Question

The table below gives the masses of the Earth, the Moon, and the Sun.

Name Mass (kg)
Earth 5.97 x 1024
Moon 7.35 x 1022
Sun 1.99 × 1030
The average distance between the Earth and the Moon is 3.84 x 108 m. The average distance between the Earth and the Sun is 1.50 x 10¹¹1 m. Use this information to answer the following questions.
Find the net gravitational force Fret acting on the Earth in the Sun-Earth-Moon system during the new moon (when the moon is located directly between the Earth and the Sun).
Express your answer in newtons to three significant figures.
Find the net gravitational force Fnet acting on the Earth in the Sun-Earth-Moon system during the full moon (when the Earth is located directly between the moon and the sun).
Express your answer in newtons to three significant figures.

Answer 1

The net gravitational force acting on the Earth in the Sun-Earth-Moon system can be calculated during the new moon and full moon phases. During the new moon phase, the net gravitational force is equal to the gravitational force between the Earth and the Sun. During the full moon phase, the net gravitational force is equal to the gravitational force between the Earth and the Moon.

Step-by-step explanation:

In the Sun-Earth-Moon system during the new moon, the net gravitational force acting on the Earth can be found by considering the gravitational forces between the Earth-Sun and Earth-Moon.

Since the Moon is located directly between the Earth and the Sun during the new moon, the gravitational force between the Earth and the Sun cancels out the gravitational force between the Earth and the Moon to an extent.

Therefore, the net gravitational force Fnet acting on the Earth during the new moon is equal to the gravitational force between the Earth and the Sun, which can be calculated using the formula:

Fnet = G * (mEarth * mSun) / dES2

where G is the gravitational constant, mEarth is the mass of the Earth, mSun is the mass of the Sun, and dES is the distance between the Earth and the Sun.

Similarly, during the full moon, when the Earth is located directly between the Moon and the Sun, the net gravitational force Fnet can be calculated using the formula:

Fnet = G * (mEarth * mMoon) / dEM2

where mMoon is the mass of the Moon and dEM is the distance between the Earth and the Moon.