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Q. 21

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 354

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Short Answer

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

See the step by step solution

Step by Step Solution

Part (a) Step 1 : Given information

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

Part (a) Step 2 : Calculation 

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.

Part (a) Step 3 : Continuation of calculation 

Now calculating we get,

Part (a) Step 4 : Final answer 

The radius of the planet is

Part (b) Step 5 : Given information

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

Part (b) Step 6 : Calculation 

The formula for escape velocity is given by :

Where 'v' is escape velocity.

Now,

Part (b) Step 7 : Final answer

The minimum speed that the rocket needs is

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