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*Subject*: R: [amsat-bb] Re: AO40 orbit drifting south, then north?*From*: "i8cvs" <domenico.i8cvs@xxxxxx>*Date*: Wed, 27 Mar 2002 05:27:47 +0100

----- Original Message ----- From: Stacey E. Mills <w4sm@cstone.net> To: <amsat-bb@AMSAT.Org> Sent: Tuesday, March 26, 2002 11:51 PM Subject: [amsat-bb] 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 > inclination. > Hi Stacey, The greater the inclination, the more the variability is not completely correct. If the inclination ( i ) is 63.34 degrees the line of the apsis that join the apogee with perigee do not rotate at all and so the rate of change of the argument of perigee ( W ) is zero degrees and the satellite subpoint SSP at apogee stay constant for ever. If the inclination is less than 63.34 degrees the line of the apsis rotate in the same direction of the satellite motion along the orbit and the rate of change of the argument of perigee is greater as more the inclination is low than 63.34 degrees. In this case the apogee subpoint as seen from the ascending node moves from the southern hemisphere to the the northern hemisphere. If the inclination is greater than 63.34 degrees the line of the apsis rotate in a direction wich is opposite to the satellite motion along the orbit and the rate of change of the argument of perigee in this case is greater as more the inclination is higher than 63.34 degrees. In this case the apogee subpoint as seen from the ascending node moves from the northern hemisphere to the southern hemisphere. The equation to calculate the rate of change of the argument of perigee ( W ) in 24 hours,not including pertubations due to moon and sun is the following: 5 2 (W ) = ------------------------------ x ( 5 cos i - 1 ) 7/2 2 2 ( a / R ) x ( 1 - e ) where: a= orbit semimajor axis in Km R= radius of the earth at the equator ( average 6378.388 Km ) e= orbit eccentricity i= orbit inclination in degrees The key of the formula is the second term because it became zero for i= 63.34 degrees,positive for i < 63.34 degrees and negative for i > 63.34 degrees > 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. > Aegree 73" de i8CVS Domenico > > > -- > ________________________________________________________________________ > Stacey E. Mills, W4SM WWW: http://www.cstone.net/~w4sm/ham1.html > Charlottesville, VA PGP key: http://www.cstone.net/~w4sm/key > ________________________________________________________________________ > > ---- > Via the amsat-bb mailing list at AMSAT.ORG courtesy of AMSAT-NA. > To unsubscribe, send "unsubscribe amsat-bb" to Majordomo@amsat.org > ---- Via the amsat-bb mailing list at AMSAT.ORG courtesy of AMSAT-NA. To unsubscribe, send "unsubscribe amsat-bb" to Majordomo@amsat.org

**Follow-Ups**:**Re: R: Re: AO40 orbit drifting south, then north?***From:*Stacey E. Mills

**References**:**Re: AO40 orbit drifting south, then north?***From:*Stacey E. Mills

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