Question

derive an expression for period of a satellite in a circular orbit round the earth​

Answer 1

$\huge\bigstar\underline\pink{Answer}$

★ T = 2πr/V

where V = √Gme/Re

Therefore,

T = 2πr√r / √Gme

(me = mass of earth)

=> T = 2πr³/² / √Gme .......(1)

Nearby earth r = Re

T = 2πr³/² / √Gme

T = 2πRe^³/² / √Gme

T² = 4π²Re³/ Gme.......(2)

putting g = Gme/Re²

Gme = gRe²......(3)

putting the value of (3) in (2)

T² = 4π²Re³/gRe²

T = 2π √ Re/g

T = 2π √1600 × 1000/10

T = 1600π sec

or,

T = 1.4ms

happy to help!

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