Question

A satellite of mass 200 kg is orbiting with a critical velocity of 20 m/s. Another satellite of mass 100
kg orbiting in same orbit will have critical velocity.​

Answer 1

Critical velocity of a satellite = Vc = ( GM/ r)1/2 where G = universal gravitational constant,

M = mass of planet and r = radius of orbit

Hence, critical velocity of a satellite is independent of its mass.

i.e the new critical velocity will be same as the first.

Answer 2

Answer:

10 √ 2 m / sec

Explanation:

Given :

Critical velocity of first satellite = 20 m / sec

Let orbital radius of satellite be r.

Radius of both satellite will be equal . [ Given ]

Mass of first satellite = 200 kg

Mass of second satellite = 100 kg

We know :

v²_critical = G m₁ / r  [  For first satellite ]

v'²_critical = G m₂ / r  [  For second satellite ]

v² / v'² = m₁ / m₂

v² / v'² = 200 / 100

v² / v'² = 2

We have value of v = 20 m / sec

400 / 2 = v'²

v'² = 200

v' = √ 200

v' = 10 √ 2 m / sec

Therefore , critical velocity of second satellite is