Question

How much time a satellite in an orbit at height 35780 km above earth’s surface would take, if the mass of the earth would have been four times its original mass? Ans : ~ 12 hrs , Solve the problem

Answer 1

Use the formula, $\bf{T=2\pi\sqrt{\frac{R^3}{GM_E}}}$
Here, T is time period, R is orbit radius
G is gravitational constant and $M_E$ is mass of earth.

Given,
$M_E$ = 4 × original mass of earth,
= 4 × 5.92 × 10²⁴ kg
Orbit radius , R = Earth's radius + height of satellite from Earth's surface
= 6400 km + 35780 km
= 42180 km = 4.2180 × 10⁷ m
G = 6.67 × 10⁻¹¹ Nm²/Kg²

Now, T = 2π√{(4.2180 × 10⁷)³/(6.67 × 10⁻¹¹) × (4 × 5.92 × 10²⁴)}
= 43309.8 sec

So, T = 43309.8/3600 ≈ 12 hrs

Hence, time to complete revolution by satellite is 12 hrs

Answer 2

Answer:

The answer is the time taken is 12 hrs