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5 October, 13:46

When it orbited the Moon, the Apollo 11 spacecraft's mass was 14800 kg, and its mean distance from the Moon's center was 1.79877 * 106 m. Assume its orbit was circular and the Moon to be a uniform sphere of mass 7.36 * 1022 kg. Given the gravitational constant G is 6.67259 * 10-11 N m2 / kg2, what is the minimum energy required for the craft to leave the orbit and escape the Moon's gravitational field?

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  1. 5 October, 16:20
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    If M be mass of moon and m be mass of spacecraft

    potential energy of moon - spacecraft system

    = - G M m / R where R is radius of orbit of spacecraft

    kinetic energy of spacecraft in the orbit

    = 1/2 m v² = GMm / 2R

    Total energy of spacecraft

    = GMm / 2R - G M m / R

    = - GMm / 2R

    for spacecraft to leave the orbit, energy required

    = GMm / 2R

    = 6.67259 x 10⁻¹¹ x 7.36 x 10²² x 14800 / (2 x 1.79877 x 10⁶)

    = 202035.8 x 10⁵ J.
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