The Moon has a mass of 7.36 times 10^22 kg and the Earth has a mass of 5.98 time
ID: 1558065 • Letter: T
Question
The Moon has a mass of 7.36 times 10^22 kg and the Earth has a mass of 5.98 times 10^24 kg. The Moon orbits the Earth once every 27.3 days in a roughly circular orbit with a radius of 384 thousand kilometers as a result of the gravitational force that the Earth exerts on it. Using only the concept of centripetal acceleration, find the magnitude of the gravitational force that the Earth exerts on the Moon. What is the magnitude of the acceleration of the Moon DUE to the gravitational force that the Earth exerts on it? To get full credit for this part of the problem, you MUST show two different ways to find the answer. What is the magnitude of the acceleration of the Earth DUE to the gravitational force that the Moon exerts on it? To get full credit for this part of the problem, you MUST show two different ways to find the answerExplanation / Answer
Given mass of moom Mm = 7.36 * 10^22 kg
mass of earth Me = 5.98 * 10^24 kg
time period T = 27.3 days
T = 27.3 * 24 * 60 * 60 s
radius r = 384 * 10^6 m
A)
the speed of the moon round the earth is
v = 2pi * r / T
the centripetal acceleration a = v^2 / r
a = (4*pi^2 * r) / T^2
a = (4 * pi^2 * 384 * 10^6) / (27.3 * 24 * 60 * 60)^2
a = 0.00272 m/s^2
the gravitational force is F = m * a
F = 7.36 * 10^22 * 0.00272
F = 2 * 10^20 N
B)
acceleration of moon is
a = F / Mm
a = 2 * 10^20 / (7.36*10^22)
a = 0.00272 m/s^2
C)
acceleration of earth is a = F / Me
a = 2 * 10^20 / (5.98*10^24)
a = 3.34 * 10^-5 m/s^2