Ok, so this is exactly what I have heard, and exactly what is baffling me.
So I understand Kepler, and why the farther out you are the slower you need to go. Otherwise, in the very much weaker gravity (inverse square law) you'd go flying off into space. What I don't get is the orbit changing stuff.
To go from a low circular orbit to a higher one, you fire your rocket behind you to pick up more speed. The "point" of the burn becomes the perigee of the new elliptical orbit, and half-way around is the new apogee. Ok, so far, so good. Now, if at the instant of apogee you did nothing, you'd fall back down to perigee, and back again to apogee on the next orbit. But since you fired your rocket to speed you up in the first place, to circularize the orbit you fire your rocket at the point of apogee to slow you down, and in fact to a slower speed than you started. I would think that would make you drop more steeply down on the next orbit, probably to a lower perigee than you started. Instead, I'd think you should fire in the same direction as the first burn, to make things round, but that would make you go even faster, which Mr. Kepler said was wrong.
My head is spinning (no pun intended)... Where did I go wrong?
Greg KO6TH
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Date: Fri, 15 Feb 2008 14:52:05 -0500 From: [email protected] To: [email protected] Subject: [amsat-bb] Re: Since We Are Off Topic Somewhat....
Bill Jones asked:
While discussing this topic of orbital decay, I wonder if someone would comment on the apparent anomoly whereby a sat in leo that encounters drag actually speeds up (since as it's altitude decreases, the orbital speed increases), and how this might be a factor in the comparison of the heating effects on an object that decays gradually from orbit vs an object like the shuttle that is taken out of orbit by actually reducing it's speed with thrust. I have my own intuitive theories on this but would like to hear more informed opinions.
What confuses people is that the orbital PERIOD (minutes/orbit) decreases with drag, and hence its reciprocal (measured in units like like orbits/day) increases. As the satellite gives up kinetic energy to heat, it falls into a lower orbit, where it must move faster. The relation is that the square of the period is proportional to the cube of the size of the orbit.
All this is is embodied in Kepler's 3rd law (see http://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion) which the Wiki states as:
* "The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axes (the "half-length" of the ellipse) of their orbits. This means not only that larger orbits have longer periods, but also that the speed of a planet in a larger orbit is lower than in a smaller orbit."An animated "movie" of Kepler's 3rd law can be seen at http://people.scs.fsu.edu/~dduke/kepler3.html .
73, Tom _______________________________________________ Sent via [email protected]. Opinions expressed are those of the author. Not an AMSAT-NA member? Join now to support the amateur satellite program! Subscription settings: http://amsat.org/mailman/listinfo/amsat-bb
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