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Derive an expression for time period of a satellite in terms of radius of the orbit?

Derive an expression for time period of a satellite in terms of radius of the orbit?

Grade:9

1 Answers

Nirmal Singh.
askIITians Faculty 44 Points
7 years ago
This is simple if you assume circular motion. The acceleration of gravity from the central body must be exactly equal to the centripetal acceleration required for the circular orbit:

GM/r^2 = v^2 / r
v = sqrt(GM/r) ... orbital speed v in terms of G, M=mass of central body, r=radius of orbit
The period is the time it takes to travel the distance 2*pi*r around the circle at speed v.

So time period T = 2 pi r / v
T = 2 pi r /sqrt(GM/r)

Regards,
Nirmal Singh
Askiitians faculty

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