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A satellite orbits the earth once each day. Given this uniform speed, and that centripetal force is provided by gravity, determine the altitude of the satellite.

a. 5,964 km
b. 10,000 km
c. 35,786 km
d. 42,164 km

User Schuyler
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Final answer:

The correct altitude of a geosynchronous satellite orbiting Earth once per day is 35,786 km above Earth's surface, which corresponds to an orbital radius of approximately 42,164 km from Earth's center.

Step-by-step explanation:

The student's question pertains to determining the altitude of a satellite that orbits Earth once every day, also known as a geosynchronous satellite. We can answer this by using Kepler's third law and the fact that a geosynchronous satellite must have an orbital period of exactly one day so that it maintains a fixed position relative to Earth's surface.

Given the choices, the correct altitude of such a satellite is 35,786 km above Earth's surface. This is because a geosynchronous orbit, where the satellite remains geostationary relative to the Earth's rotation, has a specific radius of approximately 42,164 km from Earth's center, which means the altitude is approximately 35,786 km above Earth's surface (Earth's radius being about 6,378 km).

User Jason Silver
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