(Henry Spencer) wrote in message ...
In article ,
Mike Miller wrote:
1) Virtually everything in the Inner System (starting at Pluto and
working in) has settled down into a single plane, give or take a few
degrees. It is very improbable that anything in Earth's neighborhood
would be approaching from a steep angle to end up in a polar orbit.

It doesn't have to approach from a steep angle. You can't ignore Earth's
motion around the Sun when thinking about such things. The incoming
object only has to pass Earth a few tens of thousands of kilometers to
(say) the north, and then lose some velocity while there. To pass, say,
50,000km north of Earth, the inclination of its orbit needs to be only
about 0.02deg -- remember, all this is happening 150Mkm from the Sun, so
the angle between the orbits needed to get 50,000km difference is very
small.

It's the "lose some velocity" part that's hard.

The Earth *can* capture objects from heliocentric orbit, as witness the
temporary capture of object J002E3 (which is almost certainly Apollo 12's
S-IVB!) last year. But as witness that case, the resulting orbits tend to
be very large -- well beyond the Moon's -- and rather precarious (J002E3
is gone into solar orbit again).

But an object _could_ (very small chance, I admit) be in heliocentric
orbit and yet pass over the Earth at just the right speed to enter a
circular polar orbit at 20310.8 km radius, could it not? Without
having to shed any velocity at all? (I feel like a cross-examining
attorney;"You admit that my client _could_ have been carrying that
plutonium for perfectly innocent reasons?")

2) Earth already has a big, jealous companion. I'm not sure Cynthia
could settle down into a circular orbit (it wouldn't be circular to
begin with) before Luna destabilized Cynthia's orbit to intersect
Earth, Luna, or ejected it from the area all together. I'd put my
money on "intersect Earth."

Most likely is to eject it, in fact: both Earth and Moon are rather small
targets, in the celestial scheme of things, and a near-miss that changes
your path into an escape trajectory is much more likely than an actual
collision.

In general, three-body systems which are not "hierarchical" -- one close
pair plus a distant third -- over time have a strong tendency to lose one
body by ejection.

And yet Jupiter has a number of moons in pretty stable orbits, over
millenia.