[amsat-bb] Re: Geostationary Satellites

Ken Ernandes n2wwd at mindspring.com
Tue Oct 11 12:08:01 PDT 2011

Paul -

Your final suggestion is something that is workable.  Placing a satellite say 200 km below GEO would result in the satellite drifting about 10 minutes per day or about 2.5 degrees per day.  This would result in a cycle that repeats about every 144 days (or about 2.5 times per year), relative to a ground-based observer.  I'd need to see if 200 km is safe or if that might need to be increased.  An increase would correspondingly increase the drift rate.

As I said, that could be workable for an amateur satellite, but before the calls go out for this being AMSAT's next project we need to understand what we'd need to do, and what you'd actually be getting.

To get to such an orbit from a GTO would require about 950 m/sec of delta-V to raise perigee up and establish a nearly circular orbit, slightly below GEO.  If the propulsion system had 90% efficiency and we had a bi-propellant system with a 285 sec specific impulse (Isp), the propellant mass would be about 31.5% of the total spacecraft launch mass.  That is if we are willing to also accept the inclination that the launch booster dropped us off in.  I suspect we would accept the booster's inclination for reasons that we'll see.

Now I'd like to give a quick outline of the disturbing forces at GEO, since out spacecraft would experience similar effects.  

I'll start with what's commonly called Earth triaxiality.  Many of us know the Earth bulges at the equator.  So the first of the three axes is the Earth's rotational axis.  But the equator is not perfectly circular.  The equator itself has its own ellipsoidal shape, leading to two additional gravitational axes in the equatorial plane.  The result is that satellites on the GEO belt will tend to drift east or west (depending on location).  There are four equilibrium points, two of which are stable (about 75-deg E and 105-deg E) and two of which are not stable (about 12-deg W and 162-deg E).  The unstable points are the demarcations in which you will drift either east or west depending on which side of the that point you're located.  The stable points are the graveyards where all the dead satellites that haven't been boosted out of the GEO belt will collect.  The drift rate varies and is lowest near the equilibrium points and greatest at the mid-points between the equilibrium points.  Given the case of a sub-GEO orbit, the drift due to triaxiality is of little consequence since the drift due to thee altitude difference is far greater and triaxiality would be reduced to a secondary effect.  It was provided here for understanding of what we would need to deal with if we wanted to hold at GEO and not collide with out neighbors.

A very significant effect results from the gravitational pulls on the satellite by the Sun and Moon.  (To be completely accurate, this is the difference between the pulls on the satellite and the Earth by these bodies.)  This causes the inclination to cycle between 0 and approximately 15-deg over a period of about 53 years.  Anybody familiar knows that inclination change maneuvers require a lot of propellant.  Thus, I believe we would accept this slowly-changing inclination and realize that our antennas would need to adjust slowly over the course of the day in what is typically a figure-8 pattern.  Depending on your latitude, there may be periods when the satellite dips below your horizon.

A final effect to be considered is Solar Radiation Pressure.  The impact pressure from the Sun's photons impart momentum on the spacecraft, which in turn causes a slight change in velocity.  The main effect is a change to the orbital eccentricity.  For GEO satellites, eccentricity is manifest mainly by an east/west oscillation over the course of a day.  The larger the eccentricity, the greater the amplitude of the oscillation.  At first blush this may seem like an insignificant effect for out sub-GEO for the same reasons as we became unconcerned about triaxiality effects.  But eccentricity also equates to changes in altitude - precisely what we were using as our guard against colliding with satellites in the GEO belt.  So the long-term effects would need to be considered when choosing what we consider to be a safe separation from thee GEO belt.

I hope this is somehow helpful in understanding what AMSAT would really be up against if it  wanted to have an independent GEO satellite or consider a sub-GEO drifting orbit.

73, Ken Ernandes N2WWD

Sent from my iPad

On Oct 11, 2011, at 12:05 PM, Paul Williamson <kb5mu at amsat.org> wrote:

> On Oct 11, 2011, at 3:31 AM, Ken Ernandes wrote:
>> For those believing in the large space, small satellite theory, the risk of collision is more real than one might think.
> It must be, since I would think the risk of collision is so tiny as to be effectively negligible. If we position our satellite halfway between two of those commercial "slots", we have a huge buffer on either side. Now I realize that just measuring distances doesn't capture the whole story, and that orbital dynamics can be non-intuitive, but it boggles the mind that objects spaced that far apart can't be kept from colliding without extraordinary measures. 
> I would say that I'd like to see the analysis to back up the worry, but I doubt I'd understand it. You would, though, so I can only ask whether you have seen the actual analysis and found it compelling.
> Is there no clever trick of orbit design that can be used to avoid collision? We can afford bigger position errors than the commercial guys can, because we have smaller ground station antennas and no problem with interference crowding. We can even tolerate some long-term motion, since we can certainly accept an occasional adjustment to each ground station. Perhaps these extra freedoms would make it possible to design an orbit that's close enough to geosynchronous for our purposes, but far enough from the commercial orbits to be safe?
> 73  -Paul
> kb5mu at amsat.org

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