In this problem assume that the moon is only under the influence of the earth’s
ID: 1365859 • Letter: I
Question
In this problem assume that the moon is only under the influence of the earth’s gravitational force given by a magnitude F e,m = -G(me mm / re,m ^2 )re,m .also assume that the moon is moving in a circular orbit around the earth and that the moon travels with a constant speed in that orbit. Let G = 6.6710^-11N-m^2/kg^2. The mass of the earth is me =5.98*10^24 kg. The mass of the moon is mm =7.36*10^22 kg. The radius of the orbit is re,m = 3.8*10^8
A) briefly describe how you intend to model the motion of the object? what directions are you choosing for analyzing the components of your forces and state why?
B) Calculate the period of the moon's orbit arounf the earth.
PLEASE include detailed solutions. thanks!
Explanation / Answer
A) He we can assume moon is in uniform circular motion around the earth.
The garvitational force on moon always acts towards the earth.
According to universal law of graviataion,
force between Earth and Moon,
F = G*Me*Mm/r^2 (1) (this force acts towards the center of the earth)
from Newton's second law
F = Mm*a_rad --(2)
from equations 1 and 2
a_rad = G*Me/r^2
r*w^2 = G*Me/r^2
w = sqrt(G*Me/r^3)
2*pi/T = sqrt(G*Me/r^3)
T = 2*pi/sqrt(G*Me/r^3)
= 2*pi*r^(3/2)/sqrt(G*Me)
= 2*pi*(3.8*10^8)^1.5/sqrt(6.67*10^-11*5.98*10^24)
= 2330460 s
= 2330460/(24*60*60)
= 26.973 days
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