Astrodynamics Group
Repeat Ground Track Orbits
On Tuesday 14th December 1999 we fired the two pitch thrusters on the UoSAT-12 cold gas system having rotated the satellite to align these thrusters with the orbital velocity vector. The firing duration was 200 seconds and the maximum disturbance to the spacecraft attitude during this time was less than 5 degrees.
The reason for this firing was to lower the altitude of the Uosat-12 orbit placing it into a repeat ground track orbit. This kind of orbit guarantees that a sub-satellite point will map out a pattern over the Earth's surface which will close. The closure of the pattern happens after a discrete number of days and so enables a satellite to revisit points along this track repetitively so monitoring changes in these locations.
In the case of UoSat-12, the pattern closed after 7 days which corresponded to 102 orbital revolutions of the satellite about the Earth. The pattern over the Earth's surface is shown above.
Since our groundstation is at Guildford, Surrey (UK) then it was imperative that the closed groundtrack should provide a high pass over Guildford in order to upload commands to the satellite and download imagery. This requires the orbit to be phased correctly as it passes over the equator. This was performed in stages where the altitude of the spacecraft was controlled automatically just outside of the repeat groundtrack conditions causing the track to slowly drift over the face of the Earth. By slowly bringing it into the correct phase we guaranteed that the satellite would have two passes directly over Guildford.
The eccentricity of the orbit also needs to be small as otherwise the altitudes at which the satellite passes over a given location along its ground track will vary and this will need to be compensated for when comparing imagery.
The orbital manoeuvre of UoSat-12 was performed entirely autonomously using an onboard GPS receiver for navigation. The onboard computer estimates the current orbital parameters of the satellite using the analytic epicycle model and then adjusts them in a feedback loop to bring the altitude into resonance. This required an altitude change of 323 meters which was performed using cold gas thrusters providing a thrust level of 5.274 cm/sec per minute firing.
Once the satellite is locked into the repeat groundtrack orbit we need to maintain the satellite in this orbit countering the effects of Earth oblateness and atmospheric drag. The oblateness of the Earth causes a small drift in the ascending node of the orbit which can be corrected for by a small adjustment to the altitude. For UoSat-12 we determined a reisdual drift rate of 0.026 degrees/week (or 13 arc secs per day).
Atmospheric drag requires constant correction for, and as the drag rate is quite variable needs to be estimated autonomously on the satellite. Our orbit maintenance algorithm relies on the epicycle model of the satellite orbit, which provides a reasonably high predicitve capability. Any changes in these prediciton then enables accurate estimates of drag rate to be made and accounted for. The altitude of UoSat-12 was maintained to within 10 meters over a period of 8 months. The limit of 10 meters is due to measurement errors from the GPS receiveer, principally due to ionospheric delays.
Images taken exactly one week apart enable us to test the accuracy of the orbit as well as provide images of regions under different lighting conditions. UoSat-12 was on an orbit of inclination 64 degrees so the local time at which the satellite passes was not phased with the sun. Below are two images of Dallas taken exactly one cycle of the groundtrack apart in May 2000.
