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15 April, 19:57

Assume that you stay on the earth's surface. what is the ratio of the sun's gravitational force on you to the earth's gravitational force on you?

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  1. 15 April, 21:36
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    First, let's determine the gravitational force of the Earth exerted on you. Suppose your weight is about 60 kg.

    F = Gm₁m₂/d²

    where

    m₁ = 5.972*10²⁴ kg (mass of earth)

    m₂ = 60 kg

    d = 6,371,000 m (radius of Earth)

    G = 6.67408 * 10⁻¹¹ m³ kg⁻¹ s⁻²

    F = (6.67408 * 10⁻¹¹ m³ kg⁻¹ s⁻²) (60 kg) (5.972*10²⁴ kg) / (6,371,000 m) ²

    F = 589.18 N

    Next, we find the gravitational force exerted by the Sun by replacing,

    m₁ = 1.989 * 10³⁰ kg

    Distance between centers of sun and earth = 149.6 * 10⁹ m

    Thus,

    d = 149.6*10⁹ m - 6,371,000 m = 1.496*10¹¹ m

    Thus,

    F = (6.67408 * 10⁻¹¹ m³ kg⁻¹ s⁻²) (60 kg) (1.989 * 10³⁰ kg) / (1.496*10¹¹ m) ²

    F = 0.356 N

    Ratio = 0.356 N/589.18 N

    Ratio = 6.04
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