During a solar eclipse, the moon (of mass 7.36 × 1022 kg), Earth (of mass 5.98 × 1024 kg), and Sun (of mass 1.99 × 1030 kg) lie on the same line, with the moon between Earth and the Sun. What gravitational force is exerted on the moon by the Sun? The universal gravitational constant is 6.673 × 10−11 N · m 2 /kg2 , the Earth-moon distance is 3.84 × 108 m, and the Earth-Sun distance is 1.496 × 1011 m. Answer in units of N.

The gravitational force exerted on the moon by the Sun is 4.39×10²⁰ N

From the question given above, the following data were obtained:

Mass of Sun (Mₛ) = 1.99×10³⁰ kg

Mass of moon (Mₘ) = 7.36×10²² kg

Gravitational constant (G) = 6.67×10¯¹¹ Nm²/Kg²

Earth-moon distance = 3.84×10⁸ m

Earth-Sun distance = 1.496 × 10¹¹ m

Sun-moon distance (r) = 1.496 × 10¹¹ – 3.84×10⁸

Sun-moon distance (r) = 1.49216×10¹¹ m

The gravitational force exerted on the moon by the Sun can be obtained as follow:

Therefore, the gravitational force exerted on the moon by the Sun is 4.39×10²⁰ N

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Explanation:

Newton's law of gravitation states that the force exerted by a body on another body is calculated as below:

F = GM1•M2 / r²

Where

Mass of moon is

Mm = 7.36 × 10²² kg

Mass of earth is

Me = 5.98 × 10²⁴kg

Mass of sun

Ms = 1.99 × 10^30 kg

Gravitational constant

G = 6.673 × 10^-11 Nm²/C²

Earth-moon distance is

Rem = 3.84 × 10^8 m

Earth-Sun distance is

Res = 1.496 × 10¹¹ m

So, distance from the sun to the moon can be calculated using

The distance from the sun to the moon is the difference between the distance from the earth to the sun and distance from the earth to the moon

Rms = Res — Rem

Rms = 1.496 × 10¹¹ — 3.84 × 10^8

Rms = 1.49216 × 10¹¹ m

Gravitational force exerted by the moon on the sun can be calculated using

Fms = G•Mm•Ms / Rms²

Fms = 6.673 × 10^-11 × 7.36 × 10²² × 1.99 × 10^30 / (1.49216 × 10¹¹)²

Fms = 4.39 × 10^20 N

Then, the gravitational force exerted on the moon by the sun is 4.39 × 10^20N

Extra

We can also calculate the force exerted on the earth by the sun using

Fes = G•Me•Ms / Res²

You can compute that by inserting the parameters above

Also we can find the force exerted by earth on the moon using

Fem = G•Me•Mm / Rem²

You can also compute this

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