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RE: [ans] ANS 090 (Incorrect explanation of Arg. Peri.)

Maybe a better drawing would have gotten Argument of Perigee
correct.  Think of putting your pencil on the globe at the
subsatellite point of any satellite at its perigee.  Follow
the trace that is on the ground in the plane of the orbit
as it cuts the surface of the earth.  If the earth were a
sphere, this would be a circle and for our purposes, it is
close enough. From the subsatellite point of the perigee to
the subsatellite point of the apogee, 1/2 of the circumference
of a circle is drawn on the globe or surface.  Also starting
at perigee, you follow along the trace on the surface
on the earth made by the orbital plane until you get to the
subsatellite point where the satellite orbit cuts across the
equator going from south to north.  This is the ascending
node.   If the apogee subsatellite point occurs after this,
then the argument of perigee is LESS than 180 degrees and
thus the apogee is in the NORTHERN hemisphere and the
perigee is in the southern hemisphere.  Similarly, if the
subsatellite point for the apogee occurs BEFORE we have
reached the ascending node, then the argument of perigee
is greater than 180 but the apogee is in the SOUTHERN
hemisphere and the perigee is in the northern hemisphere.

If you project a line from the center of the earth, through
the ascending node to the stars, then since the ascending
node is on the earth's equator,  this will go out and touch
the celestial equator.  The coordinates touched on the
celestial equator, which is called Right Ascension and is
given in hours by astronomers and degrees by orbital mechanics
types is thus the Right Ascension of the ascending node.
Zero degree Right Ascension means the satellite goes north
across the equator at exactly the same spot the sun's "subsat"
point goes north of the equator.

I hope this throws me light on the subject than dust in the


-----Original Message-----
From: owner-ANS@AMSAT.Org [mailto:owner-ANS@AMSAT.Org]On Behalf Of Dan
Sent: Monday, April 01, 2002 12:37 AM
To: 'ANS Release'
Subject: [ans] ANS 090

ANS 090

SB SAT @ AMSAT $ANS-090.01

BID: $ANS-090.01

AO-40 ground control station W4SM recently reported on the latitude drift
of AO-40's sub-satellite (apogee) point. The sub-satellite point of latitude
at apogee is a function of argument of perigee and the inclination of the
satellite's orbit. The greater the inclination, the more the variability.

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 equatorial plane headed north (ascending
node). If ArgP = 0 or 180, then apogee is over the equator. When ArgP
is less than 180 degrees, the apogee is in the southern hemisphere.
When ArgP is greater than 180 degrees, apogee is in the northern
hemisphere. For AO-40, ArgP is currently ~32 degrees, and increasing
0.3251 degrees each day. The duration of a full cycle is a little over

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 degrees in mid-2001, to the current value
of 7.3 degrees. Orbital element integration, factoring in solar, lunar, and
terrestrial forces show that inclination will continue to increase until
it peaks at approximately 10.3 degrees in the spring of 2004. As AO-40's
inclination and eccentricity change due to these forces, the rate of
change of ArgP will fluctuate very slightly as well.

>From a northern hemisphere perspective, the low point for elevation of
AO-40 at apogee will occur in the fall of this year. Apogee elevation will
then improve, peaking 18 months later (in the spring of 2004).

AO-40 is currently experiencing eclipse periods of nearly 30 minutes.
During a recent eclipse period, both the magnetorquers and beacon
were on when the IHU detected that the battery was running low,
triggering the low-voltage software-which turned the S-2 transmitter off.

For the last three orbits, the battery voltage during the final 45-seconds
of  the eclipse period has dropped to the point where it has triggered
S-2 shutoff.

The shutoff is set very conservatively and the scheduling software has
restarted the S-2 transmitter at MA-15 nominally each time. W4SM
lowered the shutoff threshold by one count, and this should be
sufficient to prevent further eclipse shutoffs for this cycle. If not,
additional adjustments will be made.

The current perigee eclipse cycle runs through June 19th. From
August 13th to September 18th, AO-40 will experience much longer
non-perigee eclipses that peak at 165 minutes duration. During these
eclipses the S-2 transmitter will be turned off by the scheduler.

[ANS thanks the AO-40 team for this information]


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