In the novel The Moon is a Harsh Mistress by Robert Heinlein, colonists on the M
ID: 1272523 • Letter: I
Question
In the novel The Moon is a Harsh Mistress by Robert Heinlein, colonists on the Moon wage war on the Earth by launching rocks towards the earth. Because the Moon is gravitationally "uphill" relative to the earth, this strategy works better for Moon-dwellers than for Earth-dwellers. Imagine a straight line connecting the center of the moon with the center of the earth. An object moving along this line would feel two main gravitational forces: A force pulling it towards the center of the earth, and a force pulling it towards the center of the moon. Find the distance along this line, measured from the center of the Moon, such that the net force is zero. The moon-dwellers launch a rock from the surface of the moon with just as much speed as is necessary to reach this point. Find this speed. (Use conservation of energy, taking into account gravitational potential energy due to both the moon and the earth.) Suppose that a rock is launched from the surface of the moon with a speed slightly greater than that given in (2). What will be the speed of the rock when it reaches the earth?Explanation / Answer
so at that point
Fmoon = Fearth
G mmoon/x^2 = G mearth/ (R -x)^2
where R is the distance from eath to moon
7.35E22/x^2 = 5.97E24/(3.84E8-x)^2
x=3.84E7 m
b)
then 1/2 mv^2 - G m moon/r - G mearth m/( R-r) = - G m mmoon/x - G mearth m/( R-x)
0.5*v^2 - 6.67E-11*7.35E22/1.737E6 - 6.67E-11*5.97E24/(3.84E8-1.737E6)=- 6.67E-11*7.35E22/3.84E7 - 6.67E-11*5.97E24/(3.84E8-3.84E7)
v=2273 m/s
c)
if it makes it all the way to earth then
1/2 mv^2 - G m mearth/rearth - G m mmoon/( R - rearth) = - G m mmoon/x - G mearth m/( R-x)
0.5*v^2 - 6.67E-11*7.35E22/(3.84E8-6.378E6) - 6.67E-11*5.97E24/(6.378E6)=- 6.67E-11*7.35E22/3.84E7 - 6.67E-11*5.97E24/(3.84E8-3.84E7)
v=11060 m/s
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