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This Defense Intelligence Reference Document, dated 1 November 2010, was produced by the Defense Intelligence Agency under its Advanced Aerospace Weapon System Applications (AAWSA) Program. It surveys propulsion technologies that include chemical, ion, and nuclear fission rockets, fusion schemes, aneutronic fusion, and antimatter propulsion. It also covers radiation shielding and speculates on research needs over the next 30 years for missions from low Earth orbit to Mars, Jupiter, Saturn, and Alpha Centauri. The document concludes that aneutronic fusion promises to be an important mechanism for future space propulsion.
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Appendix A: Relativistic Rockets
Since the application of a constant acceleration for a long period of time can lead to
very high velocities, these spacecraft may reach relativistic velocities where V > 0.5 c
(speed of light). At these velocities, time dilation and Lorentz contraction can be
significant. 22 Special Relativity can be used to compute these effects based on the
Lorentz factor, v, as shown below:
(A.2)
Specific impulse for relativistic rockets is usually expressed in dimensionless form:
l (" )
'I' _ ,•1/Jarn/
--r --
c C
Treating Earth as a nonaccelerating reference frame, time intervals measured on a
rocket traveling at a velocity with respect to Earth will be "dilated" according to the
following equation:
(A.3)
(A.4)
Time intervals measured by the crew on the rocket will be longer than the interval
measured on Earth. The ratio of time measured on the rocket to time measured on
earth follows the graph in Figure 12. When a spacecraft reaches 86% of the speed of
light, their "clock" will run at half the speed of a clock located on earth.
For a constant acceleration, equations for rocket performance can be written in terms of
the following variables:
t = time measured on the rocket
t' = time measured in the rest mass frame (Earth)
D = distance traveled
a = acceleration
C = speed of light
Vtinal = final rocket velocity at rocket time t'
t'=~snm('~
1
)= (~r +~ (A.5)
D = ,: [ cosh( (~/ )- Il= ,: [ I + ( a/ r-I] (A.6)
(A.7)
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