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To create a program to explore the mechanics and mathematics behind earth orbiting satellites.
Background & Techniques
This is a first adventure into Celestial Mechanics to convince myself that satellites can really orbit the earth and, by extension, planets orbit the sun. I previously thought that if an orbiting satellite dropped just a little closer to the earth gravitational forces would increase and force it into a death spiral..
Web descriptions talk about centripetal force as if that were the another
force which held the answer. But trying to incorporate centripetal force into the explanation didn't help much
because it turns out that gravity IS the centripetal force that keeps the satellite from
flying out into space. So if there is only one major natural force acting on the
satellite to drag it down, what holds it up? The answer lies in Newton's
of motion - things like to keep moving in a straight line. So if we didn't have
gravity (and air drag) we could toss a baseball and hit the
This horizontal component likely came from the rocket that put us into orbit
initially but in this simulation it is like a cannon firing from a really tall
tower . If the forward (tangential) speed is high enough, we'll miss the earth
as we fall toward it and continue on past at which point gravity works to turn
us around and drag us back. So if we don't give the satellite a big enough
initial push, it will fall to earth somewhere before it get back around to the
start point. If we give it too big a push, it will fly off into space
never to return. The speed at which this happens is called, naturally
enough, the "escape velocity" and is a function of altitude. In
theory as initial velocities increase orbits start
when the satellite just clears the earth on the far side and as starting velocities increase, become
circular and then increasingly
eccentric (longer and skinnier) until escape velocity is reached..
Escape velocity is approximately 1.4 ( square root of 2 ) times the circular orbit
Here are some program notes:
Non-programmers are welcome to read on, but may want to jump to bottom of this page to download the executable program now.
Coming soon. (How often have you seen this on websites? ) I'm tired this week, write with your questions.
Suggestions for Further Explorations
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