How would two planets with identical but perpendicular orbits affect each other?

Question

I'm exploring this idea for a fantasy world, and I was wondering how these planets would affect each other. The system would feature orbits in all three dimensions, not relatively flat like ours is.

Assume the speed of the orbits are slightly different; assume they'd pass close by each other but not hitting each other often. I know the frequent near-hits would affect the gravity of the planets somehow, and they'd have to hit each other eventually.

What would be the effects on the environment, gravity, etc. just before the collision?

Answer 1

The greater the angle between two similar orbits, the less frequent the near-hits would be - since the orbits would be slightly different, there may be a period of years where near hits occurred with increasing then decreasing proximity, then no near hits at all for a large number of orbits.

On the other hand, where the two orbits are very similar, with perhaps a small degree of eccentricity, the orbiting bodies can change position when they approach one-another. This would happen with more frequency, and a collision need not be inevitable in the short term.

Obviously, since in the real-world examples of such close approaches, the bodies involved do not disintegrate, there would be a reduction in perceived surface gravity toward and away from the other body.

As the bodies in such a system would be unlikely to retain their own satellites except in very close orbits, if there were seas of any fluid, there would be no tides other than from the system primary, until the approach of the co-orbiting body, at which time there would be tides with the high tide oriented toward the other co-orbiting body.

Depending on the closeness of the approach - this could be near the bodies Roche limit - there could also be significant stress applied to the body's structure such that if it was large enough, it could cause internal heating and earthquakes. Also, if a significant atmosphere was present, the atmospheric pressure could drop causing violent storms near the point of closest approach.

If the two bodies were large and of similar size (such that both were habitable and inhabited), their inhabitants, if sufficiently technologically advanced, would have many opportunities to travel from one world to the other at relatively little expense in rocket fuel as the worlds approached one-another and reduced the cost of leaving the worlds' gravity wells.

Answer 2

The system would feature orbits in all three dimensions, not relatively flat like ours is.

Without some form of manual intervention, this is literally impossible. For this to happen, you need some magic or advanced technology to move the planets into the 3d orbits after the solar system has formed.

While the system is being formed, it is a large cloud of particles. The center of mass of this cloud will be where the star eventually forms. Every single particle around this center of mass has some angular momentum in relation to the center.

If you compare all the particles against each other and average out their angular momentum, you will get a single vector that corresponds to the eventual plane of the ecliptic of the system. Take, for example, two particles, one going around the Center of Mass twice an hour, the other going in the opposite direction at half the speed. The angular momentum of the whole system is 1 revolution per hour in the direction of the first particle.

Over time, as these two particles go past each other they will both slow down. The slower one of the two will eventually not have enough speed to stay in orbit. It will fall into the center of mass, eventually creating a star.

The same is true even as you add more particles. The gravitational interactions of all the particles causes a 'drag' that lowers the angular momentum of each particle towards the average angular momentum of the entire system. This causes most particles to fall into the center of mass creating the system's star. Everything that doesn't fall into the star clumps together to form planets and debris (moons, asteroids, comets, etc).

At the scales we are talking about, you can almost treat an accreting solar system as a fluid. If you have water in a bucket and start spinning the water around, the water particles bumping against each other force them all to go the same direction.

Now to directly answer your question: If, against all odds, a planet formed counter/perpendicular to the direction of the rest of the system then it would slowly change orbits until it was either aligned with everything else, crashed into something (most likely the sun), or - most likely - would pass close to another body and get ejected from the system.

Answer 3

If orbits are "identical" other than inclination, they would move at the same speed: you are contradicting yourself with saying they are identical and have different speeds.

Barring that, the sameness each time around would cause a cumulative effect. The situation would not be stable.

Answer 4

As others have said, you have a big stability problem here. While there are some situations in our solar system with objects with periodic close encounters all of them involve shepherd situations--there's another more massive body that's keeping the situation stable. I don't believe you can have a shepherd situation without the bodies being in similar orbits.

Note, also, that if you're looking at travel between the worlds you have a very big problem. The fastest anyone has returned from space is 11 km/sec for the Apollo astronauts--a quick Google says 7.19g for Apollo 16. Earth's orbital velocity is 30 km/sec, though, and the other planet will have a like velocity. If I'm remembering my math right that means a spacecraft from one world will hit the atmosphere of the other at 42 km/sec. (And if my memory is wrong it's 60 km/sec.) Figuring the Apollo profile is about the best that can be done that comes out to 27.7g if my math is right, 39.2 if it's not. Even 27.7g for the duration of atmospheric entry carries a high probability of death.

You can cut these numbers somewhat if you do it in two stages--the first passage to burn off some velocity and head back out into space at something below escape velocity. Keeping the peak gs down will limit how deep into the atmosphere you can go while pulling such a maneuver, though.

If you want worlds that interact you want two worlds in a shepherding situation. The approach velocity is slow, Apollo-type spacecraft could make the crossing.