AAWSAP DIRD, Advanced Nuclear Propulsion for Manned Deep Space Missions, March 2010

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To estimate the order of magnitude of what is needed, we consider a spacecraft with a
mass of M0 = 103ton = 109g , to be accelerated by one g ~ 103 cm/s2, with a thrust
T = M0g ~ 1012 dyn. To establish the magnitude and number of fusion explosions needed
to propel the spacecraft to a velocity of v= 100 km/s = 107 cm/s, we use the equation
T= cdm
(22)
dt
where we set c ~ 108 cm/s, equal to the expansion velocity of the fusion bomb plasma.
We thus have
dm
T
-
= -
= 10 4 g/s = 10 kg/s
(23)
dt
C
The propulsion power is given by
P=~ dm =~T
(24)
2 cit
2
which in our example is P = 5 x l0 19 erg/s.
With E = 4 xl019 erg equivalent to the explosive energy of one kiloton of TNT, Pis
equivalent to about one nuclear kiloton bomb per second.
From the rocket equation
(25)
where Mo is the initial and M1 the final mass, and setting M1 = Mo - !::,M, where
t,..M <<Mo is the mass of all used up bombs, one has
(26)
Here v is the velocity reached by the spacecraft after having used up all the bombs of
mass~. If one bomb explodes per second, its mass according to equation (23) is m o
= 104 g.
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