If you were to calculate the pull of the Sun on the Earth and the pull of the Moon on the Earth, you would undoubtedly find that the Sun’s pull is much stronger than that of the Moon, yet the Moon’s pull is the primary cause of tides on the Earth. Tides exist because of the difference in the gravitational pull of a body (Sun or Moon) on opposite sides of the Earth. Even though the Sun’s pull is stronger, the difference between the pull on the near and far sides is greater for the Moon.

a. Let F(r) be the gravitational force exerted on one mass by a second mass a distance r away. Calculate dF(r)/dr to show how F changes as r is changed.

b. Evaluate this expression for dF(r) jdr for the force of the Sun at the Earth’s center and for the Moon at the Earth’s center.

c. Suppose the Earth-Moon distance remains the same, but the Earth is moved closer to the Sun. Is there any point where dF(r) /dr for the two forces has the same value?