From: spike66 (spike66@attbi.com)
Date: Thu Sep 12 2002 - 23:03:46 MDT
Harvey Newstrom wrote:
> On Thursday, September 12, 2002 11:29 pm spike66 wrote,
>
>>Harvey Newstrom wrote:
>>
>>>It loops around the earth and the sun in a weird horseshoe orbit.
>>>
>>Im a little puzzled by your discription of the orbit.
...Cruithne would scarcely notice the earth out there.
>>
>
> Your are assuming too much in your "back of the envelope" calculations. It
> goes one direction around the sun, loops around the earth and goes back in
> the opposite direction around the sun, meets the earth on the other side and
> then loops back again. It goes back and forth in a "C" shaped orbit. It
> stays on one side of the sun and never gets to the other side. This is what
> is so strange. Your elliptical orbit is totally wrong for this weird
> object.
http://www.space.com/scienceastronomy/solarsystem/second_moon_991029.html
Oh I see what is the problem. Harvey, Cruithne
orbits the sun much like the Earth does. The
description of the orbit given in the article
is confusing: it does make it sound like the
object goes most of the way around the sun, then
turns around and goes back the other way.
Let me see if I can explain it better than they
did. Assume an object on the other side of the
sun from earth, a little closer to the sun than
the earth. It orbits the sun a little faster than
the earth, so a year from now it has gone a little
more than a full rotation, say 361 degrees, so now
from the point of view of the earth, it is (say) a
degree closer. A year later it is another degree
closer, and so on.
One hundred seventy some years from now, it is
chasing the earth and catching up, and starts to
feel the slight gravitional attraction of the earth.
This causes the object to... speed up? No! It
causes the object to pick up energy, which raises
it to a higher orbit, farther from the sun, which
actually causes the object to slow down! (Aint
orbital mechanics fun?) So now the object is
farther from the sun than the earth, so its angular
velocity is somewhat slower, say a degree a year,
and it falls back, a year from now another degree,
and so on until it is back on the other side of the
sun. It goes 359 degrees in the time the earth
goes 360.
It continues to fall back for another 350 years
or so, until the earth nearly catches up with it.
Then the earth takes back its angular momentum
that it gave to the object some 350 years before,
which slows the object, which drops it into a
lower orbit, which speeds up the object, sending
it back around moving slightly faster than the
earth, and the whole process is repeated.
The example I gave takes about 700 years to do
one cycle. Note however that the orbit of the
object is only very slightly different than the
orbit of the earth. And there is nothing weird
about the object. Any object in that position
would follow the same path.
>
> See
> <http://www.space.com/scienceastronomy/solarsystem/second_moon_991029.html>
> for a diagram of the C-shaped horseshoe orbit. (This is old stuff. I'm
> surprised you hadn't heard of it.)
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