Question

If the mass of a planet is eight times the mass of the earth and its radius is twice the radius of the earth what will be the escape velocity for that planet?

Answer 1

Question :-

If the mass of a planet is eight times the mass of the earth and its radius is twice the radius of the earth what will be the escape velocity for that planet?

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Given information :

Mass of Earth  = M₁

Mass of the planet = eight times M₁

                               = 8 × M₁

                               = 8 M₁

Radius of Earth = R₁

Radius of the planet = two times R₁

                                  = 2 × R₁

                                  = 2 R₁

Escape velocity of the planet

We know that :

escape velocity = V = √ ( GM / R )

                                 = √ ( G × 8 M₁  / 2 R₁ )

                                 = √ ( 8 G M₁ / 2 R₁ )

                                 = √ ( 4 G M₁ / R₁ )

                                 = 2 √ GM₁ / R₁

                                 = 2 × escape velocity of Earth.

We know that the escape velocity of Earth is 11.2 approx.

So : escape velocity of the planet = 2 × 11.2 km / s

                                                        = 22.4 km/s approx.

ANSWER :-

The escape velocity will be 22.4 km/s approximately .

Hope it helps :-)

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