Question

A 500kg satellite revolves around the earth at a height 1000km above the earth surface. Calculate ,assuming circular orbit (I) speed of satellite, (II) angular velocity of satellite, (iii) gravitational force of the earth on satellite

Answer 1

Answer:

speed of satellite

Explanation:

calculate,assuming circular orbit

Answer 2

Answer:

(i) 7.36 x 10³ m/s (ii) 9.95 x 10⁻⁴ rad/s (iii) 3.66 x 10³ N

Explanation:

Given mass = 500 kg, g = 9.8, radius of earth = 6.4 x 10⁶ m,

(i) vₒ = $\sqrt{\frac{gR^2}{R+h} }$ = $\sqrt{\frac{9.8 * 6.4^2 * 10^6}{7.4 * 10^6} }$ = 7.36 km/s = 7.36 x 10³ m/s.

(ii) v = wr, so w = $\frac{v}{r}$ = $\frac{7.3 * 10^3}{(6.4+1)*10^6}$ = 0.995 x 10⁻³ rad/s = 9.95 x 10⁻⁴ rad/s.

(iii) We know that force of attraction = $\frac{GMm}{(R+h)^2}$,

     and g = $\frac{GM}{R^2}$, so force of attraction will be = $\frac{gR^2m}{(R+h)^2}$

     = $\frac{9.8 * 6.4^2 * 10^6 * 500}{7400}$ = 0.00366 x 10⁶ N = 3.66 x 10³ N.

Hope this helps.