A geostationary satellite

Geostationaryjava3DsideviewA geostationary satellite is a satellite in geostationary orbit, with an orbital period the same as the Earth’s rotation period. The geostationary orbit is a circular orbit directly above the Earth’s equator.

How high above the Earth’s surface must the geostationary satellite be placed into orbit?

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How long would it take to fall through the center of the Earth?

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We have a hole that leads straight through the center of the Earth. We neglect air resistance and assume that the Earth has uniform density ρ. How long would it take to fall through the center of the Earth and reach the other side of the planet?

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If the orbital speed was doubled

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Each planet has its own orbital speed. If the orbital speed was doubled, the planet would

a) enter into a closer orbit around the Sun.
b) enter into a far orbit around the Sun.
c) warm up.
d) escape the Sun.

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If the solar system were reduced

Solar System (artist's impression) If all the linear dimensions of the solar system were reduced in some proportion, then what will be the length of Earth’s year?

 

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Difference in the weight of a person.

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Is there any difference in the weight of a person on the equator and on the poles?

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An astronaut needs to speed up.

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A satellite completes 7 revolutions around the Earth in a day. For whatever reasons, an astronaut needs to speed up the satellite’s movement, so as to make 10 revolutions around the Earth in a day. What should the astronaut do?

 
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The body is lowered into a deep pit.

What will happen to the force of gravity acting on the body by the Earth, if the body is lowered into a deep pit?

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