earth like planet on opposite side of sun?

[desertmonk]

How could we determine if there is a planet exactly on the other side of our orbit around the sun? Imagine an earth like planet which is always behind the sun so we couldn't see it even during an eclipse. Would the gravitional effect give it away?

[tony873004]

That's called Earth's Lagrange 3 point. Any object placed there would be unstable, so it would quickly leave that point and become visible to us. It would even make some super-close passages to Earth before ultimately colliding with us.

If scientists took the idea seriously, they could have always pointed the Galileo spacecraft, or Cassini spacecraft, or lots of different spacecraft at the Earth's L3 point. An Earth-sized planet would easily be visible.

[archman]

There was some truly awful movie made about this back in the '60's I think. The "opposing earth" was a mirror image in every regard. "Our" Earth sent a spaceship to go visit, but it returned early. Only later was it discovered that it wasn't "their" ship, but the mirror-image ship sent by the opposing earth. The giveaway was that the ship's commander couldn't read anything unless it was placed in front of a mirror, oh and he drove on the wrong side of the road.

Fortunately mankind never learned of this opposite-earth, as all the records were destroyed when a spaceship crashed into the launch complex. Years later, the last surviving witness rammed himself into a full-sized mirror in a nursing home.

I hate that movie so very much.

[Van Rijn]

The name of that movie "Journey to the Far Side of the Sun" or "Doppelganger" ... here's the IMDB reference:

http://www.imdb.com/title/tt0064519/

Typical Gerry Anderson style flick, very weird with near zero technical accuracy.

I also recall another movie (I think it was a made for TV flick) a number of years later with the same theme. It is an old idea, but as tony said, an object at the L3 point won't stay there forever.

[montebianco]

That's called Earth's Lagrange 3 point. Any object placed there would be unstable, so it would quickly leave that point and become visible to us. It would even make some super-close passages to Earth before ultimately colliding with us.

Unless it is really big, in which case the Earth would be in its Lagrange 3 point, would be unstable, and would quickly leave that point :D

[beskeptical]

And to put it in more simpler terms, every planet in the solar system has a small gravitational effect on the other planets in the solar system which we have gotten very good at measuring. We would have detected the gravity of such a planet long ago even if we never saw it visually.

[Lance]

Unless it is really big, in which case the Earth would be in its Lagrange 3 point, would be unstable, and would quickly leave that point :D
How would it work out if the masses were identical? (Just curious)

[montebianco]

How would it work out if the masses were identical? (Just curious)

Well, if I understand correctly, they would both be unstable in all cases, but if the masses are very unequal, the effect on the larger body is so small as to be negligible. But if the masses are equal, they would both have appreciable stability problems.

At least, that's my understanding; I can work out the theoretical orbits mathematically without too much trouble, but need to practice up a bit to do the stability analysis...

N

[hhEb09'1]

At least, that's my understanding; I can work out the theoretical orbits mathematically without too much trouble, but need to practice up a bit to do the stability analysis...I'd imagine that a major contribution to the unstability (which has nothing to do with the lagrange points per se) is that the mass of Jupiter is so large, compared to the Sun (about .1%).

[montebianco]

I'd imagine that a major contribution to the unstability (which has nothing to do with the lagrange points per se) is that the mass of Jupiter is so large, compared to the Sun (about .1%).

Just to clarify, my comments applied only to the scenario (straying from the OP quite a bit) in which the only objects are the sun, the earth, and earth's evil twin in the L3 point...

[hhEb09'1]

Just to clarify, my comments applied only to the scenario (straying from the OP quite a bit) in which the only objects are the sun, the earth, and earth's evil twin in the L3 point...but in that case you have no perturbations to cause them to deviate, right?

[Ken G]

And note that technically, Lagrange points apply to test particles with no important gravity of their own, and the L3 point is not actually in the Earth's orbit, but a little farther from the Sun (it would have to be farther to have the same orbital period because it gets the Sun's gravity and the Earth's). If the test particle is actually another Earth, then indeed the L3 point lies in the Earth's orbit too, and we would just think the Sun's mass was a teensy bit higher than it is. The instability problems have been pointed out. I think the reason that these would indeed be serious even though the gravity is much weaker than, say, Jupiter's perturbing effects, is that they are always there all the time, resonant with our own orbit. But how far would we really wander due to the instability? Not far, the gravity is too weak. My guess is we'd end up like Janus and Epimetheus, the two moons of Saturn that are in essentially the same orbit but gradually overtake and switch orbits each time they meet. I'm sure the timescale for that to happen would lie within recorded history were it the case, as if, say, some primordial event had split the Earth in half.

[montebianco]

but in that case you have no perturbations to cause them to deviate, right?

Well, if everyting is spherically symmetric and perfectly placed, no :D

[suntrack2]

nice question you have raise, desertmonk.

[ToSeek]

I'm sure there are spacecraft that the presence of a planet there would have perturbed, particularly the ones, like Galileo or Cassini, using Earth to slingshot themselves to the outer solar system.

[desertmonk]

Thanks for the input folks. How much math would one need to do a stability analysis and theoretical orbit for these sorts of problems? I am going to eventually take calculus once I catch up with my math in school, and the idea of planetary orbits, escape velocities and other physics problems intrigues me.

[tony873004]

You don't need much math to get started on the simple things. Escape velocity is simple algebra. ve = sqr(2GM/r).

Stability analysis is really an n-body problem, so you could use numerical methods instead (i.e. let the computer do the work). For example, here's a rotating frame screen shot of a simulation of the original question. Two Earths were placed 180 degrees apart in the solar system, with the other 8 planets included to perturb them. After 300 years, they approached each other and repeled each other. Ken G was right, it's a lot like Janus and Epimetheus.

http://orbitsimulator.com/BA/L3earth.GIF

[jkmccrann]

Is there any possibility that planets like Venus or Mars, or for that matter Earth, could have started out in a different orbit, at a different distance, and been perturbed in some way to migrate slightly outwards or inwards to their current orbital locations?

I guess I'm wondering whether there would have ever have been any possibility of perhaps Venus and Earth being at one time in a situation similar to the one raised here, with the inherent instability causing them to eventually settle into their current orbits?