Question

With what horizontal velocity should a satellite be projected from a point at a height of 500 km above the

earth's surface, so as to revolve in a circular orbit around the earth? ​

Answer 1

height of satellite from he surface of the earth, h = 500 km

and radius of earth , r = 6400km

so, radius of circular orbit, R = r + h

= 6400km + 500km = 6900km

= 6.9 × 10^6 m

at equilibrium,

centripetal force = gravitational force

or, mv²/r = GMm/r²

or, v² = GM/r

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

putting , G = 6.67 × 10^-11 Nm²/kg² , M = 6 × 10²⁴ kg

so, v = √{6.67 × 6 × 10^(-11 + 24)}/6.9 × 10^6}

= √{6.67 × 6 × 10^7/6.9}

= 7.6 × 10³ m/s

hence, speed of satellite is 7.6 × 10³ m/s