I looked at some references on planet formation (the two most useful were
"Solar System Evolution," by S. R. Taylor, and the first "Protostars and
Planets," edited by T. Gehrels). One interesting issue is just how we
define a "normal" terrestrial planet. We have Mercury with a slow prograde
spin, but which is obviously influenced by the Solar tides. We have Venus
with a slow retrograde spin, and then we have Earth and Mars with rapid
prograde spins. The general consensus seems to be that Earth and Mars are
the oddballs. The Earth-Moon system, with its very high angular momentum
among terrestrials, is especially odd, which is used as one argument for
the theory of the collisional formation of the Moon. Just to be difficult,
one reference argued both for that theory *and* that a large collision
reversed the spin of Venus! I could find no basis for this, other than
that Venus is one of only two planets with retrograde spins (if you call
Uranus retrograde), and that he therefore thought it must result from a
collision. It was also argued, in another reference, that a collision with
Mars spun it up, and caused its northern-southern hemisphere asymmetry
(don't ask me how they think *that* worked!).
The obliquities of the terrestrial planets are apparently used to constrain
the maximum typical sizes of the objects which hit them during their
accretion phase. Small obliquities imply many impacts by small objects,
which appears to be the case for the terrestrials. *Really* big collisions
seem to be the exception, rather than the rule.
So, we go back to the picture of a protoplanet accreting "rocks" by pulling
them in from larger and smaller orbits with its gravity, but modified to be
more in line with David's comments. As I mentioned earlier, a "swarm" of
rocks coming from larger orbits will be moving faster than the protoplanet
by the time that they hit it, due to their higher specific orbital angular
momentum. But, they apparently "pepper" one entire hemisphere more-or-less
uniformly. Similarly for rocks coming from smaller orbits hitting the
other side. As a result, the only net angular momentum given to the planet
goes into its orbital motion, and not its spin. As a result, planets like
Venus (not necessarily retrotrade, but spinning slowly) are to be expected.
This still leaves the question of the different final orbital radii for the
planet derived from conservation of angular momentum and conservation of
energy. David's results do depend a bit on the values that he assumed.
For example, constant surface density is probably more appropriate in the
inner Solar System, and I would have expected that the "feeding zone" of
Venus would extend more than halfway to Mercury (not less than half) and
out to about halfway to Earth (how did you get 0.5998 AU and 0.8505 AU,
David?). A uniform density with the feeding zone defined by the
Mercury-Venus and Venus-Earth midpoints seems to lead to about twice the
required change in Venus' orbit as found for the 1/R law.
The main problem, I think, is how you could systematically boost a planet
like Venus to a larger orbit during accretion in something like the "swarm
accretion" scenario. It seems to be generally assumed that the collisions
will lead to net dissipation of kinetic energy, shrinking the orbit. To
cope with the radius discrepancy, the terrestrial planets are thought to
have transferred excess angular momentum to objects at larger orbital radii
via gravitational interactions.
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Stephen D. Murray
Physicist, A Division
Lawrence Livermore National Laboratory
phone: (925) 423-9382 FAX: (925) 423-0925
email: sdmurray@llnl.gov
web page: http://members.home.com/murraysj/
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