Question

how much time would a 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 of its original mass​

Answer 1

Use the formula,

Here, T is time period, R is orbit radius

G is gravitational constant and is mass of earth.

Given,

= 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