An Artificial Satellite Is Revolving At A Height Of 500 Km Above The Earth’s Surface In A Circular Orbit, Completing One Revolution In 98 Minutes. Calculate The Mass Of The Earth. Given:

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Question

An artificial satellite is revolving at a height of 500 km above the earth’s surface in a circular orbit, completing one revolution in 98 minutes. Calculate the mass of the earth. Given:

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Solution

Correct option is

The gravitational force of attraction exerted by the earth on the satellite is the necessary centripetal force. Therefore, if h be the height of the satellite above the earth’s surface, then

Where m is the mass of the satellite, (R_e + h) is the distance of the satellite from the centre of the earth and v₀ is the orbital velocity of the satellite. If the period of revolution of the satellite be T. then

Substituting from this the value of v₀ in eq. (i), we get

Here, orbital radius and period of revolution T = 98 × 60 = 5.88 × 10³ s.

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