FIRST STEPS TOWARD SPACE - Smithsonian Institution Libraries

NUMBER 10 29
= 2100 sec, the rate will have to be
and the fluid's expulsion velocity
300 = 0.143 kg/sec
2100
v = 65,300 m/sec
Therefore, by providing per kilogram of fuel
T = 217.2 X 10 6 kgm or 512 X 10 3 cal
one sees that the mixture H 2 + O would contain 133 times too little energy and the
most powerful explosives 360 times too little.
On the other hand, 1 kg of radium would contain 5.670 times too much]
The power of the motor necessary for our 1000 kg vehicle would be
300 X 217.2 X 10 6
= 414,000 HP
2100 X 75
We could also see that the efficiency of the jet engine is in our particular case quite
bad. Since to remove a mass of 1 kg from the earth to °o, we have to apply to it
6,371,103 kgm and we have spent 217.2 X 10 6 , so that the efficiency is
p = 0.0293
Moreover, to give a gas an ejection speed of 65,300 m/sec in vacuum, we would
have to reach the fantastic temperature of 2.525 X 10 6 degrees.
In air, it would be even worse, since added to this temperature one would need a
pressure of about the same magnitude.
IV
As an indication, we could assume the body moving to infinity, and also that we
have kept the motor working even after the critical speed is reached, so that it eventually
acquires and conserves a speed near to 10 km/sec. The times necessary to reach
the closest planets as they attain their conjunction with the Earth are respectively:
For Venus 47 days 20 hr
For Mars 90 days 15 hr
These figures are merely mentioned for curiosity and we must also notice that the
amount of work to cover this distance would not be much larger than the minimum
necessary to remove the body from the earth. In fact, once the vehicle has reached a
sufficient distance, it would keep on going due to its inertia without being slowed
down by the earth's attraction which has become quite weak.
In other words, the difficulty would be to overcome the earth's attraction; but if
some day this difficulty would be overcome, it would hardly be more difficult to
reach a very distant planet than a close one. Subject, of course, to a cramped and
hermetically closed vehicle being inhabitable for a sufficient amount of time and to
another difficulty that we will consider later on.