Stability of Counter-Planets: Examining the Possibility of Dual Planetary Orbits

[Nentuaby]

Is it possible to have two planets orbiting opposite each other across their star? Either with the two being of roughly equal mass, or with one giant planet and one terrestrial?

Everyone's heard of the old "Counter-Earth" theory, which of course is wrong, but I was wondering if given our current understanding of orbital physics it could have been right, or if the configuration just can't be stable. Could make a good element for some hard science fiction, but sadly my layman's knowledge isn't enough to know whether using it would end up with me dumped in the "Dan Brown pile." ;)

 

[Helios]

It's so unlikely that it's ridiculous. Is it possible that 5 comets could collide into each other at once? Yes, it's possible.
The planets would likely differ in their distances from the star by some amount and would eventually collide.
Even how such exact positions could come to be by any natural formative process is beyond improbable.

 

[D H]

The configuration is metastable. What that term means: Think of a pendulum, a long rod suspended from one end. The pendulum has one stable configuration and one metastable configuration. The stable configuration is with the pendulum oriented vertically and the suspension point at the top of the pendulum. The metastable configuration is with the pendulum oriented vertically and the suspension point at the bottom of the pendulum. If the pendulum is perfectly vertical it will stay in this metastable state. The slightest disturbance will make it tip. Another word for metastable is unstable.

There are two stable and three metastable states for a pair of objects orbiting a star. These configurations are called the Lagrange points. (Google that phrase.) The star and the two objects are collinear in the three metastable configurations. The configuration discussed in the original post is the L3 configuration. Suppose a counter Earth did somehow come into being. That configuration would not last very long. All it takes is the slightest of nudges to knock the Earth and counter Earth out of that configuration. The gravitational influence of a comet out beyond Pluto would suffice to provide the nudge.

 

[Nentuaby]

There are two stable and three metastable states for a pair of objects orbiting a star. These configurations are called the Lagrange points. (Google that phrase.) The star and the two objects are collinear in the three metastable configurations. The configuration discussed in the original post is the L3 configuration. Suppose a counter Earth did somehow come into being. That configuration would not last very long. All it takes is the slightest of nudges to knock the Earth and counter Earth out of that configuration. The gravitational influence of a comet out beyond Pluto would suffice to provide the nudge.

I do know the L points. As I understood it, the body in the Lagrangian orbit must be much smaller than the primary body for the system to be stable. You're saying, though, that L3 is not actually stable regardless of the ratio of masses?

And Helios, I'm aware the initial configuration is astronomically improbable. It is, however, an infinite universe. As a story element it was meant to be something of a wonder; I'm only really concerned with whether it can continue, or would fly apart inevitably.

 

[DaveC426913]

It is, however, an infinite universe.

Well, no it isn't, but your point is made.

 

[D H]

I do know the L points. As I understood it, the body in the Lagrangian orbit must be much smaller than the primary body for the system to be stable. You're saying, though, that L3 is not actually stable regardless of the ratio of masses?

The collinear Lagrange points are always unstable. Even the triangular Lagrange points are only stable if the mass of the third body is very small.

 

[Nentuaby]

I see. I'll have to abandon that idea, then. Thanks for the help.