Calculating the Radius of a Geosynchronous Satellite Orbit Around Earth

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In summary, a geosynchronous satellite is a satellite that orbits the Earth once every 24 hours in an equatorial orbit, appearing stationary with respect to a ground station. Its orbit can be calculated using the following equation: v = 2(pi)(r)/T, where v is the orbital velocity, r is the radius of the orbit (measured from the center of the Earth), and T is the orbital period. To incorporate gravity, the equation would be: v = sqrt(GM/r), where G is the gravitational constant, M is the mass of the Earth, and r is the radius of the orbit.
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aligass2004
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Homework Statement


http://i241.photobucket.com/albums/ff4/alg5045/MUG_co_6.jpg

A satellite that goes around the Earth once every 24 hours is called a geosynchronous satellite is in an equatorial orbit, its position appears stationary with respect to a ground station, and it is known as a geostationary satellite.

Find the radius R of the orbit of a geosynchronous satellite that circles the earth. (Note that R is measured from the center of the earth, not the surface) You may use the following constants:

G=6.67*10^-11
mass of the Earth = 5.98*10^24 kg
radius of the Earth = 6.38*10^6 m


Homework Equations





The Attempt at a Solution



I have no idea how to even begin this problem.
 
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  • #2
What is a geosynchronous satellite's orbital period? What are the relevant equations regarding orbital period?
 
  • #3
The orbital period is 24 hours or 86400 seconds. I think the relevant equation is v = 2(pi)(r)/T.
 
  • #4
You aren't incorporating gravity. You need to do that.
 

Related to Calculating the Radius of a Geosynchronous Satellite Orbit Around Earth

1. What is a geosynchronous satellite?

A geosynchronous satellite is a type of satellite that orbits the Earth at the same speed and direction as the Earth's rotation, allowing it to remain in a fixed position relative to a specific location on the Earth's surface.

2. How does a geosynchronous satellite work?

A geosynchronous satellite works by orbiting the Earth at an altitude of approximately 22,236 miles (35,786 kilometers) and at the same rate as the Earth's rotation. This allows the satellite to maintain a fixed position over the Earth's surface, making it ideal for telecommunications and weather monitoring.

3. What are the benefits of using geosynchronous satellites?

The main benefits of using geosynchronous satellites include their ability to provide continuous coverage over a specific location on the Earth's surface, making them ideal for communication and broadcast services, as well as weather monitoring and navigation.

4. How are geosynchronous satellites different from other types of satellites?

Geosynchronous satellites differ from other types of satellites in their orbit and positioning. Unlike low-Earth orbit satellites, which have shorter orbital periods and move across the sky, geosynchronous satellites remain in a fixed position above the Earth. They also differ from medium-Earth orbit satellites, which have higher orbits and longer orbital periods.

5. What are the potential challenges of using geosynchronous satellites?

One potential challenge of using geosynchronous satellites is the high altitude at which they orbit, which can result in longer signal delay times and potential interference from other satellites. Additionally, since they remain in a fixed position above the Earth, they are not ideal for imaging or surveillance purposes. Another challenge is the limited number of orbital slots available for geosynchronous satellites, which can lead to overcrowding and potential collisions in space.

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