geosynchronous / geostationary

[beermat]

why is apx 36,000Km the orbit for geosynchronous satellites? Isn't any orbit (at the right speed) geosynchronous?

Comments

[jhaelan.livejournal.com]

http://liftoff.msfc.nasa.gov/academy/rocket_sci/satellites/geo-high.html

[lostcarpark.livejournal.com]

I shall try to answer this, but there are probably greater scientific minds who'll do a better job.

Imagine an object travelling through space. Let's assume it's not expending any fuel, so it's speed and direction will stay the same. Now, lets imagine a large nearby planet-like object. Our original object will be pulled towards the planet-like object. Now, if it's not going fast enough, it will be pulled in by the planet's gravity and burn up in it's atmosphere. On the other hand, if the object is going too fast, it will shoot right past the planet and off into space.

But if the object is travelling at just the right speed, the planet's gravity will alter it's course at the same rate that it is moving in a perpendicular direction. This has the effect that the object will circle the planet at a fixed distance form the planet. It is especially interesting because it requires very little energy to maintain the orbet. (In a perfect universe, it would be possible to maintain a stable orbit without expending any energy. However, there are many factors such as the upper layers of the Earth's atmosphere, the gravitational effects of the moon and other bodies that affect the orbit and make course corrections necessary.)

However, the speed an object must be travelling at to orbit the Earth at a given distance is fixed. The further an object wishes to orbit from the Earth, the faster it must be travelling. However, as the circumfrance of the circle it traverses increases by a factor of Pi, the time it takes to traverse the orbit increases. At a distance of 36Mm the orbit takes 24 hours, which means that the satellite appears to stay at a fixed point in the sky.

While it would be possible for an object maintain a fixed point in the sky at any distance form the Earth, it could only do so by consuming large amounts of fuel. This could not be considered an "orbit", and any satellite we could produce with current technology would expend its fuel supply within hours.