kcarroll@utzoo.UUCP (Kieran A. Carroll) (03/20/85)
*
A couple of people have claimed that, when transferring from
low-earth orbit to geosynchronous orbit, it is generally advantageous to
perform any plane-change maneouvres required entirely at apogee,
and none at all at the perigee of the transfer orbit. Well,
"I am sorry, but that turns out not to be the case..."
If you calculate the amount of delta-v required for a LEO-to-
geosynch transfer, as a function of the amount of plane change performed
at LEO, you will find in some cases that a slight savings of delta-v
can be had by performing a small amount of plane-change at the
perigee (and most of the plane-change at the apogee) of the transfer
orbit. I recently calculated exactly this function, while taking an
orbital dynamics course. LEO was inclined 28.5 degrees to the equator,
and was 300 km high. If 2.2 degrees of plane change were done in
LEO, at the time of the perigee burn, about 0.6% of the total
delta-v could be saved. As the professor giving the course pointed
out, this saving may be small, but it's exploited quite frequently
by people launching satellites.
--
Kieran A. Carroll @ U of Toronto Aerospace Institute
{allegra,ihnp4,linus,decvax}!utzoo!kcarrollkarn@petrus.UUCP (03/22/85)
This is very interesting. I'd like to see the details of how this is so. Back when I was helping to plan the orbital maneuvers for AMSAT-OSCAR-10 we wanted to change a GTO as given by an Ariane (inclination 8.6 deg) to a Molniya approximation (63 deg). I found through some reading that for VERY large plane changes (like the one we wanted to do), the economy of plane changes at apogee is so strong that it actually saves fuel to boost apogee, do your change at the new apogee, then drop back down to the desired apogee. We didn't opt for that because of the risk involved; we easily had enough delta-vee that an overburn at perigee would have given us earth escape velocity. We didn't want to compete with Voyager. In addition, communication links at 100,000km+ might have become marginal, and with a starting perigee of 200 km, additional perturbations from the sun and moon could be serious. Even a "normal" plane change carried its risks. I realized that if the engine were to shut down midway through a large maneuver, the resulting perigee would be negative. We therefore planned a two-burn "dogleg" compromise in which the intermediate orbit would still be useful. This turnd out lucky -- the motor overburned on the first shot due to a wiring error in the control circuit, and failed to burn on the second shot due to a loss of helium pressure likely caused by the unplanned temperature excursions resulting from a collision with the launcher shortly after separation. We've got a usable, functional satellite, although it's been through a few "hard knocks". Phil