FIRST STEPS TOWARD SPACE - Smithsonian Institution Libraries

NUMBER 10 31
bring us far away from the conditions of realization which were studied previously
and which were already quite extreme.
If we use the formula representing the law of motion of a body acted on by a
constant force due to the earth and if we assume that until we have reached the maximum
velocity between earth and moon, the acceleration used is equal to 1 K0 g>
then the other maneuvres will be done with an acceleration equal to gravity. The
moon's influence can be neglected, it being so small. It is found that the vehicle has
to be reversed at a distance from the center of the earth equal to 29.5 times the earth's
radius.
The speed at this instant of time would be 61,700 m/sec, then the reversed vehicle
would be slowed down by a force equal to its weight on the earth.
The time used to reach the moon would be
t = 3 hr 5 min
But in this new case, the work to be furnished, using the assumption of a 1000 kg
vehicle of which 300 kg are consumable, would reach 67.2 X 10 6 cal/kg of fuel, i.e.,
131 times more than in the first case.
Dynamite would be 47,300 times too weak, but radium would still be 433 times
too powerful.
As to the necessary power, it would be
857 X 10 10
24,000 X 75
= 4.76 X 10 6 HP
If we now assume that this method of constant propulsion is used for voyages to
the closest planets and investigate what the times and velocities would be, we find for
the maximum velocity:
and the corresponding times:
For Venus 643 km/sec
For Mars 883 km/sec
For Venus 35 hr 4 min
For Mars 49 hr 20 min
VI
The maximum velocities we have just considered are evidently fantastic. However,
there exists at least one celestial body which reaches such velocities: Halley's comet.
Only the forces and energies which seem to be contained by molecules could
produce concentrations of power and work similar to those we just considered.
If we suppose for a moment that we have available 400 kg of radium in our 1000
kg vehicle and that we knew how to extract from it the energy within a suitable time,
we should see that these 400 kg of radium would be more than enough to reach
Venus and come back (with a constant acceleration), so that such a formidable
reservoir would be just enough for man to visit his closest planets.