Question

Q2 A geostationary satellite exists 40,000 km above the Earth's surface. Assuming that the potential energy at infinity to be zero, find the difference
between potential energy at infinity and potential energy due to Earth's gravity at the site of this satellite.
(Mass of Earth = 6 * 10 24 kg, Diameter of Earth = 12800 km and G = 6.67* 10-11 Nm[sup2/ kg[sup2)​

Answer 1

Explanation:

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Answer 2

Answer:

We must calculate the gravitational potential energy caused by Earth's gravity at the geostationary satellite's location and then deduct the potential energy at infinity, which is supposed to be zero, in order to determine the potential energy difference between infinity and the satellite's location.

The following is the calculation for gravitational potential energy:

U = − G(m1m2/r)

m1 and m2 are the masses of the two objects (in this instance, the Earth and the satellite), and r is the separation between their centres of mass. G is the gravitational constant.

When the formula's numbers are substituted, we obtain:

U is equal to -6.67 * 10-11 Nm2/kg2 * (6 * 10 24 kg). (40,000,000 Plus 6,400,000) m satellite

where m satellite denotes the kilogramme weight of the satellite.

The satellite is 40,000 km above the surface of the Planet because it is in a geostationary orbit. The radius of the Earth, which is roughly 6,400 km, must also be considered. As a result, the distance between the satellite and the core of the Earth is 46,400 km (or 46,400,000 metres) or 40,000 km plus 6,400 km.

We cannot determine the precise potential energy at the satellite's location because the mass of the satellite is not known. As a result, there is a positive disparity between the potential energy at infinity and the potential energy caused by gravity at the satellite's location.

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