Thanks for posting these responses Bob, your explanations are quite clear.. I wish my high school physics professor had been nearly as clear. Your answer made me think.. if the ellipse crosses the path of the earth (or a path through enough atmospheric resistance that sufficient energy is lost) it will not continue to orbit. Simple enough. What I'm interested in, then, is how do you determine if an object has sufficient energy to escape orbit entirely? I can comprehend that the gravitation between two objects is inversely proportional to the square of the distance between them.. that at least "stuck" back in school.. so as near as I can figure, if you double the distance of the orbiting object from the center of the earth, it would take 4 times less speed to escape. Is that even in the ball park? I'd imagine, from that, that given a measure of gravitational pull on a measurable mass you could derive a speed at which the forces would no longer be equal, and the ellipse would never return back to the original spot.
I'd once set a goal for myself of being able to do at least the rudimentary math involved in how the Apollo missions were able to orbit the Moon, even assuming the two objects were stationary, but since I never learned Calculus to me it's all just squiggles. I appreciate plain language explanations like yours.
Thanks for the elucidation,
Jason - N1XBP
BTW, if anyone else is as curious as I am, I found the ARRL Extra class study guide to have an easy to read and understand section on Kepler's laws.
Robert Bruninga wrote:
Obviously the further out, the longer it takes to do a revolution. I imagine at some point earths gravity will not be sufficient to hold an object of given mass in a circular orbit?
Exactly, If you are at a given altitude and you are going to slow, then your satellite will "fall" towards earth.. But as it falls, it speeds up as it approaches its lowest point (on the other side) and that makes it go higher to arrive back where you are on this side... In otherwords, the circular orbit becomes an elipse with a high side and a low side.