Part A) On the way to the moon the Apollo astronauts reach a point where the Moo
ID: 1792297 • Letter: P
Question
Part A)
On the way to the moon the Apollo astronauts reach a point where the Moon’s gravitational pull is stronger than that of Earth’s. Determine the distance of this point from the center of the Earth. The masses of the Earth and the Moon are respectively 5.34 × 1024 kg and 7.36×1022 kg. The distance from the Earth to the Moon is 3.97 × 108 m. Answer in units of m.
Part B)
What is the acceleration due to the Earth’s gravity at this point? The universal gravitational constant G is 6.672 × 1011 N m2 /kg2 . Answer in units of m/s 2 .
Explanation / Answer
A)
r = distance between earth and moon = 3.97 x 108 m
x = distance of the point from center of earth
M = mass of earth = 5.34 x 1024 kg
m = mass of moon = 7.36 x 1022 kg
using the equation
GM/x2 = Gm/(r - x)2
(5.34 x 1024)/x2 = (7.36 x 1022)/((3.97 x 108) - x)2
x = 3.55 x 108 m
B)
a = GM/x2
a = (6.67 x 10-11)(5.34 x 1024)/(3.55 x 108)2
a = 0.00283