Satellite Tracking

The following is from an email I sent my mates. What I'm trying to do
is some 'Satellite Spotting', where you can see one going past and try
to work out its orbit. This is a start... Do you reckon I've got it
right? Have about 2 pages of working out...

* * *

The principle of the whole thing is that the higher the orbit, the
slower the satellite moves. So it's impossible to confuse a
fast-moving distant satellite with a closer slow-moving one. Speed
across the sky determines the altitude.

I deduced the following equation:

Altitude in miles = 17645/((62.83 x Apparent Velocity) + 1.88)

Where Apparent Velocity is measured in degrees per second (i.e. if it
flew right from one horizon to the other in a second, that would be
180 degrees per second).

That equation contains a very slight approximation that is negligible
if the altitude is under 1000 miles. Also, it doesn't take into
account the rotation of the earth relative to the satellite (shouldn't
be too much nearer the poles).

I tried it out by holding a small stick at arm's length and timing how
long the satellite took to go from one end to the other. A rather
crude method but one which should give a rough answer. The answer I
came up with was 600 miles. The actual equation came up with 650, but
it wasn't directly overhead which made it a bit inaccurate (that's
another of the assumptions, that the satellite is directly overhead).

I think that's a sensible result. If it had been 125 miles or less
that would have meant it was in the process of burning up in the
atmosphere. 625 miles upwards the Van Allen Radiation belts start and
satellites generally aren't in that zone due to the electronics
getting messed up. It looked like a very slow moving satellite
compared to most that you see and given the extreme crudeness of the
experiment I suppose it's a reasonable result.

Oh well. In future I hope to be able to measure a satellite's orbit
more accurately. Taking account of stuff like the oblateness of the
Earth, the gravitational pull of the Moon and so on would probably
require a supercomputer and a double doctorate from Harvard, but using
slight approximations it would be good to calculate an orbit with
enough accuracy to predict when the satellite will next appear
(roughly)...

That's the science bit over with for tonight!

P

* * *

I don't think I could measure the path and speed of a satellite
accurately enough to exactly predict the orbit and its next
appearance, plus as I said there are a million other complex factors.
But... I think what I might try is looking at one of the slower moving
higher up ones... predicting the path and looking for its reappearance
(even if it is in the wrong part of the sky, with higher ones they are
visible over a larger area of the Earth so I can afford to be less
accurate). Then I would have two readings to go on instead of one and
perhaps I could work out its orbit from several observations.

The way I see it, any satellite follows an arc through the sky. The
highest point of this arc is when the satellite is nearest, and if you
face towards this point, then the path the satellite follows is
perpendicular to the line from you to below that point. If that makes
any sense...

Anyway, far too busy with coursework and stuff to be bothering with
all this at the moment, but it's a project for when I'm less busy!
Unfortunately I don't think this is the best time of year for this
kind of thing, if it got dark earlier I could phone a mate in London
(I'm in Devon) and see if they could see the same satellite but in a
different position. But this time of year that would be at about
midnight.