APOD: Haumea of the Outer Solar System (2017 Oct 17)

[Chris Peterson]

Well, why should it be on the equatorial plane? Satellite orbits are stable at any inclination.

I don't know, other than that nearly all of the other major moons in the Solar System orbit very near to their planet's equatorial plane.

Well, in multiple body systems there can be normalizing forces from perturbations and inhomogeneous bodies that act to alter orbits- sometimes altering eccentricity, sometimes altering inclination. But these are often weak and slow acting. Many minor moons orbit Saturn and Jupiter at high inclinations- presumably because they were captured. The major moons likely formed in place or were captured very early in the evolution of the Solar System. Nearly all the Solar System mass lies on the ecliptic (really, the invariable plane, but close enough for our discussion), and that's where we find most large bodies orbiting.

The Moon is a complex example, given that it likely resulted from a massive collision which would have produced debris at a range of random inclinations, because of the complexity of the Sun-Earth-Moon tidal forces, and because of the way angular momentum is transferred between rotations and orbits.

[MarkBour]

Finally, what is the meaning of the red "X" ? If it is not a collision, then is it the point at which the Earth was "removed" ? I am then guessing that throughout the video the mass of the Earth was perhaps being steadily reduced to zero ?

The "X" is when the Earth was removed. Otherwise, nothing was changing during the video except the scale factor (shown by the Earth-Moon distance). The actual orbit is what you see when the scale factor drops to one (the distance is just shown as 380 m.km.) That's what the lunar orbit around the Sun-Earth system looks like- a dimpled ellipse. Then the Earth is removed, and the Moon continues to follow the same orbit, just unperturbed by the Earth.

The loops/epicycles are just there at the beginning to emphasize what you can get with a three body system. They do not exist in the Earth-Moon-Sun system.

Okay, makes sense now. Thanks.
And thank you, alter-ego for the clarification of just how subtle the dimples are in the actual orbit.

[neufer]

Well, why should [the Moon] be on the [Earth's] equatorial plane? Satellite orbits are stable at any inclination.

I don't know, other than that nearly all of the other major moons in the Solar System orbit very near to their planet's equatorial plane.

The Moon is a complex example, given that it likely resulted from a massive collision which would have produced debris at a range of random inclinations, because of the complexity of the Sun-Earth-Moon tidal forces, and because of the way angular momentum is transferred between rotations and orbits.

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Actually the real mystery (so far as I'm concerned) is not why the Moon's orbit plane follows the ecliptic so closely [5.14°] but rather why the Moon's equatorial plane follows the ecliptic so closely [1.54°].

The main forces on the moon should be:

1) the initial collision impact
2) later asteroid/comet impacts
3) earth tidal forces & angular momentum transfers
4) solar tidal forces

So why do the Moon & Mercury both have permanent cold shadowy polar regions

Code: Select all

               obliquity/axial tilt
-----------------------------------
Jupiter 	       3.13°
Venus 	         2.64°
Moon 	          1.54° (with respect to ecliptic)
Mercury 	       0.034°

[alter-ego]

...
Interesting discussion about absence of epicycles in the lunar orbit. Early in the history of the Earth-Moon system there likely would have been. The inner moons of Jupiter and Saturn should also show epicycles in plots like these. But Titan, with an orbit in Saturn's 'equitorial regeim' does not show epicycles.

Making the simplest of assumptions, the existence of epicycles can be calculated: 1) All orbits are circular, radius ≡ semi-major axis (good for the inner moons). 2) Earth & Moon masses did not change significantly between the times when the moon was 5 earth radii away and present.

1. Of the 69 moons listed for Jupiter, All moons within Io's orbit (4) show epicycles (loops). Io is just beyond the epicycle limit.
2. All moons from Io to S/2003 J 5 (60) show wiggles with curvature sign change, but no loops
3. The remaining outer moons (5) curvature sign does not change (every point in the orbits are locally "convex")

For our Moon, epicycles were not physically possible. Loops could only happen at orbital radii much less than Roche's Limit. However:

1. Wiggles with curvature sign change diminishingly occurred out to ~68% of the current orbital radius.
2. For all larger radii, the orbit showed, and will show, no curvature sign change.