AAWSAP DIRD, Aneutronic Fusion Propulsion I, November 2010

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UNCLASSIFIED//POlt Offl@IAL WS& &NkY
C
•
-I ( a t')
C
-I ( a D
)
t = - sinb
-
= - cosh
-? + 1
(A.8)
a
c
a
c­
4
I
I
f
I
I
I
0. 1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Y/c
Figure 12. Time Dilation at Relativistic Velocities.
The Tsiolkovsky rocket equation is important as it relates the change in the mass of a
rocket due to fuel consumption in order to generate a desired LlV, or velocity change:
I:). V =l
Sf' 1n(m;,,;1;a1)
(A.9)
m final
For a relativistic rocket, velocity is affected by time dilation resulting in the relativistic
rocket equation:
~ V =c tanh[/•P 1n (m;,,;,;a1/
. )J
(A.10)
C
/
m f111e1 l
Through any propulsion method, kinetic energy must be added to the rocket through
reaction mass (propellant) in order to accelerate the rocket to its final velocity. Since
mass changes with velocity, we will need to use Einstein's equation to determine the
kinetic energy required to accelerate the rocket to a final velocity based on its rest
mass, mo.
(A.11)
KE= m c2 - m c2 = m y c2 - m c2
(A.12)
0
0
0
(A.13)
UNCLASSIFIED/fF&A &FFI&I:.l.k W&li &NkY
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