Jupiter's Satellites

Jupiter and its satellites are sometimes called a `miniature Solar System', but the truth is more complicated. Three of Jupiter's four satellites are locked in resonant orbits. This has interesting consequences for our weekly observations, and for the history and fate of the Jovian system.


Jupiter has four bright satellites which are easily seen with a telescope. These bodies travel around the planet in nearly-circular orbits; in order of increasing distance from Jupiter, they are called Io, Europa, Ganymede, and Callisto. Kepler's third law implies that satellites with smaller orbits move more rapidly. Thus Ganymede, Europa, and Io, which are all closer to Jupiter than Callisto, should all move faster than Callisto.

If we try to test this prediction by making observations every Monday night, we will find the satellites at the positions shown in Fig. 1. Looking at this figure, you may notice something strange. The three inner satellites, Io, Europa, and Ganymede, seem to barely move from one week to the next, while Callisto jumps all over the place. That's not what Kepler's third law led us to expect! What's going on?

Positions of Jupiter's satellites

Fig. 1. Jupiter's satellites at 20:00 (HST) on lab nights during Fall 2008. The satellites are identified by their initials.

25-Aug-2008 01-Sep-2008 08-Sep-2008 15-Sep-2008 22-Sep-2008 29-Sep-2008 06-Oct-2008 13-Oct-2008 20-Oct-2008 27-Oct-2008 03-Nov-2008 10-Nov-2008 17-Nov-2008

The answer involves two facts. One is pure coincidence; the other is a profound truth about Jupiter's satellites.

First, the pure coincidence: it takes Ganymede 7.155 days to orbit Jupiter. This is slightly more than one week, so if we observe Jupiter's satellites on the same day every week, we'll see Ganymede in almost exactly the same place each time. While we're not looking, Ganymede goes around Jupiter and almost returns to where it was the week before. This is a matter of luck; it just so happens that the 7-day week we use on Earth is almost exactly equal to Ganymede's orbital period.

Second, the profound truth: Europa's orbital period (3.578 days) is half of Ganymede's, and Io's orbital period (1.789 days) is half of Europa's! In the time it takes Ganymede to make one orbit, Europa makes two orbits, and Io makes four orbits. So when we observe once a week, we see all three of these satellites almost exactly where they were the week before. The relationship between Ganymede, Europa, and Io's orbital periods is not a coincidence; the odds of such celestial clockwork occuring by chance are very small.

If the time between our observations exactly matched Ganymede's orbital period, we would see the three inner satellites in the same places each week. But the amount of time between our observations is 0.155 days (or 3 hours, 43 minutes) shorter than Ganymede's orbital period, so Ganymede doesn't quite complete its trip around Jupiter. The result is a bit like photographing a clock once every 59 minutes; a series of such photographs shows the minute hand slowly moving backward because it doesn't quite finish its trip around the dial between photographs. In the same way, our weekly observations show Io, Europa, and Ganymede all slowly shifting backwards.

Fig. 1 shows the outermost satellite, Callisto, appearing all over the place. This happens because Callisto's orbital period of 16.689 days is somewhat more than two weeks; thus observations at weekly intervals find Callisto appearing on more or less opposite sides of Jupiter.

RESONANCES

The relationship between the orbital periods of Io, Europa, and Ganymede is an example of a resonance. More generally, we say that two orbits are resonant when the ratio of their periods is a ratio of whole numbers. For example, Pluto's orbital period is 247.7 years, while Neptune's orbital period is 164.8 years. The ratio 247.7:164.8 is equal to 3:2, so Pluto completes two orbits around the Sun in the same time it takes Neptune to complete exactly three orbits. This resonance explains how Pluto and Neptune can cross orbits without colliding: Pluto only comes within Neptune's orbit when Neptune is on the other side of the Solar System. It's also possible to have resonances between orbital motion and rotation; for example, the Moon's orbital period and rotation period are both 27.3 days, so their ratio is 1:1 exactly.

In the case of Jupiter's satellites, it's likely that Io, Europa, and Ganymede developed their resonance as a result of gravitational attraction. One possible scenario starts with Io, Europa, and Ganymede all orbiting closer to Jupiter than they do today. As a result of the tides Io created on Jupiter, Io's orbit slowly drifted outward, and as it did so it would eventually approach a 2:1 resonance with Europa. Once that happened, the orbits of the two satellites would be `locked' by gravity, and both would drift outward together. Eventually, as Europa's orbit grew larger, it would have reached a 2:1 resonance with Ganymede, and the orbits of all three satellites would lock into their present relationship. Eventually, as the orbits of the three inner satellites continue to drift outward, Ganymede may reach a 2:1 resonance with Callisto, and all four orbits will be locked together.

Resonances play an important role throughout the Solar System. For example, some of the gaps in Saturn's rings occur as a result of resonances between particles in the rings and Saturn's satellites. Likewise, there are gaps in the asteroid belt as a result of resonances with Jupiter.

OBSERVING THE SATELLITES

To see that Io and Europa really do complete four and two orbits, respectively, in the time it takes Ganymede complete one orbit, we would have to observe Jupiter in between our weekly lab meetings. However, Stellarium [www.stellarium.org] and similar planetarium programs can be used to display Jupiter's satellites and speed up their motion; we may try this out on a cloudy night.

We will continue to observe and sketch Jupiter's satellites when it's convenient. You can compare your sketches with the predictions shown above to confirm that the satellites appear in their expected positions.

Events on Lab Nights

As Jupiter's satellites orbit they periodically pass in front of or behind the planet; they also pass through Jupiter's shadow or cast their own shadows on Jupiter's disk. A passage in front of the planet is called a transit, while a bassage behind is called an occultation. An eclipse occurs when a satellite passes through Jupiter's shadow, while a shadow transit occurs when satellite's shadow falls on Jupiter.

The table below lists various events involving Jupiter's satellites which we hope to observe during lab nights. On 08-Sep we saw Europa ending a transit of Jupiter's disk, and some people may have glimpsed Europa's shadow as well.

  Date Time
(HST)
Event
 
08-Sep 19:24 Europa shadow transit begins
  19:50 Europa transit ends
 
15-Sep 19:32 Europa transit begins
  21:36 Callisto eclipse begins
 
29-Sep 19:26 Io eclipse ends
 
06-Oct 21:22 Io eclipse ends
 
13-Oct 19:40 Io occultation begins
 
20-Oct 21:36 Io occultation begins
 
27-Oct 21:22 Callisto shadow transit ends
 
03-Nov 19:35 GRS on meridian
 
10-Nov 20:25 GRS on meridian
 
17-Nov 21:14 GRS on meridian

WEB RESOURCES

REVIEW QUESTIONS


Joshua E. Barnes      (barnes at ifa.hawaii.edu)
Updated: 19 September 2008
http://www.ifa.hawaii.edu/~barnes/ast110l_f08/jupitersat.html
Valid HTML 4.01!