Some interesting celestial events to simulate in Guide

The following list describes some events easily simulated using Guide. This just lists a few events that have recently had my attention; if you have found others that might be of interest, please e-mail me.

  • View from geostationary orbit
  • View from Earth-Moon Lagrange points
  • Molniya satellite motion
  • The Earth also rises (as seen from the moon)
  • Sun 'stands still' from Mercury
  • Mutual planetary events
  • Three shadows on Jupiter
  • Earth and partially eclipsed moon
  • Trojan asteroids as seen from above
  • View from geostationary orbit

    The view from geostationary orbit is basically that which you would have if there was a mountain 35800 kilometers high, at the earth's equator; and you were sitting on top of that mountain. Therefore, if you go into the Settings... Location menu in Guide, and set your latitude to be zero degrees and your longitude to put yourself over a desired point on the equator, and set your altitude to be 35800 km, you can see the world as it appears from geostationary orbit.

    From this viewpoint, the earth goes through a full set of phases once a day, and eclipses the Sun near the equinoxes. The moon moves in a retrograde direction for much of the day, and sometimes is eclipsed by the earth. If you have the vector features and/or the grid turned on for the Earth, it will be very apparent that quite a lot less than half the earth is visible from this viewpoint; you're still close enough to the earth for perspective to matter (which is why the people at the South Pole reseach station can't get satellite TV.)

    View from Earth-Moon Lagrange points

    Guide is still a little limited when it comes to showing you viewpoints from arbitrary positions in the solar system. But you can see what the solar system would look like as seen from all five Earth-Moon Lagrange points. (Lagrange points rotate with the Earth-Moon system, and are also called "stationary" points. They exist for several pairs of objects in the solar system. Two of the points are stable; they are called "Trojan points". The other three are not stable over long periods of time.) For the Earth-Moon system, the five points are as follows:

    L1 = point about 92,000 km above the moon,  toward the earth;
    L2 = point about 92,000 km above the moon,  on the side away from the earth;
    L3 = point about 400,000 km above the earth,  opposite the moon
          (a sort of "anti-Moon" point);
    L4 = a Trojan point,  400,000 km from both earth and moon,  orbiting
           60 degrees ahead of the moon
    L5 = a Trojan point,  400,000 km from both earth and moon,  orbiting
           60 degrees behind the moon
    
                       L4         (Rotates counterclockwise as seen
                      / \     from above the North Pole)
                     /   \
                    /     \
                   /       \
                  /         \
    L3----------(E)------L1-(M)-L2
                  \         /
                   \       /
                    \     /
                     \   /
                      \ /
                       L5
    

    L4 and L5 are stable. Jupiter has collected a lot of asteroids at these points; Mars has collected at least one known asteroid, (5261) Eureka; and several of Saturn's moons have "co-orbital" moons, in their same orbit but 60 degrees ahead or behind in the orbit. There have been claims of dust clouds seen at the Earth-Moon L4 and L5 points, but nothing definite. The SOHO satellite has been deliberately placed at the Earth-Sun L1 point.

    The method for setting your viewpoint in Guide to one of these five points works because the Moon rotates synchronously in its orbit (is "tide locked"). That lets you do the following tricks. For all of them, you must go into the Location dialog and set your home planet to be the Moon, and your latitude to be zero (on the Lunar equator.)

  • Set your longitude to be zero (center of the near side) and your altitude to be 92000 km, and your viewpoint will be from L1. The Moon and Earth will appear 180 degrees apart in your sky.
  • Set your longitude to be 180 degrees (center of the far side) and your altitude to be 92000 km, and your viewpoint will be from L2. If the moon and earth were of the same density, then they would be almost exactly the same apparent size from L2. As it is, the moon is a bit less dense, so it can cover the Earth as seen from L2. There have been proposals to put a radio observatory at L2 for this very reason: you would be in zero-g, and could therefore build a truly immense dish, and you would have the Moon shielding you from the radio noise from the earth. (Unfortunately, this trick in Guide doesn't work quite well enough to get the "real" alignment. In reality, I suspect that fairly constant adjustments would be needed to keep the Moon between you and the earth.)
  • It would be nice if staying at the L2 point for the Earth-Sun system would keep the Earth between you and the Sun; then you could put a probe there and have it get down close to 3 degrees K, something that would be wonderful for some applications. But this won't work, partly because the earth is much denser than the Sun; you would only get an "annular" eclipse.

  • Set your longitude to be zero (center of the near side) and your altitude to be 800000 km, and your viewpoint will be from L3. The Moon will look to be about half its usual size as seen from Earth, and the Earth will be about two degrees across.
  • Set your longitude to be W 60 or E 60, and your altitude to be 400000 km, and your viewpoint will be from L4 or L5, respectively. The Moon will have the same size it has as seen from Earth, and will stay 60 degrees from the Earth.
  • Similar tricks will get you to the Lagrangian points of almost every satellite in the solar system. Unfortunately, it won't get you to the Lagrangian points for the planets (say, the L1 point for the Earth and Sun, where the SOHO satellite stays), because the earth rotates relative to the Sun.

    Molniya satellite motion

    Jari Suomela pointed this one out to me. The Molniya-type orbit is used by several Russian satellites. An object in such an orbit has a 12-hour period, and an inclination to the Earth's orbit of about 65 degrees. The orbit is very eccentric, with a perigee of about 1000 km and an apogee of about 39000 km. The orbit is selected so that, if you're in Northern Russia, the satellite will appear to zip up over the horizon, rise very high in the sky at apogee, appear to stay almost motionless for several hours, then drift away and streak back below the horizon.

    So you basically have a "part-time" geostationary satellite. You have to have several (at least three) in the orbit, to provide continuous coverage (one takes over just as the previous one is heading back toward perigee). But Russia has a lot of territory at far northern latitudes, where "normal" geostationary satellites are just not a reasonable prospect; they would be hugging the southern horizon.

    To see this in Guide, set your lat/lon to be around E 50, N 60 (central Russia), and hit Alt-N. This results in a view of the zenith, full-sky (180 degrees), with the horizon surrounding the chart.

    Now go into "Settings... TLE=" and select MOLNIYA.TLE. It may not appear; if so, download and save MOLNIYA.TLE (about 4 KBytes) to your Guide directory. Go into "Data Shown" and turn Satellites to On. Personally, I'd turn satellite labels off, too; they're apt to get pretty cluttered-looking.

    Now start up the Animation dialog and set the "Horizon" radio button, and start animating with, say, a 15-minute step. The pattern of Molniya motion will become very obvious. If the screen flickers, go under "Display" and make sure that "Direct to Screen" is not checked.

    Jari is in Finland, and has done some observing of Molniyas. Like geosynchs, they have the advantage that Dobsonian owners can observe them without having to worry much about tracking problems. One need not be especially close to the USSR to see them, either. After all, these objects are in 12-hour orbits; if they "hover" over, say, E 50, N 60 on one orbit, then they will wind up over W 130, N 60 on their next orbit. Observers in Canada will find that these objects are quite nicely placed.

    By the way, it can also be interesting to observe Iridium satellite orbits as seen from the Moon. Set your "home planet" to be the moon, look back at the earth, and load up a set of Iridium elements. (You can get current Iridium elements, and Molniya elements, and quite a few others, at this Web site. You'll also see that there is an example set provided with Guide... this will eventually be out of date, but can still give you the general idea of what the Iridium system looks like.)

    If you animate with a step size of a minute or so, you can see the pattern in the Iridium "satellite constellation". Over half the earth, satellites are travelling north to south. On the other half, they run south to north. They fall into "tracks"; satellites in adjacent tracks are staggered, so you get a network of equilateral triangles. Presumably, the designers of this configuration wanted to use a minimal number of satellites. Also, for any long-path call, the call would have to be passed from one satellite to the next; keeping the number of "lateral passes" needed to a minimum would be a goal. Also, you would want to be sure that all parts of the world see at least one Iridium satellite, within decent range, all the time.

    The Earth also rises (as seen from the moon)

    It's often said that, because the moon always keeps one face to the earth, that the Earth hangs in one place in the sky as seen from the moon. If you were standing at a point near the lunar limb, the earth would appear fixed at the horizon, never rising and never setting.

    This is mostly true, except that the moon doesn't keep just one face toward us; it librates ("wobbles") quite a bit. And correspondingly, you can see the Earth wobble a little bit around its fixed position in the lunar sky.

    To see this, fire up Guide, and (under the Settings menu) click on the "Location" option. Set your home planet to be 'Luna', and your longitude to be W 90 or E 90 (latitude is irrelevant for this... but either longitude will put you on the lunar limb.) Do a "Go to... Planet" and look back at the earth. You may want to turn on the Inversion Dialog and set "Alt/Az up", so you get a nicely level horizon. (Also, it helps to go into the Backgrounds dialog and turn on the "filled ground" and horizon objects. The resulting barns, houses, and streetlights are admittedly incongruous for a lunar scene, but they do give you a frame of reference.)

    Start up the Animation dialog, and click on the "horizon" radio button. Set the animation rate to about one day, and start animating.

    Over the course of a lunar month, you'll see the earth wobble in a small circle, which will cause it to rise and set. You'll also see it go through a full set of phases, which will be opposite to those seen from earth ("Full moon" coincides with "New Earth", and "New moon" with "Full Earth").

    By the way, similar stunts can be tried with all other satellites in Guide, looking back at their primaries. But except for Saturn's moon Japetus, they're in such nearly-circular orbits that the librations are quite small. Japetus is apparently far enough from Saturn that its orbit hasn't gotten quite circularized yet (check back a few billion years from now).

    Sun 'stands still' from Mercury

    This is an odd piece of solar system trivia, which can be shown in Guide now that views from the surfaces of other planets are supported.

    Usually, when tidal forces "lock" an object's rotation, one face of the object faces the primary (much as one face of the moon points to the earth, and the Galilean moons of Jupiter all have one face pointing toward Jupiter, and so on). The object rotates in the same time it takes to orbit the planet. If you're on the surface of the moon, for example, the Earth stays (basically) fixed in the sky.

    For quite a while, it was thought that Mercury did the same thing with the Sun. Based on what little could be seen in the way of features, it looked as if one face of Mercury was in perpetual sunlight (and presumably the hottest place in the solar system) and one face in perpetual shadow (and presumably the coldest place in the solar system... even colder than Pluto, probably.)

    Then in the mid-1960s, radio observations showed that Mercury does rotate, though quite slowly: once every 57 days. For every two trips around the sun, Mercury rotates three times (with respect to the stars; once with respect to the sun. It's a bit like the situation with the Moon, which rotates once every 27.5 days relative to the stars, but not at all with respect to us.) This 3:2 ratio for Mercury seems to be quite exact.

    This is a little puzzling, given that the usual ratio is 1:1, but there is a way to show that this behavior is perfectly reasonable. To do so, fire up Guide, and (under the Settings menu) click on the "Location" option. Set your home planet to be Mercury, and your lat/lon to be N0, W0. This puts you right on top of Mercury's equatorial bulge; you'll see soon why that viewpoint is important.

    Now use "Go To... Horizon Menu", and click on "Zenith". Turn on the Animation dialog, and select a step size of one or two days. Click on the "Horizon" radio button; that way, when you animate, the viewpoint will stay fixed on the zenith. Zoom out to about level 2 or so.

    Now start animating. Eventually, the Sun will come into your field of view (it may take a while, since the Sun reaches the zenith once every 176 days.) As you'll see, it zips across toward the center of the screen. But then it slows down... drags to a stop... backs up about half a degree... drags to a stop again... and goes forward!

    Which leads to two questions: (a) why does this happen? and (b) how does it relate to that 2:3 ratio?

    The answer to (a) involves Mercury's extremely elliptical orbit. On average, Mercury's rate of travel around the sun (once every 88 days) is a third slower than its rate of spin around its axis (once every 59 days). But when it gets close to perihelion, it speeds up in its orbit, courtesy of Kepler's Second Law. And for a few brief, glorious days, the angular rate of motion around the sun catches up and even slightly surpasses the angular rate of spin... so the sun stands still in the sky, then backs up a little, much as the earth stands still in the sky (all the time) from the moon. Then it gets past perihelion, and the angular rate of motion around the sun drops off, and the party's over. (If you click on "Make Ephemeris", and make an ephemeris showing the distance to the sun and its alt/az from this viewpoint over time, you'll see that perihelion always coincides with the sun being at the zenith or nadir.)

    Which brings us to (b). Long ago, Mercury (like our moon) probably spun quite rapidly. Like the moon, tidal drag slowed it down over millions of years. So it slowed down from rotating, say, once a day, to rotating once a week, to once a month... until it hit that magic 2:3 ratio, rotating once every 59 days. At every perihelion, the equatorial bulge pointed through the sun, much as the moon's equatorial bulge points through the earth. That rate represents a "local energy minimum", like a marble at the bottom of a bowl. So instead of continuing to slow down until it got to a 1:1 ratio (like the earth and moon, and like almost every other satellite in the solar system), it stayed in the 2:3 ratio.

    And now, for a little speculation. It's fair to assume that this may also explain why Mercury's orbit remains as eccentric as it is. Most planets have nearly circular orbits now, except for Mercury and Pluto. But the same forces that keep Mercury's rotation locked at the 2:3 ratio would also tend to lock the eccentricity at this value. Given suitable mathematical effort (which I may pursue someday), you could probably show that, for a 2:3 ratio, Mercury's actual orbital eccentricity of about .25 is a sort of "optimal value".

    This could also be generalized a bit. For higher eccentricities, there ought to be, say, an "optimal" 2:5 ratio and a 1:2 ratio. And had Mercury's orbital eccentricity been lower, there might have been an "optimal" 3:4 ratio. (You can't keep pushing that forever, though. If you went on to finding the 4:5 case and the 5:6 case, I think you would eventually find a point where the rotation is so close to 1:1 that there is no "minimum" point, and the object keeps getting tidally braked until it looks like our moon.) If anyone writes up a doctoral thesis on "Variations in Tidal Braking" or something like that, please send me a copy.

    Mutual planetary events

    The August 1992 issue of Sky & Telescope (p 208) has an interesting article on a mutual planetary occultation. On the night of 12 Sep 1170, Mars appeared to transit Jupiter. The event was observed and reported by the monk Gervase of Canterbury. An image of the event is available on this Web site.

    Recently, I became curious about other mutual planetary events, and wrote software to find all conjunctions of all planets with one another. A very few of these (perhaps once each century) will be close enough to appear as an occultation. The new bitmapped features in Guide make these events particularly attractive to simulate. You can click here for a list of all mutual planetary events from -1000 to +6000, but here are some of the more "interesting" events. (All dates before 1582 are Julian calendar, not Gregorian.)

    30 Jan -9, 12:33 UT: Mars transits Saturn.

    3 Jan 1613, 17:39 UT: Jupiter occults Neptune. The Sky & Telescope article has some comments on this event. It occurred just at the time that Galileo was observing Jupiter's satellites; Galileo did show Neptune in sketches made on 28 Dec 1612 and on 28 Jan 1613... but he identified it as a star.

    8 Dec 1253, 9:15 UT: A crescent Mercury transits Saturn, as seen from the Southern hemisphere. (Usually, when Mercury or Venus transit a planet, they are nearly full; not only do they spend more time near full than near a crescent phase, they also are closer to the ecliptic when on the far side of the sun.)

    25 Aug 1278, 14:18 UT: Mars occults Neptune.

    28 Dec -423, 10:50 UT. Saturn and Jupiter are about 1.5 arcminutes apart. Between the years -1000 to +3000, this is the closest they get to one another. (I had hoped to get a very close pairing, or a mutual occultation; displayed in Guide, it would make a really good screen shot for my ads in Sky & Telescope. But there wasn't even a close enough pairing to make for a good ad.)

    So large a distance may seem a little peculiar; it happens for several reasons. The most important is that these are the slowest-moving naked-eye planets, and their conjunctions are rare, at roughly 20-year intervals. (After 20 years, Jupiter has completed 5/3 orbits, and Saturn 2/3 of an orbit; you could say that Jupiter has "gained a lap" on Saturn. Sometimes you get a cluster of three conjunctions at this point, because of the motion of the Earth; but generally, you just get one. For example, there was a cluster of three conjunctions in 1980-1981; but the next conjunction, on 28 May 2000, will be a single one.)

    Anyway, the natural result is that, even over a 4000-year span, conjunctions are few, and the number of opportunities for a mutual event (or very close conjunction) are limited.

    On the bright side, we will get a conjunction to within a mere 6 arcminutes on 21 Dec 2020, with Jupiter and Saturn in the evening sky. It should be possible to see both planets in the same telescopic field of view, with some of their attending moons.

    Three shadows on Jupiter

    When I added the display of shadows cast by objects on one another (the Earth and moon on one another during eclipses, mutual events of the satellites of Jupiter and Saturn, and shadows cast by satellites on Jupiter and Saturn), I remembered a story I read as a child (Farmer in the Sky, by Robert A. Heinlein) in which at one point, all four Galilean satellites are lined up and casting shadows on Jupiter. (In the book, this results in severe tides, which cause a quake on Ganymede.) I got curious as to whether such an event might ever occur, and searched years between 1860 and 2020.

    I found no events where there were four shadows at once... had I applied reason instead of a brute-force computer search, I would have seen why immediately. As Jean Meeus points out in his new book, Mathematical Astronomy Morsels, the inner three moons have related periods, and only two can cast shadows at any given time.

    But you can get a three-shadow event: Callisto, plus two inner moons. My program found several of these. For example, if you set Guide's time to 11 Nov 1997, 4:30 UT, and look toward Jupiter. Io, Ganymede, and Callisto are casting shadows. Those of Ganymede and Io overlap slightly, and if you zoom in far enough, you'll see that Io is partly eclipsed by Ganymede.

    At the start of the shadow crossings of Io and Ganymede, Io's shadow chases that of Ganymede; toward the end of the event, just as the shadows are about to leave the disk of Jupiter, the shadow of Io catches up and slides under the shadow of Ganymede. ( Click here to see a view of the situation at this point.)

    Due to "light lag", you're seeing this event about 40 minutes after it "really" happened. If you set your "time" in Guide to 3:50 UT and your home planet to Callisto, and look toward Jupiter at about level 4 (20-degree field of view), you'll see it "as it happens".

    This event was actually visible from the southwestern US; Jupiter will be 152 degrees away from the Sun, in the evening sky. Several people observed it and collected CCD images as it progressed.

    This event is sufficiently "dramatic" that I decided it would make a good screen shot for my ads in Sky & Telescope. See the June 1997 issue, page 109.

    Just for the record, between 1975 and early 2015 there are 7 "triple shadows". Times are for the beginning of the events:

    23 Jan 1985, 22:44 UT
    30 Jan 1997, 5:26 UT
    11 Nov 1997, 3:35 UT
    28 Mar 2004, 8:00 UT
    12 Oct 2013, 4:31 UT
    3 Jun 2014, 19:02 UT
    24 Jan 2015, 6:27 UT

    A further aside: it seems this resonance between the inner three moons is not just a mathematical curiosity. It leads to tidal stresses that have caused them (in varying degrees) to remain geologically active. Callisto, which is not part of this resonance, is also fairly dead geologically, with an extremely old, heavily cratered surface. Heinlein's guess, back in 1949, that the inter-satellite tides might cause quakes was more accurate than he knew.

    Earth and partially eclipsed Moon

    Set your "home planet" to Mercury, and the time to 21 Jan 2000, 6:00 UT, and look toward the Earth. You will have to zoom in very far (about level 14 or 15) to see much detail. As the title says, you'll see a partially eclipsed moon, close to the Earth.

    Trojan asteroids as seen from above

    Go to level 3 (45 degree field of view) and go to Epsilon Doradus (or someplace nearby; the idea is to be looking in the direction of the south pole of the ecliptic). Set your "home planet" to be the Sun, and hit Ctrl-F5; this is an undocumented feature for shifting your point of view.

    When you hit Ctrl-F5, it will ask you to enter a distance in AU. Enter a distance of 20 here. Guide will redraw, showing the inner solar system and a few bright asteroids as seen from a viewpoint well above the plane of the ecliptic.

    Next, you want to switch from "some bright asteroids" to "all asteroids". To do this, go into the Data Shown menu and turn Asteroids ON. Also, it's a good idea to turn asteroid labels off; they tend to get in the way in this particular case.

    This time, Guide will take some time redrawing the screen. But you will quite clearly see two short arcs, one 60 degrees in front of Jupiter and one 60 degrees behind it, illustrating the "shapes" of the Trojan nodes. Obviously, these objects are held very close to the same distance from the sun as Jupiter, but they have some freedom to move forward and backward within the node.

    To return to a more "normal" view, hit Ctrl-F5 again, enter a distance of 0, set your home planet back to Earth, and turn the asteroids to OFF or AUTO or wherever you normally have them.