Tidal forces are gravitational forces exerted on different parts of a body by a

Question

Tidal forces are gravitational forces exerted on different parts of a body by a second body. Their effects are particularly visible ont he earth's surface in the form of tides. To understand the origin of tidal forces, consider the earth-moon system to consist of two spherical bodies, each with a spherical mass distribution. Let 're' be the radius of the earth, m be the mass of the moon and G be the gravitaitonal constant.

Part A)

Let r denote the distance between the center of the earth and the center of the moon. What is the magnitude of the acceleration 'ae' of the earth due to gravitational pull of the moon? (express you answer in terms of G, m, and r).

Part B)

Since the gravitational force between two bodies decreases with distance, the acceleraton 'anear' experienced by a unit mass located at the point on the earths surface closest to the moon is slightly different from the acceleration 'afar' experienced by a unit mass located at the point on the earth's surface farthest from the moon. Give a general expression for quantity anear - afar. (Express your answer in terms of G, m, r, and re).

Part C)

The earth is subject not only to the gravitational force of the moon by also the gravitational pull of the sun. However, the earth is much farther away from the sun than it is from the moon. In fact, the cneter of the earth is at an average distance of 1.5 x 10^11 m from the center of the sun. Given that the mass of the sun is 1.99 x 10^30 kg, which of the following statements is correct?

a) the force exerted on the earth by the sun is weaker than the corresponding force exerted by the moon.

b) the force exerted on the earth by the sun is stronger than the corresponding force exerted by the moon.

c) the force exerted on the earth by the sun is of the same order of magnitude of the corresponding force exerted by the moon.

Part D)

The occurrence of tidal forces on the earths surface is not limited to the gravitational effects of the moon. Tidal forces are produced every time different parts of a body are subject to different gravitational forces exerted by a second body. Therefore, tidal forces due to the gravitational effects of the sun are also present on the earth's surface. What can you conclude abou tthe relative effects of these two tidal forces on the earth's surface?

a) the moon exerts a stronger tidal force on the earth than the sun does.

b) the sun exerts a stronger tidal force on the earth than the moon does.

c) the moon and the sun cause tidal forces of equal magnitude.

Explanation / Answer

Part A = (G*m) / r^2

Part B = ((G*m) / (r - r_e)^2) - ((G*m) / (r + r_e)^2)

Part C = The force exerted on the earth by the sun is stronger than the corresponding force exerted by the moon. (The middle one.)

Part D = The moon exerts a stronger tidal force on the earth than the sun does. ( The top one.)

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