MadSci Network: Astronomy

Re: Would doubling the mass of the moon make it revolve slower or faster? Why?

Date: Wed Mar 17 21:15:39 2004
Posted By: Layne Johnson, Undergraduate
Area of science: Astronomy
ID: 1075865394.As

Hello, Jonathon
Let's jump back to Sir Issac Newton and some of the laws he discovered about gravity and motion.

Gravity is the mutual attraction of massive bodies. That means if two objects have mass, like the earth and the moon, both pull each other together. The closer together they are, and the more mass they have, the stronger they pull each other.

But wait---there's more! Issac Newton also taught us that an object in motion will stay in motion, going the same direction and speed until something interferes with it. If you take a bucket and fill it half full with water, you can hold on to the handle and spin it around in circles, even upside down, and the water won't spill out. If you tried that on the moon, where the gravity isn't very strong, you could spin the bucket around slower and still keep the water inside it. But if you tried it on Jupiter, where the gravity is really strong compared to Earth, you'd have to swing the bucket around very, very fast to keep the water from spilling out.

The Earth and the moon revolve around each other just fast enough to keep gravity from causing them to collide, but just slow enough that neither one escapes the eternal dance.

[MODERATOR NOTE: However, as it turns out, the orbital velocity doesn't depend on the mass of the object doing the orbiting. In particular, if you set the centripetal force (Fc) equal to the gravitational force (Fg), you can derive the oribital velocity, V, as:

MmoonV2moon/R = GMearthMmoon/R2
Solving for V2:
==> V2 = GMearth/R
which shows that the orbital velocity, V, only depends on the distance, R, between the two objects and not on the mass of the Moon (Mmoon). This means that increasing the mass of the Moon won't change how fast it orbits the Earth. -- RJS (with thanks to Dr. John Christie, MadSci Moderator)]

I hope this answers your question. Have a good year at Cheekside!

Layne Johnson

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