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Chapter: 11th Physics : Gravitation

Solved Example Problems for Escape Speed and Orbital Speed

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

EXAMPLE 6.9

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.

Solution

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.


EXAMPLE 6.10

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

Solution

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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