# Fwd(2): Re(2): camcorder tracking of Mir/STS

From: Bjorn Gimle <Bjorn_Gimle_at_lector.kth.se>
Date: Mon, 19 Jun 1995 12:01:08 -0400

David, Robert, Bart (though on vacation),

I have seen no reaction on this mail, which I sent on June 07 to David and
seesat-l.
I usually save my my outgoing mail until I get the seesat-l forwarding, or a
response.
In this case, I don't seem to have received anything.
>> Can you tell me if it did reach seesat-l and/or you, David ?

It didn't reach Robert, so I re-post it on seesat-l.
(Sorry for another set of duplicates, Robert !)

Re: Re: camcorder tracking of Mir/STS

>Robert Preston <rapr_at_med.pitt.edu> wrote:
>>> David, I don't know a formula but it's a trivial calculation from
>>> the orbital inclination and RAAN figures in the TLE. Just subtract the
>>> relevant angles, using your latitude. It's elementary solid geometry.

> Observer's latitude should have nothing to do with it surely?
> a quick bit of doodling led me to the conclusion that:
> the pole of a satellite's orbit is at
> declination=90-inclination degrees,
> R.A.=R.A.Ascending Node - 6 hours.
> Does that sound right?

That sounds just like I interpreted it from the other mails/answers.
It had me fooled for quite some time, but here are my conclusions:

A LowEarthOrbit object is observed for only a small arc, so its motion
is nearly linear, and results in a near great circle on the sphere.
If that is considered true, its pole is 90 degrees off, at
alt./elevation = 90 degrees - culmination elevation
azimuth = culmination azimuth +- 180 degrees
and the satellite moves along the "equator".
To account for the curvature of the orbit, and the rotation of earth
below it, you can convert two predicted points to rectangular coordinate
vectors, and take the vector (cross) product to get the direction of the
pole, and convert it back to spherical. You can use either alt/az or
RA/dec for this, or you can convert in the process. If you work in RA/dec
you will actually find a point which moves with the stars, so the way to
get a fix point to use as instrument axis, you should convert RA to
hour angle = siderial time-RA before computing, then back to RA using
the siderial time of the time when you set up the instrument.

To account for the fact that the satellite does not move along a great
circle, take three predicted points. Then compute the point (near the
first mentioned points) which has a constant distance (usually 90-100
degrees) from the three (or best fit to more than three) points.
I.e. the satellite moves slightly below the "equator".

I have worked through all the above methods, using an actual MIR
prediction from QuickSat. If you, or anyone else, wants the test
case and my formulae, I will mail or post them, whichever is appropriate.

> I note RAAN seems to be decreasing at about 5.0deg/day. Why? Drag?

RAAN (and AOP) moves because of Earth flattening (attraction from
equatorial bulge). I remember a formula from my early satellite days,
which includes (i)nclination, (e)xcentricity and semi-major (a)xis.
If you have MM more readily available it can be approximated by

RAANdot = ( -10 cos i ) * (MM/17.1)**(7/3) / ( 1- e*e ) ** (7/2)

Again, I verified it, and the required conversion variants, and can
mail it.

On the other hand, if you still have any use for RAANdot, you can
compute it from two elsets with Epochs not too close or distant
from each other !

Robert Preston wrote :
> What I meant was NOT
> tracking in the sense that the program controlled the scope to track the
> satellite (I use a Macintosh and a Meade LX200 and am not aware that any
> program exists to make this scope track anything - [except stars!]).

Alphose Puplier (pouplia_at_interpac.interpac.be) answered in a
"Videotaping ..." message (rather than "Camcorder..") how he
actually tracks satellites by computer scope drive.
He has also mentioned his programs and BBS in previous postings.

=========================================================
Bjorn_gimle_at_lector.kth.se == bjorn.gimle_at_duesenberg.se ==
== bjorn.gimle_at_online.dextel.se ; 59.22371 N, 18.22857 E
=========================================================
Received on Mon Jun 19 1995 - 12:26:16 UTC

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