How Does a Satellite Maintain a Stationary Position Above Earth?

[ilkjester]

Homework Statement

The weather pictures you see every day on TV come from a spacecraft in a stationary position relative to the surface of Earth, 35,700 km above Earths equator. Explain how it can stay exactly in position day after day. What would happen if it were closer? Farther out?

Homework Equations

The Attempt at a Solution

Well I was thinking that a spacecraft would be going the same exact speed as the orbit of Earth except in the opposite direction. But then i realized that couldn't be it. Because it still wouldn't follow the same place on Earth it would just be in the same place in space. So while i was just typing this i thought it would be going the same speed as in the orbit Earth in the same direction. And sort of like following it.

 

[saket]

These are called geo-stationary satellites. You are now on the correct track, I presume.
Hint : You know angular speed with which Earth rotates. Satellite must have the same. The satellite has to remain stable in that orbit. Thus, forces must be balanced on it. Do it, to get the required distance. Furthermore, looking at the same equation .. you should be possible to answer the remaining part. (Well, you can apply common sense of nature as well -- everything proceeds towards stability.)

 

[ogb p]

So, to answer the question, a satellite in a stationary position relative to the surface of Earth, 35,700 km above Earth's equator, is able to stay in that position day after day because of its geostationary orbit. This means that the satellite is orbiting at the same speed and direction as the rotation of Earth, allowing it to appear stationary from our perspective on Earth. This is possible due to the balance between the satellite's centripetal force, caused by its orbital velocity, and the gravitational force of Earth pulling it towards the center.

If the satellite were closer to Earth, it would have a shorter orbital period and would appear to move faster from our perspective. This would make it difficult to constantly receive and transmit accurate weather data. On the other hand, if the satellite were farther out, its orbital period would be longer and it would appear to move slower. This could result in delays in receiving and transmitting data, as well as potential issues with maintaining a stable orbit. Therefore, the specific distance of 35,700 km is crucial for a geostationary satellite to effectively gather and transmit weather data.