User blog:Cerne/More about Lagrange Points

Here are some more posts from the thread I made about Lagrange Points. After going through all the html attachments I have saved in my email account, it becomes clear that I need to start saving these threads somewhere else. Whenever I read through the email, it slows down considerably and becomes patchy. I have decided to save as much of the actual information inside the attachments as I can before I delete them, ass the while awarding due credit to the member who provided it.

To clarify for a minute what I mean by "awarding due credit," the actual information in itself is not what I need to credit its provider for. If it is true, then it basically exists no matter who informed me about it. It is the way in which the information is conveyed by that particular person that I need to award credit for. What they type may be merely raw data in itself, but how they type it is almost like an art. It is very individual and stylized, and I need to make sure I attribute that to the people who typed it.

Anyway, yes, I would say I need to find another means of storage. This blog doesn't serve that purpose ideally either. Aside from resetting the formatting of the posts, of which I had problemswith in my last entry, a blog doesn't strike me as something that was designed to store information in the first place. Yeah, I know. That is what the actual wiki articles are for. But I already mentioned why I can't store some types of information in the articles. Where it has to do with substantiating outside information relevent to the article in question, and dually acting as a reference, a blog seems to do just fine. I think, though, in the future I will try harder to save online bboard threads to a disk rather than as an email attachment.

And now here are some more posts from the Lagrange Points thread

Ok, then, first... they aren't moons.

Now, you'd want to put them at L4 and L5, those are most stable. L1,2,and 3 are very unstable, anything will knock them out, but 4 and 5 are fairly stable. This is described in the wiki article for Lagrange points.

They will have to be small (not as small as just dust, but they probably wouldn't be visible from the surface)

You'd also have a problem that, if they were visible, you'd only see one just before dawn that would be quickly overpowered by sunrise, and the other would only be visible long after the sun set, but it'd already be getting ready to set itself. so there'd be little time to see them if you could.

If P (smaller) orbits S (larger), and you put something into the L4 and L5 points of that system, they also will orbit S.

If you also have M orbiting P, it will not be at any of the Lagrangian points of the P-S system. You can have some more objects (M', M" etc.) at the L4 and L5 of the M-P system. But you first need the one basic M to be able to do this, as Lagrangian points aren't defined for P alone (and again, those of the P-S system won't orbit P, they'll orbit S.)

In the general sense however, Lagrangian points aren't related to orbits; they're rather the exact opposite of orbit.

The three moons share one orbital path around the planet. One of the small moons (at L4) is 60� ahead of the large moon, and the other small moon (at L5) is 60� behind the large one. This is the same as Saturn's moon Tethys, which has the smaller moons Telesto ahead of it at L4 and Calypso behind it at L5.

L4 and L5 are relatively stable points, but the other Lagrange points are less stable, so it's unlikely for a moon to appear there.

Maybe I missed it, but I don't think anyone else has mentioned it so far.

None of the Lagrangian points would be stable in a system like you've mentioned.

For L4 and L5 to be stable, the largest body has to be about almost 30 times (actually, about 24.96 times, but as the ratio goes down the initial conditions for stability become more and more persnickety, like balancing a pencil on its sharpened point instead of on the chewed-off eraser-end) as massive as the middle-sized body, and the smallest body usually almost has to be close to 0 times as massive as the middle-sized body. (The calculations to prove it's stable if its mass isn't negligible, are a bit more complicated.) [LINK]

It is not reasonable to expect to find any natural satellite occurring in an unstable Lagrangian point; if you find something there, it was put there recentishly, so it was probably put there artificially.

L1 and L2 and L3 are never stable. When the smallest body is on the straight line between the two larger bodies, it's in L1 or L2 or L3

L1 is between them, at the center-of-gravity of the system consisting of both of them.

L2 is on the other side of the middle-sized body from the largest body.

L3 is on the other side of the largest body from the middle-sized body.

L4 and L5 are on the same orbit as the middle-sized body has around the largest body

The L4 position is 60 degrees ahead of the middle-sized body; the L5 position is 60 degrees behind the middle-sized body.

[LINK]

Memorize: "4 comes before 5, so L4 is ahead and L5 is behind." or something like that.

All five Lagrangian points exist no matter what, but only L4 and L5 are ever stable, and then only if the middle-sized body is less than about 3% of the mass of the largest body, and the smallest body is close to 0% of the mass of the middle-sized body.

The L4 and L5 positions are the same distance from the largest body as the middle-sized body is.

Yes, the larger satellite would need to be at least (25+3*sqrt(69))/2 times smaller than the planet; but the smaller satellite would need to be quite a bit smaller than the larger satellite, by an even bigger ratio.

Consider the ratio of the mass of Jupiter to the mass of a Trojan asteroid.

624 Hektor is the largest Trojan asteroid at a mass of about 1.4 * 10^19 kilograms. (The total mass of all the Trojans is about one ten-thousandth of an Earth mass.)

Jupiter's mass OTOH is about 1.9 * 10^27 kg (about 318 Earth-masses or about 1/1047 of a Sol-mass).

That ratio is about 1.36 * 10^8 or 13,600,000.

Even Mars, at about 11% of an Earth-mass (about 6.4 * 10^23 kg), is still more than 100 times more massive than the total mass of all Trojan asteroids, and so about 4.5 * 10^4 times as massive as 624 Hektor.

If you want to look at actual L4-and-L5 satellites of actual planets, see here and here.

Saturn's mass is about 95 Earths.

Tethys's mass is about 1.03 * 10^−4 Earths. So Saturn outmasses Tethys about a million to one. Telesto is in the L4 point ahead of Tethys; I don't know its mass, but its radius is only about 11.8 km while Tethys's is about 533 km, so if they have the same density it's probably about a eleven millionths of the mass of Tethys. Calypso is in the L5 point behind Tethys; I don't know its mass either, but it's smaller than Telesto, with a radius of about 10.7 km.

Dione's mass is about 3.3 * 10^−4 Earths, or 1.1 * 10^21 kg.. So Saturn outmasses Dione about 300,000 to one. Helene is in the L4 point ahead of Dione, and its mass is about 25 * 10^15 kg. So Dione outmasses Helene by a ratio of about forty-four thousand to one. Polydeuces is in the L5 point behind Dione, and it masses about 30 * 10^12 kg. So Dione outmasses Polydeuces by about 36,700,000 to one.

Those are the only satellites of planets I know about that are in L4 and L5 libration points of other satellites in our Solar system.

The first post was made by fmra, the second post by Tropylium, the third post by thedukeofnuke, and the last two posts by TomHChappell who I also referred to in my previous entry. All are members of the Zompist Bulletin Board (http://www.spinnoff.com/zbb). The post made by thedukeofnuke was in response to a post made by Yiuel, another member of the ZBB, who was explaining to me the reasoning behind the occurrance of the moons orbiting a planet in this page. Two of the links in TomHChappell's first post had to be added seperately after the link text they were embedded in because the text that the links were embedded in were too long to fit into this wikia's URL tool's text box, so I added [LINK] after the text with their intended URL and embedded the URLs in there. These are not all of the posts that were in the thread but the rest of the posts that were not made by me were either too short or were simply confirming that neither of the moons orbiting my planet were on Lagrange Points, for which I offer my thanks.

That just about does it for the Lagrange Points thread. After I post this entry, I am going to delete the original thread page from my email account to save room. Information from other thread pages may go into this blog too, but no new threads will be saved as email attachments or recorded in this blog. I will probably also contact all of the ZBB members who contributed the posts that are being recorded here, just to let them know what I am doing and give them the opportunity to decide whether they want the posts recorded in my blog or not.

Thanks for reading,

Cerne 22:51, September 9, 2010 (UTC)