Can two planets inhabit the same orbit?

[astro1000000]

Imagining a clock...the middle of the face where the hands rotate from represents the sun.

If at 12 and 6 were to planets, could they inhabit the same orbit around the sun without consequence?
I imagine they would not collide as they would be moving at the same rate and in this scenario are at polar opposites of each other.

For a manuscript I'm working on I have been puzzled by an imaginary planetary alignment...
I am to provide a single planet orbiting a sun with a planetary alignment to happen like the number five appears on dice.

The sun and Earth planet too be the center dot and the 4 other planets to align at the points of the remain 4 dots on the die.

I'm not sure if I'm explaining the problem correctly as I've found most ppl have trouble comprehending the issue.

Back to the clock reference, imagine the clock again, the sun and Earth being at the middle point and the four remaining planets being at alignment at 12 - 3 - 6 - 9

Preferably they would inhabit separate orbits but with my limited knowledge of the cosmos and its physics i am not sure how to present this in a way that is plausible and believable.

I have the imagination to envisage such but not the understanding to make it practical.

 

[cadnr]

I suppose that if the orbits were geometrically perfect then it would be possible to have as many symmetrically placed planets in the same orbit as you like, as long as they are all separated by the same amount. Alas though, no orbit is perfectly circular, so such arrangements in reality are probably unstable and would tend towards chaos.

Lagrange points (http://en.wikipedia.org/wiki/Lagrangian_point) represent the places in a planet's orbit where another body can remain stable. L3 is directly opposite the star.

 

[Janus]

The problem with a planets at the "6 and 12" positions is that it is not a perfectly stable arrangement. The slightest nudge will displace them and they will drift out of position.

There is an arrangement called a Klemperer Rosette which allows multiple planets(at least 4) spaced equally around a star. The problem is that the planets must be alternating in mass (light, heavy, light heavy), and the light planets all have to have the same mass and the heavy planets have to have the same mass. It is, for all intents and practices, impossible for this to happen naturally.

 

[O-r-i-o-n]

M>>m ?

What if mass of the planet(s) is a lot less than the star they're orbiting(M>>m)? I don't think the gravity of the second planet effect the other planet's orbit? according to astro 100000 they're in the maximum mean distance condition! so the gravity force is at the minimum.

 

[D H]

The L3 point is an unstable equilibrium point. The "6-12" configuration described in this thread is similarly unstable. There is no restoring force to bring the system back to the "6-12" configuration; any deviations from the equilibrium will grow. Any other planet in the system will perturb the equilibrium.