randall@ncr-sd.UUCP (Randall Rathbun) (11/13/86)
Alright, my curiosity has gotten the best of me. Does somebody know if all 3 planets (Mercury, Venus, Earth) transit the Sun from Mars, all 4 from Jupiter, all 5 from Saturn, etc,etc. Are there some, from which transits are never seen of all the inferior planets (Pluto?) How often do the above transits occur? Would appreciate this information. Thanks.
freeman@spar.SPAR.SLB.COM (Jay Freeman) (11/14/86)
In article <1240@ncr-sd.UUCP> randall@ncr-sd.UUCP (0000-Randall Rathbun) writes: >Alright, my curiosity has gotten the best of me. Does somebody know if all 3 >planets (Mercury, Venus, Earth) transit the Sun from Mars, all 4 from Jupiter, >all 5 from Saturn, etc,etc. Are there some, from which transits are never seen >of all the inferior planets (Pluto?) How often do the above transits occur? >Would appreciate this information. Thanks. NEWSGROUPS: sci.astro Subject: Re: Transits of Planets Summary: Expires: References: <1240@ncr-sd.UUCP> Sender: Reply-To: freeman@spar.UUCP (Jay Freeman) Followup-To: Distribution: Organization: Schlumberger Palo Alto Research Keywords: Transits <*munch*> In article <1240@ncr-sd.UUCP> randall@ncr-sd.UUCP (0000-Randall Rathbun) writes: > Does somebody know if all 3 > planets (Mercury, Venus, Earth) transit the Sun from Mars, all 4 from Jupiter, > all 5 from Saturn, etc,etc. Are there some, from which transits are never seen > of all the inferior planets (Pluto?) How often do the above transits occur? > Would appreciate this information. Thanks. Each planet should see transits of all planets inferior to itself. Proof: The orbital planes of every pair of planets necessarily intersect in at least a line. By happenstance, sooner or later both planets will both be on the same side of the Sun, "on" that line. At that time, the superior planet will see a transit of the inferior. The "on" is in quotes because what I really mean is "sufficiently close to the line that the angle Sun-superior-inferior is less than the angular radius of the Sun's disc as seen from the superior planet." Actually, if the angle between the two orbital planes is sufficiently small, the two planets can both be quite far from the actual intersecting line, in the same direction around the orbits, and still have a transit. If both planets orbited in the same plane or sufficiently close to it, there would be a transit every time the inferior one caught up to the superior and passed it. Stroboscopic effects might lead to long intervals in which no transits were seen. A way to think about the probabilities is: At the distance from the Sun of the superior planet's oribt, how wide is the cone of space within which an observer would see the inferior planet in transit? What are the odds that the orbit of the superior planet lies within that cone? What are the odds that the superior planet is in the right place in its orbit at that time? Jay Freeman -- Schlumberger Palo Alto Research -- Canonical Disclaimer
freeman@spar.SPAR.SLB.COM (Jay Freeman) (11/14/86)
<*munch*> In article <1240@ncr-sd.UUCP> randall@ncr-sd.UUCP (0000-Randall Rathbun) writes: > Does somebody know if all 3 > planets (Mercury, Venus, Earth) transit the Sun from Mars, all 4 from Jupiter, > all 5 from Saturn, etc,etc. Are there some, from which transits are never seen > of all the inferior planets (Pluto?) How often do the above transits occur? > Would appreciate this information. Thanks. Each planet should see transits of all planets inferior to itself. Proof: The orbital planes of every pair of planets necessarily intersect in at least a line. By happenstance, sooner or later both planets will both be on the same side of the Sun, "on" that line. At that time, the superior planet will see a transit of the inferior. The "on" is in quotes because what I really mean is "sufficiently close to the line that the angle Sun-superior-inferior is less than the angular radius of the Sun's disc as seen from the superior planet." Actually, if the angle between the two orbital planes is sufficiently small, the two planets can both be quite far from the actual intersecting line, in the same direction around the orbits, and still have a transit. If both planets orbited in the same plane or sufficiently close to it, there would be a transit every time the inferior one caught up to the superior and passed it. Stroboscopic effects might lead to long intervals in which no transits were seen. A way to think about the probabilities is: At the distance from the Sun of the superior planet's orbit, how wide is the cone of space within which an observer would see the inferior planet in transit? What are the odds that the orbit of the superior planet lies within that cone? What are the odds that the superior planet is in the right place in its orbit at that time? Jay Freeman -- Schlumberger Palo Alto Research -- Canonical Disclaimer
news@cit-vax.Caltech.Edu (Usenet netnews) (11/15/86)
Organization : California Institute of Technology Keywords: Transits From: jon@oddhack.Caltech.Edu (Jon Leech) Path: oddhack!jon In article <13@spar.SPAR.SLB.COM> freeman@spar.UUCP (Jay Freeman) writes: > > Each planet should see transits of all planets inferior to itself. Proof: >The orbital planes of every pair of planets necessarily intersect in at least a >line. By happenstance, sooner or later both planets will both be on the same >side of the Sun, "on" that line. At that time, the superior planet will see >a transit of the inferior. > It seems to me that with the right sort of resonant orbits this would not always be true (nitpicking admittedly). I'd be interested in hearing more about this from someone better informed. -- Jon Leech (jon@csvax.caltech.edu || ...seismo!cit-vax!jon) Caltech Computer Science Graphics Group __@/
freeman@spar.SPAR.SLB.COM (Jay Freeman) (11/18/86)
<*MUNCH*> In article <1183@cit-vax.Caltech.Edu> jon@cit-vax.UUCP (Jon Leech) writes: >In article <13@spar.SPAR.SLB.COM> freeman@spar.UUCP (Jay Freeman) writes: >> Each planet should see transits of all planets inferior to itself. Proof: >>The orbital planes of every pair of planets necessarily intersect in at least a >>line. By happenstance, sooner or later both planets will both be on the same >>side of the Sun, "on" that line. At that time, the superior planet will see >>a transit of the inferior. >> > It seems to me that with the right sort of resonant orbits >this would not always be true (nitpicking admittedly). I'd be interested >in hearing more about this from someone better informed. Bill Jefferys also made a similar comment in private mail, which I was unable to answer directly due to mailer problems: Subject: Re: Transits of Planets > Interestingly enough, your argument fails for Pluto. Neptune and > Pluto are locked in an exact 3:2 resonance, so it is possible that > the configuration you propose would never come about for these > two planets. (You implicitly recognize this possibility when you > mention "stroboscopic effects", of course.) > Cheers, Bill Jefferys I indeed intended to include resonance in "stroboscopic effects", but now I am curious. Let's see, now. If Neptune and Pluto are in 3:2 resonance, that means that whenever Pluto is at ecliptic longitude (say) zero, then Neptune is at either ecliptic longitude theta or ecliptic longitude theta plus pi, for some particular value of theta. My question is, how strong is the resonance? In specific, in what manner does theta vary over the long term? A range of theta of pi radians would be sufficient to make the proposed transit possible. (Did I get that all right?) A truly constant value of theta is only likely in an undergraduate classical mechanics course. A quite strong resonance might have theta oscillating quasiperiodically about a constant value, in which case transits could happen only if the range of oscillation were greater than pi or in case of fortuitous near coincidence of theta-nought and the line of intersecion of the orbital planes. A still weaker resonance might have theta not "bound" (in the sense of an oscillator) but still changing at a very slow rate compared to the rates of revolution of the planets. (Possible opportunity to quibble about the precise definition of "resonance".) Do you happen to know what condition obtains with Pluto / Neptune? I wonder if anyone has attempted numerical searches for times of planetary transits as seen from other planets than Earth? Are transits of Neptune in fact visible from Pluto, or not? Hmnn. With a lot of luck on the orbital elements of the two planets, it might be possible that instead of a transit one would have an eclipse of the Sun, by Neptune, as seen from Pluto. (The perihelion of Pluto is inside the orbit of Neptune -- the issue is where the orbit of Pluto crosses the orbital plane of Neptune. I know the orbits themselves do not intersect.) (At the distance of Neptune from the Sun, Neptune's umbra is on the order of one astronomical unit long.) Cordially, Jay Freeman