Q. 21

Expert-verifiedFound in: Page 354

Book edition
4th

Author(s)
Randall D. Knight

Pages
1240 pages

ISBN
9780133942651

You have been visiting a distant planet. Your measurements have determined that the planet’s mass is twice that of earth but the free-fall acceleration at the surface is only one-fourth as large.

a. What is the planet’s radius?

b. To get back to earth, you need to escape the planet. What minimum speed does your rocket need?

a. The radius of the planet is

b. The minimum speed that the rocket needs is

The planet’s mass is twice that of the earth.

Acceleration due to gravity is given by :

Where 'G' is the universal gravitational constant.

is the mass of the planet.

is the radius of the planet.

a is the acceleration due to gravity.

Now calculating we get,

The radius of the planet is

Free-fall acceleration is one-fourth of the gravity of the earth.

The formula for escape velocity is given by :

Where 'v' is escape velocity.

Now,

The minimum speed that the rocket needs is

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