APOD: Saturns Moon Dione in Slight Color (2012 Nov 05)

[Chris Peterson]

Were the inner moons somehow pushed out to the orbit of Dione
they would be expected to have the less angular velocity than Dione.

No, they would have the same angular velocity if they were at the same orbital radius. Any mechanism that pushes a body into a different orbit does so by adding or removing angular momentum.

Both the leading and trailing faces will see impacts at the same velocity from debris in a prograde orbit similar to Dione's. The leading edge sees impacts from retrograde debris, and there is a clear asymmetry when considering either debris in solar orbit, or in highly eccentric orbits around Saturn.

[dougettinger]

It makes perfect sense to me that Dione should be most heavily cratered on its trailing side, because that is the direction from which the vast majority of material comes, including the vast majority of fast impacts. Smaller orbits have a faster angular velocity than larger orbits. They approach the trailing side of an object in a higher orbit.

Smaller orbits have less angular momentum than larger orbits.

Were the inner moons somehow pushed out to the orbit of Dione
they would be expected to have the less angular velocity than Dione.

Since Dione's escape velocity (0.5 km/s) is negligible as compared to its orbital velocity (10 km/s)
Dione would be expected to be most heavily cratered on its leading side on purely kinetic arguments.

How can Dione's escape velocity be so much smaller than its orbital velocity? Escape velocities are larger than orbital velocities.

What is wrong with the following logic? Asteroids being captured by Saturn's gravity field will possibly, while falling, orbit at higher velocities than the orbiting satellites. Hence, asterioids captured by Saturn should more often run into the trailing side of Dione and other satellites. I also like in combination the idea of dust from previous collisions in the same orbital region being swept by the leading side of Dione.

Riding high on satellites,
Doug

[neufer]

Were the inner moons somehow pushed out to the orbit of Dione
they would be expected to have the less angular velocity than Dione.

No, they would have the same angular velocity if they were at the same orbital radius.

Any mechanism that pushes a body into a different orbit does so by adding or removing angular momentum.

Indeed, most mechanisms that push a body into a different orbit do so by adding or removing angular momentum.

Nevertheless:

Every elliptical orbit with an apoapsis intersecting Dione's circular orbit will have less angular velocity than Dione at collision.

And:

Every elliptical orbit with a periapsis less than half of Dione's circular orbit radius will have less angular velocity than Dione at collision.

Hence, in most situations, inner moons (or inner dust) forced to collide with Dione will do so on Dione's leading edge.

[Contrariwise, in most situations, outer moons (or outer dust) forced to collide with Dione will do so on Dione's trailing edge.]

[StarCuriousAero]

For anyone interested in a more visual/learning/fun aid to understanding orbits a bit better (and velocities at apoapses/periapses), the smart-phone game/app called Osmos is quite a lot of fun. I found myself visualizing the game while reading through these comments at least.

[Chris Peterson]

Indeed, most mechanisms that push a body into a different orbit do so by adding or removing angular momentum.

Nevertheless:

Every elliptical orbit with an apoapsis intersecting Dione's circular orbit will have less angular velocity than Dione at collision.

But there are orbits with the same eccentricity. And we need to consider inclination, as well, which may be different.

[neufer]

...we need to consider inclination, as well, which may be different.

I have no inclination to do so.