During a solar eclipse, the Moon is positioned directly between Earth and the Sun. Find the magnitude of the net gravitational force acting on the Moon during the solar eclipse due to both Earth and the Sun. The masses of the Sun, Earth, and the Moon are 1.99 * 10 30 kg, 5.98 * 10 24 kg, and 7.36 * x10 22 kg, respectively. The Moon's mean distance from Earth is 3.84 * 10 8 m, and Earth's mean distance from the Sun is 1.50 * 10 11 m. The gravitational constant is G = 6.67 * 10 - 11 Nm 2 / kg 2.

Question

Nigel Hughes

Geography

29 May, 10:28

During a solar eclipse, the Moon is positioned directly between Earth and the Sun. Find the magnitude of the net gravitational force acting on the Moon during the solar eclipse due to both Earth and the Sun. The masses of the Sun, Earth, and the Moon are 1.99 * 10 30 kg, 5.98 * 10 24 kg, and 7.36 * x10 22 kg, respectively. The Moon's mean distance from Earth is 3.84 * 10 8 m, and Earth's mean distance from the Sun is 1.50 * 10 11 m. The gravitational constant is G = 6.67 * 10 - 11 Nm 2 / kg 2.

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Answers (1)

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Alan Davies · Answer 1

2.3733 x 10²⁰ N

Explanation:

mass of sun Ms = 1.99 x 10³⁰ kg

Mass of earth Me = 5.98 x 10²⁴ kg

Mass of moon m ' = 7.36 x 10²² kg

Mean distance between sun and earth r = 1.5x10¹¹ m

Mean distance between earth and moon r ' = 3.84 x10⁸ m

Gravitational constant G = 6.67 x 10⁻¹¹N m² / kg²

Gravitational force between earth and moon F = GMem' / r '²

Substitute values you get F = 1.9908 x 10²⁰ N

This force is towards earth.

Gravitational force between sun and moon is F ' = GMsm' / (r - r ') ²

Substitute values you get F ' = 4.3641x10²⁰ N

This force is towards sun.

Net force on moon F net = F ' - F

= 2.3733 x10²⁰ N

Direction : Towards sun