🚀 go-pugleaf

In article <BwstxI.IL3.1@cs.cmu.edu> nickh@CS.CMU.EDU (Nick Haines) writes:


   In article <STEINLY.92Oct27103531@topaz.ucsc.edu> steinly@topaz.ucsc.edu (Steinn Sigurdsson) writes:

      [about Swift-Tuttle vs. other comets, stuff deleted]

      Probably can, but most will be dominated by Jupiter perturbations,
      Swift-Tuttle doesn't look like it's going anywhere (caveat: this is
      guesstimate from eyeballing the orbit parameters, somebody will
      actually have to find out for real bu integrating the sucker),
      ie it will keep coming by until it hits as far as I can tell, but
      that's most probably a few million years off...

   I keep reading this, and have a couple of questions to ask:

   1. S-T crosses Earth orbit twice every 120 years. The risk of
   encounter is something very small, like 1e-6. So the expected time

It's more like 1e-5 per orbit, basically its node is near Earth's
orbit and the question is where along the orbit the Earth is.

   until impact is 6e7 years. So any concern about S-T should also apply
   to the bodies in the ecliptic, which I assert have an (order of
   magnitude) similar expected time before impact (because there are far
   more of them).  Now obviously this calculation depends on my `1e6'
   assertion, but I can defend that (brief handwave: in order to hit, S-T
   has to be at the right angle and distance from the sun when it crosses
   the ecliptic. One can visualize the possible positions of S-T (as
   perturbed by outgassing) at that point as a long oval. The length can
   be judged from the fact that S-T was 17 days late this time, so S-T
   can be perturbed between orbits by times of 17 days. 17 days = 27
   million km at Earth orbital speed, 73 million km at S-T orbital
   speed).

No, the delay is along the orbit, perturbations orthogonal to
the orbit are small, basically there is an uncertainty in the
aphelion and small outgassing at perihelion is effective in
shifting the period due to changes in the aphelion - note the limit
as eccentricity approaches 1 infinitesimal changes in perihelion
velocity can produce arbitary changes in period but not in
the nodes.

   2. On any encounter, it's much more likely that S-T will pass very
   close to Earth (say, within 10 radii) than actually hit (could be a
   cool display :->). Wouldn't such an encounter radically change S-T's
   orbit?  Could it throw it into the ecliptic? OK, whatever orbit
   results will be an earth-encounter one, but what are the chances that
   it will also be, say, a Jupiter-encounter one (i.e. an ecliptic one),

This is the interesting bit, P/Swift-Tuttle has inclination of about
117\deg - ie it is mildly retrograde and near orthogonal! It does not
come near the other planets and I don't think the very weak
perturbations it sees can build up enough to get it away from
Earth crossing. The Earth can't give it a delta v of more than
about 3 km/sec, enough to drop it from Oort cloud orbit to
50AU aphelion, nowhere near enough to perturb it significantly
towards the ecliptic, the Earth can perturb it back up into 
higher aphelion orbit, but those are still Earth crossing.

The short period comets in the ecliptic (suspected Kuiper belt
comets) are dominated by giant planet encounters which are likely to
eject them (or collide with them) so although there are many of them
the Jovian planets effectively form a barrier that reduces Earth
collision probability drastically - part of the reason Nemesis was
proposed to increase the comet rate enough to get decent collision
probabilities.

   throwing it into the planetary bar-billiards game (and therefore
   equally to be accounted with the other ecliptic bodies)? A simplistic
   momentum-conservation argument occurs to me, saying "no chance, S-T's
   ecliptic-perpendicular momentum will be conserved," but I intuit that
   that is flawed (but can't see why).  Anyone want to help me out with
   more handwaving? Anyone got any PD software (for Unix) that lets me
   play planetary bar-billiards?

PD software is not adequate to track P/S-T for more than a couple of
orbits.

*  Steinn Sigurdsson   			Lick Observatory      	*
*  steinly@lick.ucsc.edu		"standard disclaimer"  	*
*  The laws of gravity are very,very strict			*
*  And you're just bending them for your own benefit - B.B. 1988*