Neptune has a mass that is about 17 times the mass of earth. the distance between the sun and neptune is about 30.1 times the distance between the sun and earth. if the gravitational force between the sun and earth is 3.5 x 1028 n, which is closest to the force between neptune and the sun?

Given:

Mass of Neptune (M₁) = 17 M₂

Here, mass of the Earth is M₂ and the distance between the Earth and the Sun is R₂. The gravitational force between the Sun and Earth (F₂) = 3.5 x 10²⁸ N

The distance between the Sun and Neptune(R₁) = 30.1 R₂

Let M be the mass of the Sun

Apply, Newton's Law of attraction

The force of attraction between the Earth and the Sun

                 (F₂) = G× M×M₂ / R₂² (i)

The force of attraction between the Neptune and the Sun

                 (F₁) = G× M×M₁ / R₁² (ii)

Now, substituting the value of M₁ and R₁ in equation (ii)

                    (F₁) = G× M× 17 M₂  / (30.1 R₂ )²

or,                (F₁) = [17 / (30.1)²] × [G× M×M₁ / R₁²]

or,                (F₁) = [17 / (30.1 )²] ×F₂

or,                (F₁) = [17 / (30.1 )²] ×3.5 x 10²⁸ N

or,                (F₁) = 6.6 x 10²⁶ N

Hence, the required force of attraction between the Neptune and the Sun will be 6.6 x 10²⁶ N

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