Question

2. Calculate the minimum velocity and period of revolution of an artificial Satellite at a 'h from the surface of the earth . height​

Answer 1

Answer:

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Answer 2

Answer:

Velocity of the Artificial satellite:

h- height of a satellite from the surface of the earth,  

R- the radius of the earth,

the radius of the orbit of the satellite

r = R + h.

The gravitational attraction of the earth provides necessary centripetal force on the satellite for its rotation.

velocity of the satellite is v,

GMm/r2 = mv2/r.

M, m are respectively the masses of the earth and the satellite,

v2 = GM/r

or, v = √(GM/r)

= √ [(GM)/(R + h)] ---------- (1)

Time period of the satellite:

T- time period of the satellite, i.e., if the time to revolve around the earth once at a height h from the surface of the earth is T, then its linear velocity will be,

v = [2π (R + h)] / T

[2π (R + h)] / T = √ [(GM)/(R + h)]

or, T = [2π (R + h)] [√ (R + h) / GM] ------- (2)

Height of the satellite:

H- height of the artificial satellite from earth’s surface, then by squaring both sides of equation (1) we get,

T2 = [4π2 (R + h)3] / GM

or, (R + h)3 = GMT2 / 4π2

so, h = [GMT2 / 4π2]1/3 – R.