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-   -   [Space] Orbital Mechanics of Moons (http://forums.sjgames.com/showthread.php?t=63645)

Prime Evil 10-25-2009 03:12 AM

[Space] Orbital Mechanics of Moons
 
A couple of quick questions for the astronomers out there that don't seem to be covered by GURPS Space...

If a planet has natural satellites, what would be the best way to determine the inclination of the orbits of the various moons with respect to the ecliptic plane?

Is the rotational axis of a moon related to the axial tilt of the planet that it orbits or should you randomly determine the axial tilt of the moon with respect to its own orbital plane?

The table on p.118 of GURPS Space makes it possible to randomly determine the axial tilt of planets. However, the Wikipedia article on axial tilt seems to suggest that the presence of one or more large moons orbiting a planet may provide a stabilizing influence that prevents large variations in axial tilt over time. Is this true? Or am I mis-reading the article? Does this make it less likely that planets with large moons will have a high axial tilt?

malloyd 10-25-2009 03:25 PM

Re: [Space] Orbital Mechanics of Moons
 
Quote:

Originally Posted by Prime Evil (Post 872500)
A couple of quick questions for the astronomers out there that don't seem to be covered by GURPS Space...

If a planet has natural satellites, what would be the best way to determine the inclination of the orbits of the various moons with respect to the ecliptic plane?

Most moons orbit in the plane of the planet's equator, so it's the axial tilt of the planet. Our moon is an odd exception, its massive enough compared to the Earth it hasn't yet been tidally dragged into that situation, but for most moons the planet's equatorial bulge will force that in a few million years.

Quote:

Is the rotational axis of a moon related to the axial tilt of the planet that it orbits or should you randomly determine the axial tilt of the moon with respect to its own orbital plane?
Again there are tidal forces trying to make the rotational axis perpendicular to its orbital plane, but these are weaker. A lot of non-tidelocked moons have axes pointed in all sorts of directions. Use the random system.

Quote:

The table on p.118 of GURPS Space makes it possible to randomly determine the axial tilt of planets. However, the Wikipedia article on axial tilt seems to suggest that the presence of one or more large moons orbiting a planet may provide a stabilizing influence that prevents large variations in axial tilt over time. Is this true?
Stablize just means the axis doesn't move around a lot, not that there is any particular reason for it to be at a low or high angle to the orbital plane. The forces involved are the same ones that drag the moon into an equatorial orbit, acting the other way. If the equator and the orbital plane of the moon differ, they act to bring them back together. Both planes move, large moons mean the ratio of the tipping of the equatorial plane relative to the orbital plane is going to be larger.

Prime Evil 10-25-2009 04:26 PM

Re: [Space] Orbital Mechanics of Moons
 
Thanks for the reply!

This level of detail isn't really necessary when worldbuilding for a space campaign, but it is very interesting.

Agemegos 10-25-2009 05:34 PM

Re: [Space] Orbital Mechanics of Moons
 
Quote:

Originally Posted by malloyd (Post 872677)
Most moons orbit in the plane of the planet's equator, so it's the axial tilt of the planet. Our moon is an odd exception, its massive enough compared to the Earth it hasn't yet been tidally dragged into that situation, but for most moons the planet's equatorial bulge will force that in a few million years.

According to de Pater and Lissauer Planetary Sciences (University Press, Cambridge, 2001) the Moon is actually far enough from Earth and it's equatorial bulges that it is tidally forced by interactions with the Sun and Earth towards the plane of Earth's orbit more strongly than into the plane of Earth's rotation. The inclination of the plane of the Moon's orbit to the plane of Earth's orbit is 5.15, so apparently tidally forcing by Earth's equatorial bulges is opposing the reduction of inclination. Given immense depth of time the orbital and rotational planes of the Earth and Moon would be driven to coincide.

We have to bear in mind that most of the objects actually called moons are not, in GURPS Space's terms, major moons, but moonlets. The only major moons in our system are the Moon/Luna, Io, Europa, Ganymede, Callisto, Titan, and Triton. Apart from the Moon, they all have very small inclinations of their orbits to their primaries' equatorial planes: Europa's is the largest among prograde moons at 0.47. Triton is retrograde and inclined at 3.17. Inner moonlets also have very small to negligible inclinations.

Quote:

Again there are tidal forces trying to make the rotational axis perpendicular to its orbital plane, but these are weaker. A lot of non-tidelocked moons have axes pointed in all sorts of directions.
Again, non-tidelocked moons are moonlets, not major moons. I think that are all outer moonlets too, but I am not sure that we have measured the rotations of all inner moonlets. The only free-rotating moons that I am sure of are Himalia, Elara, Hyperion and Phoebe. They are all outer moonlets, and Hyperion's rotation is chaotic rather than free.

Quote:

Stablize just means the axis doesn't move around a lot, not that there is any particular reason for it to be at a low or high angle to the orbital plane. The forces involved are the same ones that drag the moon into an equatorial orbit, acting the other way. If the equator and the orbital plane of the moon differ, they act to bring them back together. Both planes move, large moons mean the ratio of the tipping of the equatorial plane relative to the orbital plane is going to be larger.
Yep. And the solar tides tip both towards the plane of the planet's orbit, while working the plane of the planet's orbit towards the equatorial plane of the star. The solar tides are small in our system, but in the life zone of a dimmer star they would be stronger and might have had longer time to work.


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