4) According to the ancient Greeks, the Earth was the center of the universe and
ID: 1696166 • Letter: 4
Question
4) According to the ancient Greeks, the Earth was the center of the universe and the sun, moon, stars, and planets all went around the Earth. In the 1543 Copernicus proposed the heliocentric theory of the universe in which the Earth was just another planet orbiting the Sun and only the moon orbited the Earth.
a) What is the speed at which the Moon goes around the Earth?
b) How does the Moon's orbital acceleration compare to the acceleration of objects near the surface of the Earth?
c) What is the magnitude of the force that the Earth's gravity exerts on the Moon to keep it in orbit?
d) According to Newton's third law, all forces occur in pairs. What is the reaction to the Earth's gravity on the moon? Explain.
Explanation / Answer
(a)
orbital speed of the moon = sqrt(GM/r)
where G is the universal gravitational constant = 6.67*10^-11 N-m^2/kg^2
M is the mass of the moon = 7.34*10^22 kg
r is the distance between moon and earth = 3.82*10^8 m
now orbital speed of the moon = sqrt(6.67*10^-11* 7.34*10^22 / 3.82*10^8)
= 112.89 m/sec
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(b)
acceleration of the moon = GM/r^2
= 6.67*10^-11*7.34*10^22/(3.82*10^8)^2
= 3.3*10^-5 m/sec^2
acceleration of the earth = 9.8 m/s^
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(c)
force F = GMm/r^2
where M is the mass of the earth = 5.98*10^24 kg
m is the mass of the moon = 7.34*10^22 kg
r is the distance between moon and earth = 3.82*10^8 m
F =6.67*10^-11* 5.98*10^24*7.34*10^22/3.82*10^8
= 20*10^19 N
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(d)
According to the Newton's third law
the same force will exerts on earh by moon .
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