Question

Jupiter has a mass approximately 300 times greater than Earth's and a radius about 11 times greater. How will the gravitational acceleration at the surface of Jupiter compare to that at the surface of the Earth?

- Greater
- Less
- About the same
- Not enough information

Final Answer

(a)

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This is College Physics Answers with Shaun Dychko.
Jupiter has a mass approximately 300 times greater than Earth’s and a radius 11 times greater. So how will the gravitational acceleration at Jupiter compare to that at the surface of Earth? We have the formula here for gravitational acceleration at Jupiter surface equals the gravitational constant times the mass of Jupiter divided by Jupiter’s radius squared. We can substitute the data that the question gives us, we can substitute 300 times mass of the Earth in place of the mass of Jupiter and we’ll substitute 11 times radius of the Earth to replace the radius of Jupiter. And we square this denominator which makes it 121, so we have 300 over 121 times

*G ME*over*rE*squared. This is the gravitational acceleration at the surface of Earth. So we have 300 over 121 times*gE*. We don’t need to calculate what this number is, it’s good enough to know that since the numerator is greater than the denominator, this is a number more than one. And so the gravitational acceleration on Jupiter’s surface is going to be greater than the gravitational acceleration on Earth. So the answer is a.