# RE: PAS 1R

From: Randy John (rjohn@axarosenberg.com)
Date: Wed Apr 03 2002 - 16:23:05 EST

• Next message: Robert G Fenske Jr: "Re: 23h 56m vs 24h"

```Jonathan,
The GEO is NOT "synchronous with the stars".  That would be a satellite that is not moving at all but hanging in space with the Earth rotating under it.  The period of the Earth and a GEO with respect to the stars is 23:56:04.  The period of the
Earth and a GEO with respect to the Sun is 24:00:00.  If you measure the periods with respect to anything else you will get some other number but they will be the same.

The Mean motion given in a TLE is "with respect to the stars".  In order to see if it is geosynchronous you must compare it to the rotation period of the earth "with respect to the stars".

wrt to stars        wrt to Sun
Earth       23:56:04          24:00:00
GEO         23:56:04          24:00:00

Notice that both the Earth and the GEO have the same period as long as you use the same column.

The only reference frame that makes sense from physics point of view is a non-rotating one ("with respect to the stars") and that is what is shown in a TLE.  The 24 hour day is very convient for those of us to live by the sun but it is actually quite
arbitrary.  One might as well measure periods with respect to Mars or Pluto.  Measuring the period of Earth's rotation wrt the Sun links the period of rotation to it's period of revolution.  If you were to suddenly place the Earth in a 6 month orbit the
rotation period wrt the Sun would change but the period wrt to the stars (sidereal period) would remain the same.

I hope this clears up everyone's confusion about this point but it probably won't.  It is very difficult to let go of our solar bias.  Imagine viewing the Earth from a distant star through a telescope whose field of view only includes the Earth (no Sun).

I hope that people will praise Jonathan for his question rather than flame him.  I'm sure that many others are confused by this point.  I know I was when I first learned it.
Randy

-----Original Message-----
From: Jonathan T Wojack [mailto:tlj18@juno.com]
Sent: Wednesday, April 03, 2002 12:51 PM
To: SeeSat-L@satobs.org
Subject: Re: PAS 1R

> The earth rotates once every 23 hours 56 minutes 4 seconds RELATIVE
> TO THE STARS (24 hours 0 minutes 0 seconds, on average, relative to
> the sun).

That I know, and agree with.

>And incidentally, the "1.00270296" revolutions per
> [24-hour]
> day in the TLE may well include small factors due to perturbations,
> but that is not the major issue here; the true sidereal rotation
> period of the earth is 24 hours / 1.0027379.. .

The difference between the two figures amounts to 2.59 seconds per day.

But what is the point in making a geosat synchronous with the stars?
It's not going to stay over an area of Earth (more or less).  What is the
purpose for a geosat to track the stars?

------------------------------
Jonathan T. Wojack                 tlj18@juno.com

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