Question about spheres in rotation
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28-07-2011, 12:17 AM
Question about spheres in rotation
I have wondered for a long time,

is the equator actually rotating at a different rate than the area closer to say, the poles? I'll use earth as a particular example

I will call the length of the equator around the earth X, and the length of any line parallel to the equator Y for this example.

D = RT, distance = rate x times

X = R24 (24 hours in a day)

R = X/24 (in other words, the rate of rotation at the equator is X divided by 24, which happens to be 40,030.2 km. This means, the rate is 1667.9 kilometers per hour, approximately.)

Now, lets calculate for Y.

D = RT

Y = R24

R = Y/24 (in other words, the rate of rotation at any latitude not the equator is Y divided by 24. Since the equator has the longest latitude, we can plug in any values lower than 40,030.2 km for the Y values)

Calculations of Y Rates: (remember the X rate was 1667.9 km/h)

Y = 40,000 km, R = 1666.6 km/h
Y = 30,000 km, R = 1250 km/h
Y = 20,000 km, R = 833.3 km/h

To conclude, I ask you this: Does the equator spin faster than any other point, considering, not only does the math back it up, but also if you think about it: it is traveling a longer distance in the same time as the earth rotates.

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28-07-2011, 06:34 AM
RE: Question about spheres in rotation
I think you answered your own question. My knowledge Of physics is limited but the answer is yes.

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28-07-2011, 09:31 AM
RE: Question about spheres in rotation
That is basically the same thing as gears in a transmission. If a larger gear and a smaller gear are being powered by the same shaft then any point on the larger gear must being moving at a higher rate than any point on the smaller gear because it covers a larger distance in the same amount of time. So you are correct. It is a very odd concept to think about that those at the equator are moving faster.

Another interesting fact is that the Earth bulges out at the equator due to centripetal force. This bulge means that the point on Earth that is closest to space is not Mount Everest but is a peak in Equador called Mount Chimborazo (http://www.npr.org/templates/story/story...=9428163). The equator is an interesting place.

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28-07-2011, 10:47 PM
RE: Question about spheres in rotation
The bulge at the equator could also mean that gravitational pull is greater at the equator than at the poles. I don't think it's significant though. You need allot of mass to make a difference since gravity is such a weak force. Launching things into orbit is more energy efficient at the equator.

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29-07-2011, 10:11 AM
RE: Question about spheres in rotation
(28-07-2011 10:47 PM)DeepThought Wrote:  The bulge at the equator could also mean that gravitational pull is greater at the equator than at the poles. I don't think it's significant though. You need allot of mass to make a difference since gravity is such a weak force. Launching things into orbit is more energy efficient at the equator.

Gravity is less at the equator since it is further from the center of the Earth, I think you got that a little mixed up. That is why the we launch our shuttles (or did) from Texas and Florida, since they are the closest to the equator. The difference in gravity is not very much, as you say it is a rather weak force, but one technique that geologists use is flying a plane with a gravitometer on it that measures the difference in the gravitational force below them. This technique helps to show how much or little crust is in an area and can outline trenches and ridges in the ocean. Pretty neat stuff.

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30-07-2011, 02:40 AM (This post was last modified: 30-07-2011 02:52 AM by DeepThought.)
RE: Question about spheres in rotation
Gravity is directly linked to mass. In my mind if you add up the vectors you would get the most gravitational downward pull at the equator where there is most mass beneath your feet. I'm not claiming to be an expert though. I'm just going from what I remember at high-school physics.

I wonder how much effect centripetal acceleration would have at the equator for counteracting gravity. I thought things are launched closer to the equator to get the maximum benefit of earths rotation. Every little bit helps for fuel savings!

Well, you motivated me to look it up - so here it is for anyone that wants to know.
Wikipedia - Equatorial Bulge Wrote:The acceleration that is required to circumnavigate the Earth's axis along the equator at one revolution per sidereal day is 0.0339 m/s². Providing this acceleration decreases the effective gravitational acceleration. At the equator, the effective gravitational acceleration is 9.7805 m/s². This means that the true gravitational acceleration at the equator must be 9.8144 m/s² (9.7805 + 0.0339 = 9.8144).
At the poles, the gravitational acceleration is 9.8322 m/s². The difference of 0.0178 m/s² between the gravitational acceleration at the poles and the true gravitational acceleration at the equator is because objects located on the equator are about 21 kilometers further away from the center of mass of the Earth than at the poles, which corresponds to a smaller gravitational acceleration.
In summary, there are two contributions to the fact that the effective gravitational acceleration is less strong at the equator than at the poles. About 70 percent of the difference is contributed by the fact that objects circumnavigate the Earth's axis, and about 30 percent is due to the non-spherical shape of the Earth.
The diagram illustrates that on all latitudes the effective gravitational acceleration is decreased by the requirement of providing a centripetal force; the decreasing effect is strongest on the equator.

http://en.wikipedia.org/wiki/Equatorial_bulge
When I was a kid I was fascinated with science stuff. I remember having fun flushing the aircraft toilet after we crossed the equator.. watching the liquid swirl around the other way.

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30-07-2011, 06:52 PM
RE: Question about spheres in rotation
(30-07-2011 02:40 AM)DeepThought Wrote:  Gravity is directly linked to mass. In my mind if you add up the vectors you would get the most gravitational downward pull at the equator where there is most mass beneath your feet. I'm not claiming to be an expert though. I'm just going from what I remember at high-school physics.

I wonder how much effect centripetal acceleration would have at the equator for counteracting gravity. I thought things are launched closer to the equator to get the maximum benefit of earths rotation. Every little bit helps for fuel savings!

Well, you motivated me to look it up - so here it is for anyone that wants to know.
Wikipedia - Equatorial Bulge Wrote:The acceleration that is required to circumnavigate the Earth's axis along the equator at one revolution per sidereal day is 0.0339 m/s². Providing this acceleration decreases the effective gravitational acceleration. At the equator, the effective gravitational acceleration is 9.7805 m/s². This means that the true gravitational acceleration at the equator must be 9.8144 m/s² (9.7805 + 0.0339 = 9.8144).
At the poles, the gravitational acceleration is 9.8322 m/s². The difference of 0.0178 m/s² between the gravitational acceleration at the poles and the true gravitational acceleration at the equator is because objects located on the equator are about 21 kilometers further away from the center of mass of the Earth than at the poles, which corresponds to a smaller gravitational acceleration.
In summary, there are two contributions to the fact that the effective gravitational acceleration is less strong at the equator than at the poles. About 70 percent of the difference is contributed by the fact that objects circumnavigate the Earth's axis, and about 30 percent is due to the non-spherical shape of the Earth.
The diagram illustrates that on all latitudes the effective gravitational acceleration is decreased by the requirement of providing a centripetal force; the decreasing effect is strongest on the equator.

http://en.wikipedia.org/wiki/Equatorial_bulge
When I was a kid I was fascinated with science stuff. I remember having fun flushing the aircraft toilet after we crossed the equator.. watching the liquid swirl around the other way.

Right...I stand corrected...more at the equator.

“Science is simply common sense at its best, that is, rigidly accurate in observation, and merciless to fallacy in logic.”
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30-07-2011, 11:41 PM
RE: Question about spheres in rotation
No - wikipedia is correcting me. It says that since you are further from earths center of mass there is less gravity. It just seems a little counter intuitive to me. I know gravity is less when you are further away but I thought the extra mass from the bulge would have a different effect and that the difference in distance would be trivial (it's only a ~42km bulge.)

Standing on top of all that extra mass made me think it would be different though I guess the difference in density - crust vs core composition might account for this. All those heavier elements in the core.

“Forget Jesus, the stars died so you could be born.” - Lawrence M. Krauss
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31-07-2011, 08:37 AM
RE: Question about spheres in rotation
Gravity = m1 * m2 / r^2

gravity equals the product of the mass of the two objects, divided by the distance squared.

This means that distance has a bigger impact than mass, since its being squared

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31-07-2011, 10:26 PM (This post was last modified: 31-07-2011 10:29 PM by DeepThought.)
RE: Question about spheres in rotation
If all of earth had uniform density (mass per unit volume) how would that effect gravity? Note that the bulge only accounts for 40km... Trivial compared with the total diameter.

“Forget Jesus, the stars died so you could be born.” - Lawrence M. Krauss
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