On the Water-Snake’s Tongue

Juno, the Third Asteroid, is at a fairly good opposition.

“Opposition” means the middle of the best time to see a body, and “fairly good” means, for Juno, that it reaches magnitude 8.1. This is 16 times fainter than the faintest star the naked eye can see in average conditions (magnitude about 5), but Juno is findable, with skill, in binoculars or small telescope, using this chart from page 53 of Astronomical Calendar 2015.

astch15Juno

The loop of stars forming the “head” of Hydra the water-snake is the most easily found pattern between Orion and Leo. Then you have to search in the field about two degrees west and a little north from 4.5-magnitude Sigma Hydrae. The 274-kilometer-wide asteroid is a passing molecule sensed by the Water Snake’s forked tongue.

Juno is at right ascension 8h 31m, declination 3° 40′. Or rather, it was, at the moment of opposition, Jan. 29 15h Universal Time (10 AM EST). The day being now Jan. 30, because I’m late getting this ready, Juno is now a little farther along its track: moving northwest at a third of a degree a day, it is between 8h 30.7m 3° 43′ and 8h 29.8m 3° 53′, depending on when in Jan. 30 you look. A day won’t make the asteroid appreciably dimmer. The Moon, just past First Quarter, is 50 degrees away, getting low in the west as Juno’s part of the sky climbs in the southeast.

Considering where Juno will be the day after opposition brings to mind a question. Could it instead have been at opposition at one of these points farther along its track, such as where it is today or tomorrrow? Or could it, some other year, be at opposition at a point a few degrees north or south of where it is now? An asteroid can venture to almost any place around the sky, that is, any point within the swath swept out by the tracks it makes over the years; but are all of those points potentially ones where it could be at opposition?

The answer is no. It can be at opposition only in a limited set of places: indeed, along a certain line of points.

Jean Meeus asks himself this question (about asteroids and outer planets in general) on page 240 of his Mathematical Astronomy Morsels (1997). He asks the question in the simple form: where can a body’s oppositions be? It depends on the inclination, eccentricity, size, and orientation of the body’s orbit, and he gives a page of formulae, which I managed in 2008 to reduce to a 15-line “subroutine” of programming. What my subroutine does is find, for any longitude at which the body may be along its orbit, the geocentric latitude at which it would have to be at opposition.

The interesting thing about Juno is that the line of points along which it can be at opposition – the “locus” of its oppositions – is almost flat along the celestial equator. In other words, every time Juno arrives at opposition it has come down to, or up to, a point within about 5 degrees north or south of the equator. This January it is 3° 40′ north, in Hydra; in 2016 April it will be only 43′ south, in Virgo; and so on.

Here is a chart showing the loci of oppositions for the first four asteroids, Ceres (gray), Pallas (green), Juno (orange), Vesta (cyan). The actual tracks of the asteroids are traced in black for spans of two months around some sample oppositions.

OppsJuno

You might think the hilliness of the curve would depend mainly on the orbit’s inclination. Yet Juno’s inclination (13 degrees) is greater than those of Ceres (11) and Vesta (7). Pallas’s inclination of 35 is unusually great for an asteroid, so its oppositions range far from the ecliptic – but, because of the orbit’s orientation, not so far from the equator. These relations make sense because inclination means how much the body can get away from the ecliptic, not the equator. It also seems surprising that little effect is made by the large eccentricity of Juno’s orbit – it can come nearer in than all the others and almost as far out as Pallas.

And despite coming nearer in it is not a star asteroid. As we never tire of remarking about poor Juno, though named for the supreme Roman goddess it in most years fails to become as bright as the other three of what used to be called the Big Four, and often is outdone by several that were discovered much later. This time, however, it is more than a magnitude brighter than Pallas will be in June, and worth looking for.

 

8 thoughts on “On the Water-Snake’s Tongue”

  1. Guy, you’re right, I was certainly a little loose and imprecise with my terminology. Although I started off talking about near simultaneous oppositions, it is true that my actual goal was “very close when very bright,” although that means that the two planets are going to be very close to opposition time if “very close when very bright” happens. I started my search by finding the oppositions of Mars, then down-selecting only the ones with Jupiter also at opposition within a week or so, and then checked the magnitudes and separations day by day around the opposition dates to find the closest / brightest sweet spot. As you always point out in the AC during a Martian opposition year, the date of Mars being brightest can precede or follow the opposition date by up to a week. So the dates in my table are no more than a week away from Martian opposition. At least two of those five I listed turned out to also be triple conjunctions, like I believe the 1980 event was.

    1. What differs by up to a week from Mars’s opposition date is the date when it is nearest to Earth – because of the inward or outward slope of its orbit. But this difference verges on zero when Mars is near its aphelion or perihelion (the orbit not sloping in relation to us). For instance at the great perihelic opposition of 2003, the date of nearness was scrcely more than a day different. So if you were including only the very brightest oppositions of Mars, i.e. near perohelion, the dates of opposition and of maximum brightness would be virtually the same.

  2. Very interesting post, Guy! The question of “where can an outer solar system body be at opposition?” also maddeningly results in the fact that when Mars is at its best oppositions, it *must* be well south of the ecliptic in Sagittarius, Capricornus, or Aquarius, to the disadvantage of us northern-hemisphereans (-ians?). I once used ephemeris calculating software to painstakingly try to determine if and when Jupiter and Mars would have coincident perihelic oppositions, or more accurately when Jupiter and Mars would have coincident oppositions when Mars’ opposition was perihelic or nearly so. The answer was something like the year 2744 A.D! But even then, Mars must be well south of the ecliptic in Aquarius, so the two planets will not really be any closer than about 5 degrees in the sky, not really looking like a double planet. Apparently there never will be a time when the two planets will ever be (1) at or very near their absolute brightest and (2) extremely close together in the sky (within a degree or less). But I have wandered far afield from Guy’s discussion of Juno. Better go outside and see if I can find it!

    1. The question of nearly-simultaneous oppositions of e.g. Mars and Jupiter may be investigated in one of Jean Meeus’s “Morsels” books, though I haven’t found it in the cumulative index in “Morsels V”.
      I’ve done some more to my program for plotting the locus of oppositions and plan to use it for the opposition of Jupiter on Feb. 6. It will be very clarifying for the oppositions of Mars, but unfortunately there isn’t one of those in 2015.

      1. My study of the near-simultaneous oppositions of Mars and Jupiter revealed the following pattern (assuming the planetarium software I was using was accurate): Mars and Jupiter have near-simultaneous oppositions about every 46 – 47 years (the last was in 1980, the next will be in 2027), but the interesting thing is that when you plot them all out for 1,000 years or so, most of them seem to be in the Cancer – Leo – Virgo part of the sky (as our 1980 event was), and then they drift with ever greater rapidity toward the Aquarius – Pisces – Aries part of the sky for a short time, and then quickly drift back toward the Leo direction. Must be related to the fact that the aphelia of Mars and Jupiter are more or less in the Leo direction from the Sun, and perihelia both more or less in the Aquarius – Pisces – Aries region (Guy’s watery abyss).

        1. I think that if I wrote a program to find the oppositions of the planets hundreds or thousands of years in the past or future. I would not trust it to be very accurate.
          Keywords you might search for are “resonance” and “harmonic”. If there are resonances between the orbits of Mars and Jupiter, like the 8:13 one between Earth and Venus, then that surely would bring them to opposition in certain cycles.

          1. I agree with you that it could be dangerous relying on an ephemeris calculator to accurately predict planet positions hundreds of years into the future. I think the program I used was called ephemeris (I don’t even have it on my computer anymore owing to several “rebuilds” after being afflicted by viruses). I found a reference online (a paper by P. A. Semi published in 2009) which stated that there is no orbital resonance between Mars and Jupiter. At any rate, for what it is worth, I found my summary of the results I obtained using the ephemeris software:

            Aug 22, 2697 – Mars (mag -2.85) and Jupiter (mag -2.85), 7.5 deg apart
            Nov 4, 2699 – Mars (mag -2.52) and Jupiter (mag -2.93), 2 deg apart
            Jun 6, 2742 – Mars (mag -2.03) and Jupiter (mag -2.55), 3 deg apart
            Aug 7, 2744 – Mars (mag -2.77) and Jupiter (mag -2.81), 6 deg apart
            Oct 29, 2746 – Mars (mag -2.60) and Jupiter (mag -2.95), <3 deg apart

            I apologize for cluttering your blog with all this nonsense! At the time I did this I was curious as to whether it was ever possible to see these two planets at their brightest close together, and the nature of their mutual oppositions surprised me as I discovered how rare they are. Notice that the August pairings are relatively far apart because Mars always must be well south of the ecliptic then, but the October / November ones are much closer. But, who knows how reliable these predictions are anyway? Back to reality: 2027 is my last shot unless I live to be 111 years old LOL.

          2. Interesting, though it’s not clear to me from your list how close the planets were to their oppositions at the dates you list (I thought you were hunting for nearly-simultaneous oppositions rather than conjunctioons-when-very-bright).

            The programming I was saying I wouldn’t trust so far ahead was my own, not any planetarium software – I’ve still never used any. But the software you maybe could trust to be accurate at any date might be Aldo Vitagliano’s Solex. I got it because the great Jean Meeus looks up to it with respect, but I’m afraid I still haven’t actually made any use of it. It’s based not on equations from elements but on long-term integration, which, roughly speaking, is finding all the solar system bodies’ effect on each other at a date to move them to the next date.

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