Geosynchronous Orbits
Published on Mar 22, 2006 at 11:01 am.
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Filed under Earth, science fiction, space exploration.
A bit over a decade ago, I remember watching an episode of Star Trek:  Next Generation in which Captain Picard orders the Enterprise to go into a geosynchrnous orbit over a planet’s south pole. That is not possible, even in the world of Star Trek! Let me explain why not.
Let’s get straight just what we mean by orbit. First, think back to Newton’s Laws of motion. Newton’s first law says that a body will remain in uniform motion unless a force is applied to it. Thus, if there were no force on an object, it would move in a straight line without changing speed or direction. An orbit occurs when a body is moving in such a way that through no action on its own part it follows a path through space around another object. This means that the path is a curve, not a straight line. The most commonly found orbits would be a body (satellite or planet) moving around something else (planet or star) as a result of gravitational forces between the two bodies. The easiest orbits to understand are circular orbits, so we’ll stick with them for this posting. Without any applied force, the orbiting body would fly off into space along a straight line. So, some force must act on the object deflecting its path. If this force always acts perpendicular to the object’s motion, then it will not make it speed up or slow down. Instead, this force will simply change the direction of motion. If the force remains constant, then the bending of the path will be constant as well. The gravitational force is spherically symmetric and its magnitude depends only upon the distance between two objects. So, as long as you are a certain distance from a massive body, you will experience the same magnitude force, and that force will always be directed towards that body. A circle is a shape that is always the same distance from its center, and the line between the edge of the circle to the center (the radius) is always perpendicular. Thus, a circular orbit of one object with mass around another object with mass would always have a force of constant magnitude directed perpendicular to the motion. This meets our criteria for an orbit.
However, there is a very important relationship between the size of an orbit, the speed of the orbit, and the strength of the force making the orbit. The faster that an object goes, the bigger the force needed to make an orbit of the same size. The slower it goes, the less the force needed to make the orbit that size. Gravitational forces depend upon distance, so the farther the bodies are from one another, the weaker the forces. The distance between the objects also determines the size of the orbit (the circumference of the circle is pi times the diameter of the orbit). So, there is only a certain speed that matches a certain altitude orbit. The higher the orbit, the slower the speed, and the longer it takes to go around. So, for an orbit around a planet, at a certain distance out, the orbit matches the rotational rate of the planet. So, an object that orbiting at that distance will appear to move around the planet at just the same rate that the planet rotates. If the direction of orbital motion is the same as the direction of planet rotation, then an orbiting object will appear to hang over one spot on the planet. For Earth, we call this a geosynchronous orbit, and it is at about 22,300 miles altitude.
An important point, though, is that the orbit must be in the SAME direction as the rotation of the planet. Also, the line from the orbit to the center of the planet must be the same as the line from the orbit to the center of the orbit’s circle. Both of these conditions are only met for a very specific orbit — an orbit over the equator of the planet in the direction of the planet’s rotation. So, Picard’s order for a stationary orbit over the south pole wouldn’t work. That would require the Enterprise to simply hover over the south pole without moving. That could only be done by continually firing the Enterprise’s engines to hold it at altitude. Well, I guess if you have fuel to spare you could do that, but …
Anyway, that’s just something that popped into mind while thinking of what might be something to blog about.
-Astroprof
