Question

To increased by a time period of satellite by 4 times. It's mean radius should be increased by ____

Answer 1

Radius should be increased by 2 times as the circumference is 2 pie r

Answer 2

According to Kepler's 3rd law ( Law of periods)
:-

T² ∝ D³

Let the initial time period = T.

The time period should be increased by 4 times = 4T.

Let the mean distance be D.

The final mean distance be xD .

As they are directly proportional,

T²/(4T)² = D³/(xD) ³

T²/16T² = D³/x³D³

1/16 = 1/x³

x³ = 16

x = $2 \sqrt[3]{2}$

Therefore, the mean distance should be increased by $2 \sqrt[3]{2}$ times.