Angular Momentum: Earth vs Geo-Stationary Satellite

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A geostationary satellite moves with the same angular velocity as the Earth, resulting in it appearing at rest to observers on the ground. This characteristic is what defines geostationary or geosynchronous satellites. The ability to maintain a fixed position in the sky allows for permanent installation of satellite dishes aimed at a specific location. Consequently, users do not need to adjust their dishes to track the satellite's movement. This functionality is essential for reliable communication with the satellite.
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suppose the angular momentum of the Earth is omega (w) and a geo stationary satellite also moves with the same angular velocity then will the people on Earth see the satellite at rest or in motion??
 
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It will be at rest relative to people on the Earth, that's where they get their name geostationary/geosynchronous satellites.
 
It will appear at rest to the people on the ground, that is the whole point. That way you can bolt a satellite dish on the ground permanently pointing at the one patch of sky where the satellite sits that it is communicating with and not have to worry about the dish tracking the satellite.
 
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