Question

Mass of Jupiter is 319 times more than that of the earth, but the acceleration due to gravity of Jupiter is only 2.5 times greater the that of the earth.why?
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Answer 1

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Answer 2

$\bf\huge{\pink{Meow \:Meow ♡︎}}$

The force due to gravity is proportional to the mass divided by the square of the distance you are from the object’s center of gravity.

Surface gravity (which, I presume is what you’re talking about) is measured at a distance equal to the radius of the planet. (We mostly only care about Earth’s gravity here on the surface - and not at the bottom of very deep holes or on the tops of mountains).

So although Jupiter is MUCH heavier - it’s also much larger - and since gravity decreases with the SQUARE of the distance - the effect of all that mass is largely counteracted by the enormous size of the planet.

It’s the same deal with the moon - the mass of the moon is only about 1% that of Earth - but the surface gravity there is 1/6th of Earth’s. That’s because, the moon is not only lighter than Earth - but also much smaller (About 27% of Earth’s). Since you’re closer to the center of the moon when you’re standing on it - the gravity is much larger than you’d expect from looking at it’s mass alone.

This also explains why black holes are so bizarre. Their mass may be no more than that of a large-ish star…nothing too terrifying about that. But because they have collapsed until their size is (effectively) zero - the gravity at the center is (effectively) INFINITE!!

But if you were to be in a spaceship (say) 100,000 kilometers from the center of Jupiter, the gravity would indeed be 319 times higher than if you were 100,000 kilometers from the center of the Earth.