Question

How much time would a satellite in an orbit at a height of 35780 km above the earth’s surface take to complete one revolution around the earth, if the mass of the earth were four times its original mass?

Answer 1

Given: R (Earth) = 6400 km = 6.4 × 10⁶ m,

M (Earth) = 6 × 10²⁴ kg

∴ M’ = 4M = 4 × 6 × 10²⁴ kg

h = 35780 km = 3.578 × 10⁷ m = 35.78 × 10⁶ m,

G = 6.67 × 10^-11 N·m²/kg², T = ?

The time that the satellite would take to complete one revolution around the earth,

= Approx 4.303 × 10⁴ s

= Approx 11.95 h

or 11 hours 57 minutes 10 seconds.