# Protoplanetary disks, angular momentum and prograde orbits

Very similar question at Astronomy SE: https://astronomy.stackexchange.com/q/6183/4042

Given a typical protoplanetary disk made up of the usual planetary system stuff, dust and gas and whatnot, orbiting a common center: Material coalesces into planets, clearing the soupy disk in favor of a handful of massive objects.

And this is where my question begins: the conventional wisdom of orbital mechanics is that the smaller the orbit, the faster the motion:

The orbital speed is given by:

$$v = \sqrt{\frac{GM}{r}}$$

so in the diagram $v_1 > v_2$ i.e. the inner body is moving faster.

So say you've got an asteroid belt that gathers itself up into a proto-Mars. In this case our two bodies aggregate into a single body. If we zoom in to the centre of mass of the two bodies their relative velocities look like:

So the two bodies are revolving clockwise about their centre of mass i.e. in a retrograde direction to the accretion disk as a whole. Doesn't this mean the average angular momentum of the Mars-forming belt will be retrograde with respect to the orbit, given that the inside of the belt moves faster than the outside of it? Why then is the prevailing rotational direction of the planets prograde?

I realize that that assumes circular orbits for all the particles involved, which obviously is unlikely. I suppose in a system of elliptical orbits, a particle or object is probably more likely to be captured by a coalescing mass if it is on the climbing (and therefore slowing) portion of its orbit, which would tend toward an overall prograde contribution of momentum. But is that effect sufficient to explain the overwhelming prevalence of prograde rotation in our solar system?

• This question is rather confused, and because of that its rather confusing how to answer it. I don't know where to begin. – David Hammen Jan 3 '15 at 10:25
• @DavidHammen comments on the specific aspects of the question which are confused would allow the asker to edit it appropriately, which would probably grease the gears a bit. – Asher Jan 3 '15 at 10:42
• That something inward of Venus is moving faster (a whole lot faster) than something outward of Jupiter has nothing to do with "prograde" versus "retrograde". What matters is the direction in which the specific angular momentum vector $\vec h = \vec r \times \vec v$ points. In the disk, all such vectors point in more or less the same direction. – David Hammen Jan 3 '15 at 11:46
• Asher, I've attempted to clarify your question with a couple of diagrams. If you don't like what I've done please shout and I'll back out the changes. To potential downvoters - please don't downvote if you don't like my edit because that's unfair on Asher. Just shout at me instead :-) – John Rennie Jan 3 '15 at 11:48
• @JohnRennie no, that's great. I'm limited to posting from my phone for the time being, so your edit is a large help. Thanks. – Asher Jan 3 '15 at 11:59