Hello, ceasar_19134!

A ficticious space probe recently discovered a perfectly spherical moon of Jupiter.

While taking photos of the surface, the probe orbited directly above the moon's equator.

If the probe's orbit was exactly 2km longer than the circumference of the moon,

how high above the moon did the probe orbit?

It looks like there isn't enough information given in the problem,

. . but the answer is surprisingly simple.

LetR= radius of the moon on kilometers.

Then the circumference of the moon is: 2πR km.

Lethbe the height of the probe above the moon's surface.

Then the circumference of the probe's orbit is: 2π(R + h) km.

We are told that two distances differ by 2 km.

. . 2π(R + h) - 2πR .= .2

and we have: .2πR + 2πh - 2πR .= .2 . → . 2πh = 2 . → . h = 1/π

Therefore, the height of the probe is about 0.3183 kilometers.

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The answer didnotdepend on the size of Jupiter's moon.

The answer would be same if the probe circled the Sun or a baseball.