Amazing Facts About Saturn’s Moons

Saturn is very peculiar and distinct from other planets with regard to the orbits of its moons. Here's some amazing facts....Hang in there 'til the end; I've saved the best for last.

Amazing fact #1: No other planet has 2 moons (or more) that follow exactly the same orbit; (only Jupiter has two that are somewhat close in orbital period).

Amazingly Saturn has several moons with multiply occupied orbits:
Dione and Helene, though having a vast difference in mass, occupy the same orbit at mean radius of 377,400 km. (Only a very slight difference in eccentricity and inclination - but never mind that for now).

Amazing Fact #2:
Even more amazingly Tolesto, Calypso, and Tethys ALL THREE orbit at exactly the same radius from Saturn AND ALL three have perfectly circular orbits (no
eccentricity). . Thus all three have the same orbital period.
However, Tethys (the larger by far) has a slight inclination (1.1 degree), whereas Tolesto & Calypso orbit EXACTLY around Saturn's equator.
(Tolesto & Calypso are small ~ 17km. radius, whereas Tethys is large ~ 530km.)
All 3 have mean orbital radii of 294,660 km.


*Amazing fact #3; *my Prediction; *and a problem to solve:

My prediction: Saturn has two other moons, Janus and Epimeteus, that I predict will (may) in the near future (whatever that means) begin to orbit each other! OK, before you call the paddy wagon let me explain.

Amazing Fact #3:
It is a little known fact that Janus and Epimetheus, are said to occupy the 'same' orbit, but in reality they have a difference in mean orbital radii of ~50km.

Epimetheus at 151,422 km.
Janus at 151,472 km.

This is extremely close to the Roche' limit (but that's not the point here.... there are others even closer to Saturn). The point is that the orbital period of both of these moons is short: Janus = .6945 days
Epimeteus = .6942 days
The DIFFERENCE in Orbital period is only 26 seconds!

Therefore, I have calculated that the inner moon overtakes the outer one every 1602.8 days, (4.388 yrs.), after Janus makes another 2307.8 revolutions about Saturn.
Someone double check me just to make sure.

Now here's the amazing fact #4:
**Due to the close proximity of these two moons' orbits, EACH time the inner moon overtakes the outer, THE TWO MOONS TRADE ORBITS!! Gravitational attraction is such that the exchange in momentum causes a precise trade in orbits, until of course, another 2308 revolutions brings them back together again, and another exchange takes place. I believe Janus currently occupies the outer orbit (as given in above data).

Now the lunar sizes are:
Janus radius (in km.) 98x96x49 (both are somewhat potato shaped).
Epimetheus radius ...... 72x54x49 km.

You may be wondering how it is possible that one moon can overtake the other in the first place. The difference in orbital radii (50 km) is less than the radius of the moons themselves; so why isn't there a collision?

Well, there's one thing I didn't mentioned. There is a slight difference in inclination of the two orbits by 0.20 degrees. By using a bit of trig. and my $7.95 Radio Shack calculator I have determined that their closest approach (even assuming they didn’t exchange orbits) to be about ~530 km. or 5.5 to 6 Janus radii…..and most of that is in the North - South direction. (Someone check the calc. just to make sure).
So why is this important? Well, I’m glad you asked.

First, I think there should be orbital capture. Now there’s no easy way to estimate possible orbital capture; but I do so by comparing the two moon’s relative velocity with the escape velocity of the larger. First, the relative velocity (velocity at which the inner moon overtakes the outer) I calculated to be 7 m./sec.. (Someone check me using the two orbital periods given just to be sure).
Now I want be sure that this relative velocity exceeds the escape velocity of Janus at the distance of closest approach. Actually, I want to find at what distance the escape velocity of Janus just exceeds the 7 m/sec. relative velocity. May sound simplistic but that's how I'm doing it.

Using the mass of Janus (2.01 e^18 kg.) one can easily calculate the escape velocity AT THE SURFACE (at the 98 km radius) as being 52.2 m/sec. At first glance one may think that since gravity tapers off as the inverse square there’s no way at ~6 radii there would be enough gravity to beat 7 m/sec. BUT we are not determining gravitational acceleration here; we are talking about the ESCAPE VELOCITY, which only goes as the inverse square root of radius! It turns out that, in order to have an escape velocity of 7 m/sec. (relative to Janus), one has to go out to over 55 Janus radii ! Anything inside of that should not be able to escape and will begin accelerating toward Janus, eventually going into orbit around a common barycenter. (Again, check my figures).

So why do we still see these two moons blithely ignoring my calculations? I thought I had finally found the answer in a slight difference in eccentricity which could extend the minimum distance of approach. Janus e is .007 and Epimetheus is .009. But my calculations show even if the relative eccentricities were rotated by 90* wrt each other, so that the full differences of semi-major and semi-minor axis’ were included, there would still only be a maximum separation of around 26 Janus radii at their conjunction. This appears to be far short of 55 radii needed to evade orbital capture.
Can someone show me different? Am I missing something during the momentum exchange that would preclude lunar gravitational capture? Furthermore, to me, it seems that during that exchange there would likely be an even closer approach as the outer moon speeds up, the inner slows, and there is a reversal in both inclinations.

So my conclusion is : Eventually, as more conjunctions occur, there will be a gravitational matrimony between Janus and Epimetheus, (in fact it should have happened already). If anyone has reason to believe that this marriage should not take place let him speak now or forever hold his peace.
Mass of Epimetheus = 5.6e^17 kg.

G^2





<font size=-1>[ This Message was edited by: Gsquare on 2002-12-20 08:50 ]</font>

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