# [amsat-bb] Re: Since We Are Off Topic Somewhat....

Tom Clark, K3IO k3io at verizon.net
Fri Feb 15 11:52:05 PST 2008

```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
```

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