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I am developing a small computer program that involves moderately simple simulation of elliptical Kepler orbits for fictional, generated star systems. I'm doing this without much prior knowledge of orbits (apart from some basic equations) or astrophysics in general.

I'm attempting to create loosely realistic orbits in the sense that they are not all in one plane and that they are elliptical with the parent body at one focus. The program assumes there are only interactions between a body and the one it orbits. Planets do not affect other planets' orbits. All other forces are explicitly ignored with orbits following only Kepler's laws.

The axis of rotation of each body in this simulation will be static (ie. without precession) and the axial tilt will be pseudorandomly generated. I wish to align an orbit with zero inclination with the equatorial plane of the parent body.

The real question, then, is the following: are there are any important constraints to the direction of the axis of rotation of an arbitrary hypothetical body orbiting another hypothetical body of significantly greater mass that I should take into consideration when determining the axis and axial tilt?

Which is to say, can the axis of rotation of, say, a planet, "point" in any arbitrary direction?

(The axis can be assumed to be a vector in the direction of the north pole. The north pole is here simply the pole that is "above" the orbital plane when axial tilt is zero.)

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I'd say yes, but I have no evidence to back this up. –  ChrisF Jun 15 '13 at 22:44
There are really at least 2 questions : -1- does it naturally occur when systems form ? -2- can it be stable in any direction, for example if a body is captured as satellite ? Venus has a retrograde rotation, i.e. its axis is reversed compared to other planets, and its rotation is very slow. –  babou Jun 15 '13 at 23:16
@babou I suppose - but for my purposes it's not absolutely necessary that it naturally occurs when systems form as it could simply have happened because of some reason afterwards (this program pretty much has to assume the system was formed so long ago that such changes could have occurred) –  Esa Lakaniemi Jun 15 '13 at 23:32

2 Answers 2

up vote 4 down vote accepted

Uranus has an axial tilt of 97.77 degrees (it's on its side). So we have axial tilts ranging from 23.5 degrees (earth) to uranus's axis to venus's retrograde rotation. I think its safe to say that the axis of rotation can point in any direction. Remember that the axis of rotation is in fact the direction of the angular momentum, which can be changed by torque, i.e. collisions that are not directed right at a planet's center-of-gravity. Considering that the early solar system featured many of these types of collisions, I imagine that over time the axial tilt of a plant may be in any conceivable direction. For more re: Uranus's tilt, check this.

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Well, I'd say the jury is still out on how Uranus and Venus ended up rotating the way they are. It is difficult to torque a planet that much via a collision without obliterating it. But these are just details. –  Chris White Jun 16 '13 at 4:38
Alright, that suggests that there are no real big constraints to how I can generate the axes. I'll probably make only a slight tilt the norm, with larger ones appearing occasionally. Thanks. –  Esa Lakaniemi Jun 17 '13 at 12:03

I understand that angular momentum can be exchanged between bodies, for example through tidal effects, but is it to the point of changing the axis of rotation.

See for example ... Angular momentum power plant on Earth, Why does the moon drift away from earth?, Are tidal power plants slowing down Earth's rotation?.

If the retrograde motion of venus is due to the influence of the solar system (open question apparently) then is it really much harder to very slowly modify the orientation of the axis ? Tidal effects have significant long term results. Typically, this is the reason the moon is always showing the same side. It used to rotate faster. What would have happened with a tilted initial axis like Uranus ?

That is why I was wondering whether you were concerned with long term preservation of the axis orientation.

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