# Gravity and angular momentum

1. Jul 21, 2004

### mee

Is our angular momentum altering our gravitational attraction to the earth so that if the rotation of the Earth was stopped we would all be attracted to the earth more? If we stopped or slowed the rotation of mars would the gravity be closer to earth normal (and btw the temperature, if rotation was stopped or made so that one sol = one martian year, might go up to liveable conditions on the light side?)

2. Jul 21, 2004

### BobG

No, the magnitude of the gravitational attraction of the Earth is not affected by the Earth's angular momentum.

Both the gravitational force and angular momentum depend upon a common parameter, the Earth's mass, but do not affect each other (angular momentum is equal to the moment of inertia times the angular velocity, and the moment of inertia depends upon mass)

If you wanted the precise answer, the direction of gravitational force would change slightly after a period of time. The rotation of the Earth has resulted in a slightly flattened sphere with more mass being distributed towards the equator than the poles (this has an important effect on orbiting satellites). Being somewhat liquid under the crust, the Earth's mass can eventually redistribute itself in response to the slowing spin (in fact, plate tectonics is at least partially due to the slowing rate of the Earth's spin rate). With no spin, the Earth would eventually assume a shape closer to a perfect sphere.

Trivia question: On the surface of the Earth, what location is given credit for being the furthest point away from the center of the Earth?

3. Jul 21, 2004

### mee

thank you bob

I was perhaps not clear or I just dont fully understand you. I was wondering about the angular momentum of the people on the earth more than the earth itself, as if our inertia which tries to fly us of the earth somehow negates some of the gravitational force trying to hold us on the earth.

4. Jul 21, 2004

### BobG

Well, again I'd say no.

Do you weigh more at the North Pole than you do at the equator?

Do you weigh less at the top of a mountain?

If you wanted to be extremely precise, the answer to both would be yes. You're closer to the center of the Earth at the poles and you have zero velocity relative to the center of the Earth. You're further from the center of the Earth on top of a mountain, which also means you have a higher linear velocity (angular velocity has to stay constant).

For all practical purposes, though, your weight (the measurement of the net force of gravity on your body) will be the same anywhere on the surface of the Earth.

5. Jul 21, 2004

### mee

thanks bob

I feel a bit silly now. Nice explanation. :)

6. Jul 22, 2004

### remcook

"Trivia question: On the surface of the Earth, what location is given credit for being the furthest point away from the center of the Earth?"

Would I be close if I say: the Kilamanjaro? (sp?)

7. Jul 22, 2004

### BobG

Close, as in "Is its distance close to the furthest?" Yes, very.

Close, as in geographically? No, you're off by almost 8,000 miles.

But, you clearly have the right idea.

8. Aug 11, 2004

### pervect

Staff Emeritus
It's probably a bit late to respond, but there is some variation in the earth's surface gravity due to its spin.

See for instance

http://curious.astro.cornell.edu/question.php?number=465
http://curious.astro.cornell.edu/question.php?number=310

But the effect is very small - on the order of half a percent

9. Aug 12, 2004

### BobG

It's probably a bit late for me to respond, as well, but the answer to "On the surface of the Earth, what location is given credit for being the furthest point away from the center of the Earth?" is:

Mt Chimburazo in Ecuador. Big mountain located almost right on the equator.