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 http://en.wikipedia.org/wiki/Square_%28algebra%29 of the orbital periods http://en.wikipedia.org/wiki/Orbital_period of planets are directly proportional http://en.wikipedia.org/wiki/Proportionality_%28mathematics%29 to the cubes http://en.wikipedia.org/wiki/Cube_%28arithmetic%29 of the semi-major axes http://en.wikipedia.org/wiki/Major_axis (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 http://people.scs.fsu.edu/%7Edduke/kepler3.html.
73, Tom