During a solar eclipse the Moon is positioned directly between Earth and the Sun

Question

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 then, due to both Earth and the Sun. The masses of the Sun, Earth, and the Moon are 1.99 x10^30 kg, 5.98 x 10^24 kg, and 7.36 x 10^22 kg, respectively. The Moon?s mean distance from Earth is 3.84 x 10^8 m, and Earth?s mean distance from the Sun is 1.50 x 10^11 m. The gravitational constant is G = 6.67 x 10^-11 Nm^2/kg^2. What is the direction of this force? Elsewhere Toward Earth Toward Venus Toward the Sun

Explanation / Answer

mass of sun M = 1.99 x 10 30 kg

Mass of earth m = 5.98 x 10 24 kg

Mass of moon m ' = 7.36 x 10 22 kg

Mean distance between sun and earth r = 1.5x10 11 m

Mean distance between earth and moon r ' = 3.84 x10 8 m

Gravitational constant G = 6.67 x 10 -11 N m 2 / kg 2

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

Substitute values you get F = 1.9908 x 10 20 N

This force is towards earth.

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

Substittue values you get F ' = 4.3641x10 20 N

This force is towards sun.

Net force on moon F net = F ' - F

                                    = 2.3733 x10 20 N

Direction : Towards sun

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