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Re: AO40 orbit drifting south, then north?

The drift in the latitude of AO-40's subsatellite point at the time of 
apogee is an interesting topic. The subsatellite point latitude at apogee 
is a function of argument of perigee and the inclination of the orbit. The 
greater the inclination, the more the variability. Those who remember 
AO-13, will recall how dramatic this change was due to its much higher 

Argument of Perigee (ArgP) needs a drawing to fully visualize, but it 
represents the angle between the perigee of the orbit and the point where 
the orbit crosses the earth's equatorial plane headed north (ascending 
node). If ArgP = 0 or 180, then apogee is over the equator. When ArgP is 
less than 180 degs, the apogee is in the southern hemisphere. When ArgP is 
greater than 180 degs, apogee is in the northern hemisphere. If ArgP = 270 
deg., then apogee is as high as possible in the northern hemisphere. At 
this time the subsatellite latitude at apogee is the value of the 
inclination angle. If ArgP = 90 degs, then apogee is as high as possible in 
the southern hemisphere. At this point the latitude is the negative 
inclination angle. ArgP changes with time due primarily to the oblateness 
of the earth. Mathematical equations are available to precisely predict 
this change which is a function of inclination, and major/minor axis 
lengths. For AO-40, ArgP is currently ~32 degs, and increasing 0.3251 
deg/day. The duration of a full cycle is thus a little over 3 years.

Inclination is a measure of the tilt of the orbital plane with respect to 
the earth's equatorial plane. For satellites with highly elliptical orbits 
such as AO-40, the inclination is subject to significant solar/lunar forces 
which tend to alter it in a non-linear fashion. AO-40's inclination has 
been increasing from about 5.2 degs in mid-2001, to the current value of 
7.3 degs. Orbital element integration, factoring in solar, lunar, and 
terrestrial forces shows that inclination will continue to increase until 
it peaks at approximately 10.3 degs in the spring of 2004. As inclination 
and eccentricity change due to these forces, the rate of change of ArgP 
will fluctuate very slightly as well.

In the northern hemisphere, the maximum elevation of a satellite with 
respect to the southern horizon is a function of the latitude of your QTH, 
the latitude of the subsatellite point, and the altitude of the satellite. 
At infinite satellite altitude, the maximum elevation from the southern 
horizon in the northern hemisphere is:

(90-QTH latitude) + SubSat Latitude
(max. el. > 90 indicates pass to the north of QTH)

The true maximum elevation decreases from this theoretical maximum value as 
the satellite altitude decreases. This decrease is only a few degrees for 
AO-40, but is highly significant for LEO's. From a northern hemisphere 
perspective, the low point for elevation of AO-40 at apogee will occur in 
the fall of this year when ArgP = 90 degs.  Apogee elevation will then 
improve, peaking 18 months later in the spring of 2004, when ArgP = 270 
degs. Beneficially from our perspective in the north, inclination also 
peaks at 10.3 degs during this time. Thus, the subsatellite latitude at 
apogee will be 10 degs into the northern hemisphere in the spring of 2004. 
Running orbital predictions during these two time periods will show the 
difference in maximum elevation at your QTH. My maximum elevation in 
Virginia, for October 2002, will only be 41 degs, but for March 2004, 
maximum elevation will be 56 degs.  Using the simple equation above, 
theoretical maximum elevation at infinite satellite altitude for my 38 deg. 
QTH latitude and +10 deg subsatellite latitude = 62 degs.

  Stacey E. Mills, W4SM    WWW:    http://www.cstone.net/~w4sm/ham1.html
    Charlottesville, VA     PGP key: http://www.cstone.net/~w4sm/key

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