@S1-A.ARPA,@MIT-MC.ARPA:linnig%ti-eg.csnet@csnet-relay.arpa (06/04/85)
From: Mike_Linnig <linnig%ti-eg.csnet@csnet-relay.arpa> > > > > Not if the force is along the velocity vector, at least. If you > > push away a mass along the velocity vector one object will go > > into a higher orbit and the other into a lower orbit. If the > > force is not along the velocity vector things get complex. > > Whoops! After exactly one orbit you will meet up again, and will every > orbit until one party or the other is disturbed. Sorry .... > Now wait a minute, suppose I throw a *BIG* rock fast enough to give myself escape velocity. When exactly, will I meet that rock again ? Since the last time I saw my rock it was heading away from me, and I am no longer in orbit........... "Thought experiments are wonderful things." -- Mike Linnig
@S1-A.ARPA,@MIT-MC.ARPA:mcgeer%ucbkim@Berkeley (06/04/85)
From: Rick McGeer <mcgeer%ucbkim@Berkeley> If you threw yourself into an escape orbit, you'd throw the rock into an impact orbit. I think. Well, know, that's not quite true. Snce MV = MV, if the rock was very large in mass compared with you (or if both you and the rock were in near-escape orbits), you'd merely throw the rock into a lower orbit. Rick.
throopw@rtp47.UUCP (Wayne Throop) (06/06/85)
> From: Rick McGeer <mcgeer%ucbkim@Berkeley> > > If you threw yourself into an escape orbit, you'd throw the rock into > an impact orbit. I think. > > Well, know, that's not quite true. Snce MV = MV, if the rock was very > large in mass compared with you (or if both you and the rock were in near-escape > orbits), you'd merely throw the rock into a lower orbit. Not quite. The ground rules state that you eject some mass (a large rock in this case) and acheive escape velocity. Now then, how do you get that the rock must be in a "lower orbit"? Starting with both you and the rock in the same orbit and assuming that the rock masses more than you do, if you throw the rock into an escape orbit with a velocity vector that points 180 degrees from your common vector, it seems to me that both you and the rock are liberated. Clearly, there are other situations where both you and the rock escape, or you escape and the rock has a "higher orbit" or whatnot, but this example shows with no quantitative calculations a situation that 1) has you in an escape orbit as requested, and 2) has the rock in an escape orbit also (which I take to be a "higher orbit"). Regarding "higher" or "lower" orbits, there is an interesting property of the orbit that results from a single impulse, such as the one applied to the rock in this situation. When you have this situation: - object is in orbit. - single impulse is applied to object. - object is then in (a possibly different) orbit. it must always be the case that *some* point on the new orbit is exactly as "high" as some point in the old orbit. In particular, P <= X <= A where P is the new perigee, A is the new apogee, and X is the height at the point of impulse. Note that even escape and impact orbits obey this rule. For escape orbits, A=infinity and P<=X, and for an impact orbit, P=0 and A>=X. (for the quick thinker: which of the above listed three conditions is not necessary to show the result P <= X <= A ?) -- Wayne Throop at Data General, RTP, NC <the-known-world>!mcnc!rti-sel!rtp47!throopw