FIRST STEPS TOWARD SPACE - Smithsonian Institution Libraries

NUMBER 10 27
III
Let us consider what would be the required energies if we wanted, by this method,
to transport a body from the earth to the moon and back.
Let us consider that the operation will take place in three phases:
1°) The body is accelerated until it reaches the critical velocity of liberation
2°) The motor is stopped, and the body keeps moving due to its acquired velocity
3°) At the desired point, the body is turned upside-down and the motor that has
been re-started diminishes the velocity until it becomes zero at the surface of
the moon.
First Phase
We apply to the body a force
F = ^P, therefore A = {fag
which seems acceptable assuming that the vehicle would carry live beings.
The critical distance is then
v — 2JL.p
x - TT**
corresponding to an altitude of 5,780,000 m above the surface.
The velocity at that instant would be
V = 8180 m/sec
The time necessary to reach that point would be approximately
Second Phase
t — 24 min 9 sec
The body continues on its path due to its inertia; it is constantly attracted by the
opposite gravitational forces of the earth and its satellite.
Let P be the weight of the body at the earth's surface, Pt its weight at the moon's
surface and p the radius of the moon, D = x + y the distance between the two
planets; the calculation gives
v= 12 (g— + 0.165-*- + 0.82 X 10 6 j
At the point where the respective gravitational forces of the earth and moon cancel
each other, the velocity would be
v = 2030 m/sec
It is the lowest velocity.
At the moon's surface it would become approximately
v = 3060 m/sec