Equation for Satellite in geosynchronous oribt

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However, since you cannot use velocity in the solution, you will need to find another equation that relates the orbital period, angular velocity, and radius. In summary, to find the velocity of a satellite in geosynchronous orbit around Earth without using r, you can use the equation V=Sqroot of G*Me/r, where Me is the mass of Earth. And to find the radius of a satellite in geosynchronous orbit without using velocity, you can use the equation for centripetal force and find an equation that relates the orbital period, angular velocity, and radius.
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emerica1254
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Homework Statement



Find Velocity of satellite in GS orbit around Earth but you cannot use r in the solution

And find r of satellite in GS orbit but you cannot use velocity in the solution

Homework Equations



V=Sqroot of G*Me/r, Me being the mass of the Earth but you can't use r from this equation

The Attempt at a Solution


I know at GS the satellite would travel around the Earth in 24 hours and a full revolution around a circle is 2pi, so i can get the angular revolution but then i can't figure out v without using r still
 
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The velocity depends on the radius r. I am not sure how they want you to answer the first part.

As for the second part, you can get out easily by using the centripetal force =mω2r
 

1. What is the equation for calculating the orbital speed of a satellite in geosynchronous orbit?

The equation for calculating the orbital speed of a satellite in geosynchronous orbit is given by v = √(GM/R), where v is the orbital speed, G is the gravitational constant, M is the mass of the Earth, and R is the distance between the satellite and the center of the Earth.

2. How is the radius of a geosynchronous orbit determined?

The radius of a geosynchronous orbit is determined by the distance from the center of the Earth to the point where the satellite's orbital period is equal to the Earth's rotational period, which is approximately 22,236 miles or 35,786 kilometers.

3. What is the significance of a satellite being in geosynchronous orbit?

A satellite in geosynchronous orbit appears to be stationary in the sky from the perspective of an observer on Earth. This allows the satellite to maintain a constant position over a specific location on the Earth's surface, making it ideal for telecommunications and weather monitoring.

4. How does the equation for satellite in geosynchronous orbit differ from other orbital equations?

The equation for satellite in geosynchronous orbit is similar to other orbital equations, but it includes the additional factor of the Earth's rotational period. This is because the satellite's orbital period must match the Earth's rotational period for it to remain in a fixed position in the sky.

5. Can the equation for satellite in geosynchronous orbit be used for any type of satellite?

No, the equation for satellite in geosynchronous orbit is specifically for satellites in geosynchronous orbit. Other types of satellites in different orbits will have different equations for calculating their orbital speed and radius.

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