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30 June, 09:40

Mercury has a mass of 3.30 1023 kg and a radius of 2.44 106 m.

(a) What is the acceleration due to gravity on Mercury?

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  1. 30 June, 10:11
    0
    The answer is - 3.697 m/s².

    According to Newton's Second Law:

    F = m·g

    But if there is gravity, force must be expressed as:

    F = - G · M · m / r²

    where:

    F - the force

    m - the mass of the object

    M - the mass of the planet

    g - the gravitational acceleration

    G - the gravitational constant

    r - the radius of the planet.

    Now, let's merge these formulas:

    m · g = - G · M · m / r²

    After dividing by m:

    g = - G · M / r²

    It is known:

    g = ?

    G = 6.67 · 10⁻¹¹ Nm²/kg²

    M = 3.30 · 10²³ kg

    r = 2.44 · 10⁶ m

    Consequently:

    g = - G · M : r²

    = - 6.67 · 10⁻¹¹ · 3.30 · 10²³ : (2.44 · 10⁶) ²

    = - 22 · 10 ¹² : 5.95 · 10 ¹²

    = - 3.697 m/s²
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