speeds for aircraft and chemical rockets are limited by material science, chemical reaction rates, and engineering factors to only a few thousand meters per second. To date, there is no technology that can achieve the active control of gravity. If one could eliminate or otherwise control the Earth's gravity field, then one has the ability to dramatically reduce the amount of propellant, its tankage, and the overall structural size and mass of an aircraft or rocket because there will no longer be any need for these to overcome the pull of Earth's gravity while transporting a payload across the globe or into space. Instead, aerospace vehicles will only need to have the propellant mass and infrastructure necessary to change their kinetic energy from rest to a final velocity necessary to achieve atmospheric flight or space orbit. The Earth's gravitational well will no longer have any impact on aircraft, launch vehicle, or spaceflight dynamics if one were to achieve active gravity control. Aerospace vehicles would merely "levitate" in air and their propulsion systems would be optimized for change-in-velocity missions. However, it is possible to envision a form of active gravity control propulsion that would not require a change in kinetic energy. One of the primary concepts for the goal of affecting gravity is "antigravity," which is a colloquial expression that specifically means the negation or repulsion of the force of gravity. A more general term that encompasses this notion and other possibilities is "gravity control." [번역 실패: TooManyRequests] If antigravity exists, it can be exploited to counteract or nullify the gravitational pull, or attraction, of a planetary (or stellar) body that acts upon a much smaller body. Einstein's General Theory of Relativity gives a prescription for a variety of different antigravity generators. Even Newton's law of gravity offers several different classical prescriptions. Newton's law of gravity can be used to simply nullify the gravity field of one body acting on another body by using a clever arrangement of masses. The 1 UNCLASSIFIED//FOA OFFI€1.t.k YS& 0,.k\f UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥ theoretical possibility of antigravity also appears in quantum gravity theories, cosmological vacuum or dark energy, and quantum field theory. This report reviews all of these topics. The report will also review the topics of gravity control that include the production of antigravity (self-lifting) forces induced by quantum vacuum zero-point energy and by nonretarded quantum interatomic dispersion forces in a curved spacetime (that is, in a background gravitational field). The reader should bear in mind that many of these concepts are nowhere near having any form of practicable engineering implementation. However, the report will provide theoretical estimates to guide the way toward technologica l implementation of antigravity. II. Concepts for Antigravity Within Newtonian Physics The basic form of Newton's law of gravity is given by the standard expression for the gravitational force {Fgrav) that mutually acts between two masses (Reference 1): (1) where the negative sign indicates that Fgrn" is a (mutual) force of attraction, G is Newton's universal gravitation constant (6.673 x 10-11 Nm2/kg2), m1 and m2 are two interacting masses, and r is the radial distance between the two masses (note: MKS units are used throughout). Observe in Equation (1) that the force of gravity acting on a small test mass becomes stronger when the other (gravitating) mass is larger in magnitude or when the distance between them is very small, or both. Also recall that Equation (1) and Newton's second law of motion (F = ma) to define the magnitude of the gravitational acceleration a8 that acts on a small test mass m due to a larger (gravitating) mass M (Reference 1): GM ag = - r-? (2) If Earth is chosen to be the larger gravitating mass so that M = M@( 5.972 x 1024 kg), then according to Equation (2) a small test mass m placed near the Earth's surface, whereby r~ R@ (6.378 x 106 m), will experience a downward gravitational acceleration of ag =g = 9.81 m/s2. NEGATING NEWTONIAN GRAVITY It is possible to design an antigravity machine that can nullify Earth's gravity field using Newton's law of gravity. One way to use Equation (1) to nullify the Earth's gravitational pull at a particular location would be to locate another planet of equal mass above that location (Reference 2,3). The forces from the two Earth masses will cancel each other out over a broad region between them . Everything within this broad region will be in free fall. However, this is not a practical solution for aerospace flight since there is no way to manipulate and control another planetary sized body. Along similar lines, Forward (Reference 2,3) suggested to consider using a ball of ~ ultradense compact matter, corresponding to dwarf star or neutron star matter ( 1011 - 1018 kg/m3), having a diameter of 32 cm and a mass of 4 million metric tons. This ultradense ball will have a surface gravitational (attractive) force of 1-g. This small 2 UNCLASSIFIED/ /FOA OFFI&il.t.k Y&li 8,.LY UNCLASSIFIED/fFOA OFFIEIAL: U&i QPIL:¥ ultradense ball could be placed near the surface of the Earth and its 1-g gravity field will cancel the Earth's 1-g gravity field. All test objects placed in the broad region between the small ultradense ball and the Earth will thus be in free fall. Another option Forward (Reference 2-5) suggested would be to shape the compact ultradense matter into a disk that is 45 cm in diameter and 10 cm thick, and having the same mass and density as the small ultra dense ball. Its gravitational acceleration is a g = 4Gp,, where p is the mass density of the disk and t is its thickness. In this case, the disk will have a force of gravitational attraction that is the same on both sides, and it will be uniform near the center of the disk where the strength of the gravitational force will be 1-g. If this disk were to be placed very close above the Earth's surface, then there will be a [번역 실패: TooManyRequests] gravitational force of 2-g above the disk (= 1-g due to the Earth's gravity field plus 1-g due to the top-side gravity field of the disk) while underneath the disk near its center there will be a gravity-free (or free fall) region because the Earth's gravity field underneath is canceled by the gravity field of the disk's bottom-side. While these are interesti ng antigravity machines, they are unfortunately not feasible from an engineering standpoint since one does not yet have the technology or means to create and handle ultradense compact matter. ENERGY ESTIMATE FOR NEWTONIAN LEVITATION An ideal propulsion breakthrough could take the form of the antigravity-based levitation of an aerospace vehicle within the Earth's atmosphere. Rockets like the Air Force DC-XA can hover above the ground for a time that is limited by the amount of rocket fuel available (Reference 6). But an ideal antigravity propulsion device should allow for the indefinite levitation of a vehicle above the Earth's surface. It is illustrative to estimate the energy required to levitate a 1-kg test mass above the Earth's surface. This will help quantify a potentially key engineering parameter for such a levitation system . A generic estimate can be found by considering the amount of energy per unit mass required to nullify the (magnitude) of the Earth's gravitational potential energy for a E1ev test mass m hovering at height It above the Earth's surface: E =GMffl m (J / ko) (3) lcv h b Equation (3) can also be derived by calculating how much energy is required to completely remove a test mass from the Ea
원문 (English) 펼치기
UNCLASSIFIED//1'8R: 81'fl@liltL I.I§& 8Ptb>f
Defense
Intelligence
Reference
Document
Acquisition Threat Support
30 March 2010
!COD: 1 December 2009
DIA-08-1003-018
Antigravity for Aerospace
Applications
UNCLASSIFIED//FOR OFFl&IAL I.IS! 8HL I
UNCLASSIFIED//F&R: GFFl61tl.L W&lii QtlL¥
Antigravity for Aerospace Applications
Prepared by:
Acquisition Support Division (DW0-3)
Defense Warning Office
Directorate for Analysis
Defense Intelligence Agency
Author:
AAP Person 58
Administrative Note
COPYRIGHT WARNING: Further dissemination of the photographs in this publication is not authorized.
This product is one in a series of advanced technology reports produced in FY 2009
under the Defense Intelligence Agency, Defense Warning Office's Advanced Aerospace
Weapon System Applications (AAWSA) Program. Comments or questions pertaining to
I
this document should be addressed tolAAP Person 1 AAWSA Program
Manager, Defense Intelligence Agency, ATTN: CLAR/DWO-3, Bldg 6000, Washington,
DC 20340-5100.
ii
UNCLASSIFIED/f,J;QA GFJ;IGlifil W&& 8HLV
UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥
Contents
Foreword.................................................................................................................v
I. Introduction ....................................................................................................... 1
II. Concepts for Antigravity Within Newtonian Physics .......................................... 2
Negating Newtonian Gravity .............................................................................. 2
Energy Estimate for Newtonian Levitation ......................................................... 3
III. Concepts for Antigravity Within General Relativity .......................................... 4
Antigravity via Gravitomagnetic Forces.............................................................. 4
Historical Foundations ................................................................................... 4
Forward's Dipole Gravitational Field Generator.............................................. 4
Felber's Relativistic Antigravity Effect................................................................ 7
Negative Energy-Induced Antigravity ................................................................ 9
Examples of Exotic or "Negative" Energy Found in Nature ........................... 10
Toy Model Estimate for Negative Energy-Induced Antigravity...................... 10
Cosmological Antigravity.................................................................................. 13
Pressure as a Source of Gravity.................................................................... 13
Vacuum Energy of Einstein's Cosmological Constant.................................... 13
Dark Energy ................................................................................................. 15
Antigravity Propulsion Application of Dark/Vacuum Energy ........................ 17
IV. Quantum Antigravity Propulsion Concepts ..................................................... 17
Antigravity via Quantum Vacuum Zero-Point Fluctuation Force ....................... 19
Antigravity via Nonretarded Quantum Interatomic Dispersion Force ............... 21
V. Conclusion: The Way Forward .......................................................................... 24
Appendix A ........................................................................................................... 29
Static Radial Electric & Magnetic Fields ............................................................ 29
Squeezed Quantum Vacuum ............................................................................. 29
Gravitationally Squeezed Electromagnetic Zero-Point Fluctuations.................. 30
iii
UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f
UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥
Quantum Vacuum Field Stress: Negative Energy from the Casimir Effect ......... 31
Dynamical Casimir Effect: Moving Mirrors ........................................................ 32
References ........................................................................................................... 34
Figures
Figure 1. Dipole Electric Field Generator ................................................................ 5
Figure 2. Diople Gravitational Field Generator........................................................ 6
Figure 3. Dipole Gravitational Field Generator: Inside-Out Whirling Dense
Matter Torus............................................................................................ 7
Figure 4. Illustration of the Casimir Effect........................................................... 31
Figure 5. Negative Energy Flux {Gold) Emanating From a Moving Mirror ............. 33
iv
UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f
UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥
Antigravity for Aerospace Applications
Foreword
Antigravity effects can be implemented by manipulating spacetime. This
paper reviews several different theoretical approaches for exploring the
possibility of controlling gravity by generating forces that counteract, or
otherwise modify, gravity for the purpose of aerospace propulsion. Einstein's
General Theory of Relativity is the theoretical framework guiding this study.
The paper also reviews other antigravity approaches via the interaction of
quantum theory with gravitation. And it explores the question of which
method or technique is best suited for aerospace applications and evaluates
the make-or-break issues that limit them.
V
UNCLASSIFIED//FOA OFFI&IAk Yi& 8,.k\f
UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥
I. Introduction
Gravity is the bane of aerospace transportation. The force of the Earth's gravitational
field acts to pull all objects, whether in motion or at rest, downward towards the Earth's
surface. Because aerospace transportation involves the motion of vehicles through the
atmosphere and/or into space, propulsion engineers are always faced with the
requirement that aerospace vehicles will have to carry enough propellant and
associated tankage in order to provide enough propulsive thrust to overcome the
downward pull of gravity and achieve rectilinear motion. Energy has to be expended by
a propulsion system to overcome the force of gravity in addition to providing for
rectilinear motion, and the majority of propulsive energy is dedicated to overcome
gravity. The aerospace propulsion engineer is faced with two choices for the control of
gravity in this regard: passive control and active control. Modern aerospace propulsion
technology, which is based on accumulated scientific knowledge since recorded history,
can only achieve the passive control of gravity whereby a given propulsion device must
develop a thrust that will passively counteract the Earth's gravitational pull, lift a
vehicle off the surface, and propel it through the air or into space. Newton's laws of
motion and gravity require that the fuel fraction of any aerospace vehicle can never be
less than that given by a simple function of the ratio of the vehicle's maximum speed to
the speed of its rocket plume, jet, fan, or propeller wake. For example, this limit implies
that a single-stage rocket that accelerates to escape velocity must be composed of
more than 93 percent fuel. That is because a rocket must accelerate its working fluid
from rest (relative to the rocket) up to its exhaust speed. Thus, exhaust speeds for
aircraft and chemical rockets are limited by material science, chemical reaction rates,
and engineering factors to only a few thousand meters per second.
To date, there is no technology that can achieve the active control of gravity. If one
could eliminate or otherwise control the Earth's gravity field, then one has the ability to
dramatically reduce the amount of propellant, its tankage, and the overall structural
size and mass of an aircraft or rocket because there will no longer be any need for
these to overcome the pull of Earth's gravity while transporting a payload across the
globe or into space. Instead, aerospace vehicles will only need to have the propellant
mass and infrastructure necessary to change their kinetic energy from rest to a final
velocity necessary to achieve atmospheric flight or space orbit. The Earth's gravitational
well will no longer have any impact on aircraft, launch vehicle, or spaceflight dynamics
if one were to achieve active gravity control. Aerospace vehicles would merely "levitate"
in air and their propulsion systems would be optimized for change-in-velocity missions.
However, it is possible to envision a form of active gravity control propulsion that would
not require a change in kinetic energy.
One of the primary concepts for the goal of affecting gravity is "antigravity," which is a
colloquial expression that specifically means the negation or repulsion of the force of
gravity. A more general term that encompasses this notion and other possibilities is
"gravity control."
If antigravity exists, it can be exploited to counteract or nullify the gravitational pull, or
attraction, of a planetary (or stellar) body that acts upon a much smaller body.
Einstein's General Theory of Relativity gives a prescription for a variety of different
antigravity generators. Even Newton's law of gravity offers several different classical
prescriptions. Newton's law of gravity can be used to simply nullify the gravity field of
one body acting on another body by using a clever arrangement of masses. The
1
UNCLASSIFIED//FOA OFFI€1.t.k YS& 0,.k\f
UNCLASSIFIED/fFOA OFFIEIA~ W&li QPI~¥
theoretical possibility of antigravity also appears in quantum gravity theories,
cosmological vacuum or dark energy, and quantum field theory. This report reviews all
of these topics. The report will also review the topics of gravity control that include the
production of antigravity (self-lifting) forces induced by quantum vacuum zero-point
energy and by nonretarded quantum interatomic dispersion forces in a curved
spacetime (that is, in a background gravitational field). The reader should bear in mind
that many of these concepts are nowhere near having any form of practicable
engineering implementation. However, the report will provide theoretical estimates to
guide the way toward technologica l implementation of antigravity.
II. Concepts for Antigravity Within Newtonian Physics
The basic form of Newton's law of gravity is given by the standard expression for the
gravitational force {Fgrav) that mutually acts between two masses (Reference 1):
(1)
where the negative sign indicates that Fgrn" is a (mutual) force of attraction, G is
Newton's universal gravitation constant (6.673 x 10-11 Nm2/kg2), m1 and m2 are two
interacting masses, and r is the radial distance between the two masses (note: MKS
units are used throughout). Observe in Equation (1) that the force of gravity acting on
a small test mass becomes stronger when the other (gravitating) mass is larger in
magnitude or when the distance between them is very small, or both. Also recall that
Equation (1) and Newton's second law of motion (F = ma) to define the magnitude of the
gravitational acceleration a8 that acts on a small test mass m due to a larger
(gravitating) mass M (Reference 1):
GM
ag = - r-? (2)
If Earth is chosen to be the larger gravitating mass so that M = M@( 5.972 x 1024 kg),
then according to Equation (2) a small test mass m placed near the Earth's surface,
whereby r~ R@ (6.378 x 106 m), will experience a downward gravitational acceleration
of
ag
=g = 9.81 m/s2.
NEGATING NEWTONIAN GRAVITY
It is possible to design an antigravity machine that can nullify Earth's gravity field using
Newton's law of gravity. One way to use Equation (1) to nullify the Earth's gravitational
pull at a particular location would be to locate another planet of equal mass above that
location (Reference 2,3). The forces from the two Earth masses will cancel each other
out over a broad region between them . Everything within this broad region will be in
free fall. However, this is not a practical solution for aerospace flight since there is no
way to manipulate and control another planetary sized body.
Along similar lines, Forward (Reference 2,3) suggested to consider using a ball of
~
ultradense compact matter, corresponding to dwarf star or neutron star matter ( 1011
- 1018 kg/m3), having a diameter of 32 cm and a mass of 4 million metric tons. This
ultradense ball will have a surface gravitational (attractive) force of 1-g. This small
2
UNCLASSIFIED/ /FOA OFFI&il.t.k Y&li 8,.LY
UNCLASSIFIED/fFOA OFFIEIAL: U&i QPIL:¥
ultradense ball could be placed near the surface of the Earth and its 1-g gravity field will
cancel the Earth's 1-g gravity field. All test objects placed in the broad region between
the small ultradense ball and the Earth will thus be in free fall. Another option Forward
(Reference 2-5) suggested would be to shape the compact ultradense matter into a disk
that is 45 cm in diameter and 10 cm thick, and having the same mass and density as
the small ultra dense ball. Its gravitational acceleration is a g = 4Gp,, where p is the mass
density of the disk and t is its thickness. In this case, the disk will have a force of
gravitational attraction that is the same on both sides, and it will be uniform near the
center of the disk where the strength of the gravitational force will be 1-g. If this disk
were to be placed very close above the Earth's surface, then there will be a
gravitational force of 2-g above the disk (= 1-g due to the Earth's gravity field plus 1-g
due to the top-side gravity field of the disk) while underneath the disk near its center
there will be a gravity-free (or free fall) region because the Earth's gravity field
underneath is canceled by the gravity field of the disk's bottom-side. While these are
interesti ng antigravity machines, they are unfortunately not feasible from an
engineering standpoint since one does not yet have the technology or means to create
and handle ultradense compact matter.
ENERGY ESTIMATE FOR NEWTONIAN LEVITATION
An ideal propulsion breakthrough could take the form of the antigravity-based levitation
of an aerospace vehicle within the Earth's atmosphere. Rockets like the Air Force DC-XA
can hover above the ground for a time that is limited by the amount of rocket fuel
available (Reference 6). But an ideal antigravity propulsion device should allow for the
indefinite levitation of a vehicle above the Earth's surface. It is illustrative to estimate
the energy required to levitate a 1-kg test mass above the Earth's surface. This will
help quantify a potentially key engineering parameter for such a levitation system . A
generic estimate can be found by considering the amount of energy per unit mass
required to nullify the (magnitude) of the Earth's gravitational potential energy for a
E1ev
test mass m hovering at height It above the Earth's surface:
E =GMffl m (J / ko)
(3)
lcv h b
Equation (3) can also be derived by calculating how much energy is required to
completely remove a test mass from the Ea