Question

A remote - sensing satellite of earth revolves in a
circular orbit at a height of 0.25 x 106 m above
the surface of earth. If earth's radius is 6.38 x 106m
and g=9.8 m/s", then the orbital speed of the
satellite is':
(2) 7.76 km/s
(1) 6.67 km/s
(3) 8.56 km/s :
2015
(4) 9.13 km/s​

Answer 1

The orbital speed of the satellite is 7.76 km/sec.

Given-

• Height from the surface of the earth = 0.25 × 10⁶ m

• Radius of the earth = 6.38 × 10⁶ m
• Value of g = 9.8 m/sec

We know that at equilibrium orbit centrifugal force is equals to Gravitational force. So,

mv²/r = GMm/r²

v = $\sqrt{\frac{GM}{r} }$

where r = Re + h

And h is the distance of the satellite from the earth

We also know that

g = GM/Re²

M = gRe²/G

Substituting these values in the equation of v we get

v = (gRe²/(Re+h))^1/2

v =  7.76 km/sec