Re: mars and venus

[Stephen Murray <murray8@LLNL.GOV>]

> If this reasoning is all wet would someone explain where the error is?
>
> David Bowman
> dbowman@georgetowncollege.edu

I believe that everything you've said is correct, *if* all we consider is
the p/p (I'll continue to call it a protoplanet) "plowing through" the
planetisemals orbiting the Sun (or being plowed into by the ones on smaller
orbits), essentially sweeping up everything in its direct path, but no more
than that.

You need to consider the fact that the smaller objects are coming from
further away than just immediately adjacent orbits.  The gravity of the
protoplanet is pulling the objects from orbits which would not otherwise
cause them to collide with the protoplanet.

Consider a rock being pulled in by the Earth from an orbit further away
from the Sun.  As you say, the rock is initially orbiting the Sun more
slowly than the Earth.  But, its specific orbital angular momentum is
greater than that of the Earth .  As it is pulled toward the Earth, its
orbital speed increases to conserve angular momentum.  By the time it
collides with the Earth, it is at the same distance from the Sun as is the
Earth, but with a higher specific angular momentum, and so is moving at a
*higher* speed than the Earth.

This does ignore any changes to the orbital angular momentum resulting from
the gravitational interaction with the Earth.  Those are small, and will
tend to increase the orbital angular momentum of the rock (because the
Earth is passing it by on a shorter period orbit).

Reverse everything I said above for a rock pulled in from a smaller orbit.

I believe that this goes right along with Michael's comment about angular
momentum conservation, which would make it very difficult for a protoplanet
to reverse the sense of the angular momentum of the material that it
accretes.

===============================================
  Stephen D. Murray
  Physicist, A Division
  Lawrence Livermore National Laboratory
  L-022, P.O. Box 808
  Livermore, CA  94550
  phone: (925) 423-9382   FAX:    (925) 423-0925
  email: sdmurray@llnl.gov
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