Question

Jupiter is 300 times more massive than the Earth and 10 times the diameter of the Earth. An astronaut lands on a planet that is the mass of Jupiter but the same radius as the Earth. On this planet the force of gravity is:

a) The same as on the surface of Jupiter

b) Between that on the Earth and the surface of Jupiter

c) The same as on the Earth

d) A little bit higher than on the the surface of Jupiter e) Much higher than on the surface of Jupiter

Answer 1

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Let be the mass of the Earth, be the radius of the Earth and be the mass of the astronaut.

Therefore, Force of gravity on astronaut at the surface of the earth is given by:

Let be the mass of the Jupiter, be the radius of the Jupiter.

Therefore, Force of gravity on astronaut​​​​​​​ at the surface of the Jupiter is given by:

Given that:

Jupiter is 300 times more massive than the Earth,

Diameter is 10 times the diameter of the Earth,

Substituting from (1):

That is Force of gravity on astronaut​​​​​​​ at the surface of the Jupiter​​​​​​​ is 3 times greater than the force of gravity on astronaut​​​​​​​ at the surface of the earth.

Now, Let be the mass of the new planet, be the radius.

Therefore, Force of gravity on astronaut​​​​​​​ at the surface of the new planet is given by:

Given that:

Substituting from (1):

Substituting from (2):

Comparing results, we can see that the force of gravity on astronaut on the surface of the new planet is 100 times greater than the force of gravity on astronaut on the surface of the Jupiter.

So the correct option is (e) Much higher than on the surface of Jupiter.

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