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**Determine the minimum velocity an Earth satellite must have in order to purse a stable orbit without falling to the ground.**

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- Thread starter mcolem
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- #1

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- #2

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- #3

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I know the velocity has to be less than 11 km/sec (escape velocity).

- #4

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GMm/r^2=mv^2/r

For a satelite orbiting close to the earth, its radius of orbit is approximately equal to the radius of earth.

You can find v then.

- #5

tony873004

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A geosynchronous satellite has a velocity of 0 with respect to the ground. The distance between your house and the satellite that feeds you TV is constant, and since average velocity = delta distance/ time, and delta distance is 0, your average velocity is 0.

But orbital velocity is different. You use circumference of the orbit / time to get orbital velocity of a circular orbit. So what is the circumference of the orbit? It depends on the altitude.

The Moon has an orbital velocity of about 1 km/s. Even if you cut it down to 0.5 km/s, it would still be in a stable, but very elliptical orbit.

The Moon is near the Earth's stability radius, which is roughly defined as 1/3 the radius of the Hill Sphere. So if you compute the orbital velocity at apogee of an object whose apogee is around 400,000 km and whose perigee is around 6478 kilometers (radius of Earth + 100 km altitude), that could be the answer. Or, like you said, 0 could be the answer too.

Ask your teacher to clarify the question.

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- #7

tony873004

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Just use a little algebra on the formula Harmony gave you to solve for v. Or just look up the orbit velocity formula in your book.

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