Physics : Gravitation : Solved Example Problems for Escape Speed and Orbital Speed

Moon is the natural satellite of Earth and it takes 27 days to go once around its orbit. Calculate the distance of the Moon from the surface of the Earth assuming the orbit of the Moon as circular.

We can use Kepler’s third law,

Here *h* is the distance of the Moon from the surface of the Earth. Here,

By substituting these values, the distance to the Moon from the surface of the Earth is calculated to be 3.77 ×105 *km*.

Calculate the energy of the (i) Moon orbiting the Earth and (ii) Earth orbiting the Sun.

Assuming the orbit of the Moon to be circular, the energy of Moon is given by,

where ME is the mass of Earth 6.02 ×1024 kg; Mm is the mass of Moon 7.35 ×1022 kg; and R is the distance between the Moon and the center of the Earth 3.84 ×105 km

The negative energy implies that the Moon is bound to the Earth.

Same method can be used to prove that the energy of the Earth is also negative.

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