Question

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

1) Earth is subject not only to the gravitational force of the Moon but also to the gravitational pull of the Sun. However, Earth is much farther away from the Sun than it is from the Moon. In fact, the center of Earth is at an average distance of 1.5×1011m from the center of the Sun. Given that the mass of the Sun is 1.99×1030kg, which of the following statements is correct?

A) The force exerted on Earth by the Sun is weaker than the corresponding force exerted by the Moon.
B) The force exerted on Earth by the Sun is stronger than the corresponding force exerted by the Moon.
C) The force exerted on Earth by the Sun is of the same order of magnitude of the corresponding force exerted by the Moon.

2) The occurrence of tidal forces on Earth's surface is not limited to the gravitational effects of the Moon. Tidal forces are produced every time different parts of a object are subject to different gravitational forces exerted by a second object. Therefore, tidal forces due to the gravitational effects of the Sun are also present on Earth's surface. What can you conclude about the relative effects of these two tidal forces on Earth's surface?

A) The Moon exerts a stronger tidal force on Earth than the Sun does.
B) The Sun exerts a stronger tidal force on Earth than the Moon does.
C) The Moon and the Sun cause tidal forces of equal magnitude.

Answer 1

1.

B) The force exerted on Earth by the Sun is stronger than the corresponding force exerted by the Moon.

Step-by-step explanation:

Gravitational force is proportional to the products of the masses of the bodies and inversely proportional to the square of their distance apart.

2.

A) The Moon exerts a stronger tidal force on Earth than the Sun does

Step-by-step explanation:

the Moon produces a greater tidal force on the Earth than the Sun, even though the Sun exerts a greater gravitational attraction on the earth than that exerted b the moon on the earth.

The Sun's gravitational pull on the Earth is about 175 times stronger when compared to that exerted by the Moon but has a much smaller effect on the tides. This is due to the inverse square law. The Earth's diameter is a tiny fraction of the total distance between the Sun and Earth which means that the difference in gravitational force across the Earth varies by a very small amount. On the other hand, the Moon is much closer than the Sun, thus the difference in gravitational force from the Moon across the Earth is much greater. The Sun has approximately only 44% of tidal influence than that of the Moon.