# Thread: Trojan gas giants?

1. ## Trojan gas giants?

How's that for ridiculous sci-fi?

Lets say there's a star similar to our sun. In a low-eccentricity orbit around that star is a very massive jovian. Say, about, 11 Jupiters. Could a significantly smaller gas giant, say, a Uranus-sized planet, be able to remain in one of the trojan lagrangian spots of the 11-jupiter-mass planet's orbit?

2. The classic three-body problem has a stable solution if the central mass is more than about 25 times the mass of the second mass and if the third body is of negligible mass. You can look that up easily in many places; for example,

http://www.cdeagle.com/ommatlab/crtbp.pdf

Now, if the third body has a non-negligible mass, the analysis is more difficult. I recall a thread on the BAUT fora a few years ago which discussed this very problem. As I recall, tony873004 provided some very nice numerical results -- can he or anyone else find this thread? -- which suggested that as long as the combined mass of bodies two and three is less than about 4 percent of the central body, the orbit is _relatively_ stable on reasonably long time scales.

Since the mass of the Sun is of order 1000 times that of Jupiter, a system consisting of a) a solar-mass star, b) a planet 11 times Jupiter's mass and c) another planet of roughly Jupiter's mass, would satisfy the condition mentioned above: total mass of bodies two and three is less than about 4 percent that of the central star.

3. Actually, the third body is a Uranus mass object, which should probably work out in its favor?

4. Established Member
Join Date
Jun 2010
Posts
652
Originally Posted by PlutonianEmpire
How's that for ridiculous sci-fi?

Lets say there's a star similar to our sun. In a low-eccentricity orbit around that star is a very massive jovian. Say, about, 11 Jupiters. Could a significantly smaller gas giant, say, a Uranus-sized planet, be able to remain in one of the trojan lagrangian spots of the 11-jupiter-mass planet's orbit?
1:1 resonances are considered an open possibility that some planet searchers are looking for. So I don't think it's ridiculous. The mass ratios they talk about are much closer than your example.

5. Originally Posted by StupendousMan
Now, if the third body has a non-negligible mass, the analysis is more difficult. I recall a thread on the BAUT fora a few years ago which discussed this very problem. As I recall, tony873004 provided some very nice numerical results -- can he or anyone else find this thread? -- which suggested that as long as the combined mass of bodies two and three is less than about 4 percent of the central body, the orbit is _relatively_ stable on reasonably long time scales.
These might be relevant.

http://www.bautforum.com/showthread.php/38142.html
http://www.bautforum.com/showthread.php/36345.html

I tried searching google with the terms tony873004 site:bautforum.com, and added phrases like 3-body, jupiter, trojan. Guaranteed to find plenty interesting threads!

6. Established Member
Join Date
Mar 2005
Posts
1,246
Originally Posted by StupendousMan
As I recall, tony873004 provided some very nice numerical results -- can he or anyone else find this thread? -- which suggested that as long as the combined mass of bodies two and three is less than about 4 percent of the central body, the orbit is _relatively_ stable on reasonably long time scales...
http://www.bautforum.com/showthread....Earth-changes?

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•
here