Fate of the Moon

trakar wrote:

I probably should have just responded that, "the mechanism behind the
Moon's recession is fairly well understood, and it does not in itself,
allow for the moon's eventual escape from the Earth's gravity."

One thing he might have been talking about is the tidal evolution
of the Moon moving it so far outward that the lunar orbit might become
unstable due to solar perturbations. A simple esitmate of the
tidally-locked end state of the Earth-Moon system predicts an
Earth-Moon distance of around 93 Earth radii (it's currently about 60
Earth radii out), and a "day" = "month" = 52 current days long. If you
take the Earth's core into account, it's a little closer (a_final =
86.4 Earth radii & "month" = 46.8 current days long), but it's still
way out there. Earth's current Hill sphere limits the stability of
orbits: roughly (i.e., empirically), orbits inside 1/3 a_hill are
stable in a long term sense, while those outside are not. 1/3 a_hill
for the Earth is about 78 Earth radii, so you're right on the edge of
stability (probably beyond it).
To really figure out of the Moon would ever get outside that
stability limit, you have to consider the time evolution of the system
with both lunar & solar tides. It's not a case of one functioning at
one time and a second mechanism taking over later, but a shift in
dominance. And this shift may allow the Earth to retain the Moon.

I had found several supporting sites, unfortunately I also found several
university sites that had misleading and even incorrect information up
on their websites,

I'd be *very* curious about these. Can you provide any URL's?

--
Brian Davis

On 9 Jul 2003 10:04:27 -0700, (Brian Davis) wrote:

One thing he might have been talking about is the tidal evolution
of the Moon moving it so far outward that the lunar orbit might become
unstable due to solar perturbations. A simple esitmate of the
tidally-locked end state of the Earth-Moon system predicts an
Earth-Moon distance of around 93 Earth radii (it's currently about 60
Earth radii out), and a "day" = "month" = 52 current days long. If you
take the Earth's core into account, it's a little closer (a_final =
86.4 Earth radii & "month" = 46.8 current days long), but it's still
way out there. Earth's current Hill sphere limits the stability of
orbits: roughly (i.e., empirically), orbits inside 1/3 a_hill are
stable in a long term sense, while those outside are not. 1/3 a_hill
for the Earth is about 78 Earth radii, so you're right on the edge of
stability (probably beyond it).
To really figure out of the Moon would ever get outside that
stability limit, you have to consider the time evolution of the system
with both lunar & solar tides. It's not a case of one functioning at
one time and a second mechanism taking over later, but a shift in
dominance. And this shift may allow the Earth to retain the Moon.

I wish that it had been something of this level, and I was actually
open to some such discussion when I initiated the conversation.
However, he did not seem to understand the forces that were
responsible for lunar recession in the first place, initially claiming
that it was a mysterious, not understood phenomena (and I'm sure it
was from his perspective). Then he began trying to argue that the Moon
was just slightly above escape velocity and it was just slowly
climbing out of the Earth's gravity well. After verbally "ribbing" him
pretty hard (he's actually fairly informed about many things but I do
so enjoy finding these knowledge holes and hooking a finger in them!),
I went into some detailed discriptions of the general processes and
directed him to some websites and text books. I generally only catch
him on major things like this once or twice a year, mainly because he
pouts and sulks for a few months afterward, but hey, what else are
friends for?!

I had found several supporting sites, unfortunately I also found several
university sites that had misleading and even incorrect information up
on their websites,

I'd be *very* curious about these. Can you provide any URL's?

I've already contacted the sites I encountered, and even though I may
sound like a cold-hearted *******, I'll give them a couple weeks to
address the issue before I start publically trashing them too hard
(besides it may have just been matters of my own misunderstanding of
their explanations---heaven forbid!
The main mistake that I ran across was a conflation of orbital period
and velocity. The impression from the websites is that the object was
losing velocity or travelling slower and going into a higher orbit.
This is contradictory to my understanding of orbital mechanics. The
object in orbit gains velocity and moves to a higher orbit which takes
a longer time for it to complete a full orbit.

I would like to find the original papers I read discussing these
issues, but I read them many years ago, and have no idea who the
authors were. I slogged through search engine results for two days and
gave up. If any of this strikes a cord of familiarity in anyone, I'd
appreciate any helpful hints, tips, urls, university or professional
references, Thanks