REM@IMSSS (Robert Elton Maas, this host known locally only) (01/17/86)
phil%dean@BERKELEY.EDU says this message was rejected by USENET because of problems with the message-id, so I'm resubmitting without any message-id. Arpanet members please ignore duplicate. Date: 1986 January 13 10:47:14 PST (=GMT-8hr) From: Robert Elton Maas <REM@imsss> (this host known locally only) To: SPACE@mit-mc.arpa Cc: "Dave-Platt%LADC"@cisl-service-multics.arpa Subject: Nemesis = Jupiter et al resonating the asteroids DP> Date: Fri, 10 Jan 86 14:32 PST DP> From: Dave Platt <Dave-Platt%LADC@cisl-service-multics.arpa> DP> Subject: Timing of comet showers DP> ... for the asteroid to drop into an orbit that crosses DP> Earth's. There may be some subtle second- or third-order interactions DP> between Jupiter, Saturn, the asteroids, Earth, and maybe the other DP> planets which would lead to a periodic change in the number of DP> asteriods perturbed into Earth-crossing orbits. DP> So... Nemesis may exist, and be sitting right in front of our faces: DP> it's Jupiter! As "Connections" host James Burke likes to point out, nobody comes up with a new invention in vacuuo, each merely adds a little to what existed already. Here's my little "value-added" enhancement to yours which was an enhancement of the original Nemesis theory: First, consider stable geometrically-fixed potential wells in two-plus body systems, that is tiny test bodies trying to orbit in phase space around two large orbiting bodies. I.e. consider L4 and L5 regions in such places as Earth/Moon or Sun/Jupiter systems. With just the two large bodies, in circular co-orbits, the potential wells are fixed in shape and depth, so that a test body is either trapped or it isn't, and if it is it'll stay there forever. With a third large body (distant Sun in case of Earth/Moon, or Saturn in case of Sun/Jupiter), the depth and shape of the wells are periodicaly purturbed according to the phase (angle) relationship between the third body and the line connecting the two main bodies. A test body (asteroid in our Nemesis context) that is just barely trapped for most of the cycle could escape when the well is shallowest if it happened to be visiting the perimiter at that moment. After a few tens of cycles virtually all just-barely-trapped test bodies will have escaped, leaving only deeper trapped bodies. But now consider a fourth large distant body that further purturbs the wells (Venus or Mars or Jupiter in case of Earth/Moon system, Uranus in case of Sun/Jupiter system). This produces additional sloshing of the shape/depth of the wells, with a very long period. Perhaps test bodies that survive tens of thousands, or even millions, of years will find every 30 million years or so the well gets shallower than it ever was between times, and a few test bodies will overflow the perimiter. Possibly the fourth body provides two effects, first continually supplying knetic energy to test bodies in the well so that if they were previously sitting at the bottom they will now be orbiting highly, and secondly the aforementionned periodic change of shape of the well. The result could be that for all time a particular tiny fraction of the contents of the well are sloshed out on a periodic basis (the tiny fraction may vary depending on the exactitude of the phase at each major cycle, unless the four bodies are locked in some immense rational-number relationship of orbital periods). So, anyway, the Trojan asteroids may thus be periodically sloshed out of their wells into random orbits including some Earth-crossing, and over long time (4 billion years) the intensity of "radiation" of these asteroids may follow an exponential-decay curve with a half life perhaps 0.5 to 10 billion years. Likewise in phase space of the two original bodies (Sun/Jupiter for this knock-to-Earth-crossing example) there may be many more complicated stable orbits, around each of which (in phase space) there is a potential well. Just like the L4 and L5 (trojan) points, third and fourth bodies (Saturn and Uranus) may cause periodic sloshing out of the well, whose pulse period is a few million years and whose longterm envelop is exponential decay. Note that the periodicity of these additional wells would be exactly the same as the trojan wells, because the phase relationships of the four bodies are the same for all systems. The particular times that the pulse of spilling (overflow) occurs for the various systems may all be different, or there may be some correlation where a whole bunch of systems spill at about the same time. In the latter case, we have periodic extinctions from the bunch of spills occurring together. In the former case, probably most spillage from strange stable orbital wells actually falls into the trojan wells rather than colliding with Earth, so that the trojan wells are resupplied from the other wells. During the interval between trojan spills, lots of little spills from other wells would have filld the trojan wells quite full, so that the trojan spill when it comes is quite large. Then the major contribution to Earth-crossing asteroids would be from the trojan wells periodially overflowing, and again we have periodic mass extinctions with not much bad happening between times. So, could some expert in celestial mechanics offer a critique of my theory?
henry@utzoo.UUCP (Henry Spencer) (01/19/86)
> ... So, anyway, the Trojan asteroids may thus be periodically > sloshed out of their wells into random orbits including some > Earth-crossing... Small problem: the Trojan potential wells are very shallow, and the forces involved in planetary perturbations are small. How do you get "random orbits" from that? You'll get only very small changes in orbit, which will hardly suffice to turn a near-circular orbit in the outer Solar System into an Earth-crossing orbit. Perhaps later encounters with Jupiter could account for it, but I have doubts. I'd also like to see a quantitative analysis of the effect of other planets on the Trojan gravity wells. Remember the inverse-square law, and the distances in the outer Solar System: those effects are going to be pretty small. -- Henry Spencer @ U of Toronto Zoology {allegra,ihnp4,linus,decvax}!utzoo!henry