From: henry@spsystems.net (Henry Spencer)
Newsgroups: sci.space.science
Subject: Re: Earth motion
Date: Mon, 5 Jul 1999 03:36:58 GMT

In article <7lihns$1po$1@msunews.cl.msu.edu>,
Stephen Asman <asman@pilot.msu.edu> wrote:
>From the perspective of someone standing on the Moon (near side): does the
>Earth appear completely motionless? Or, does it appear to move around a bit?

It moves around a little.  There are two main reasons.  First, the Moon's
equator is not exactly in the plane of its orbit, so Earth moves North and
South once per orbit.  Second, the Moon's rotation rate is constant, but
its orbital motion isn't, because the orbit is slightly elliptical, so
Earth also wobbles East and West.  These two motions happen to be of about
the same size, roughly +-7deg.

A secondary complication is that neither motion is *exactly* periodic,
because the Moon's orbit shifts around, slowly and slightly, in a
hideously complex manner due to perturbations from Earth's equatorial
bulge, the Sun's gravity, etc.  Precise prediction of the Moon's position
is one of the most difficult problems in computational astronomy.  Isaac
Newton -- who found it a soothing recreation to spend an evening solving a
problem that had baffled the rest of Europe's mathematicians for months --
said that trying to compute the Moon's orbit made his head ache!  Not
until the end of the 19th century was a fully satisfactory solution
achieved.  What this means in practice is that any simple formula for
Earth's "true position" in the lunar sky is good for only a limited time,
perhaps a few years.

>...I'm wondering how effective the Earth would be as a
>navigation aid to some one trying to determine their location on the lunar
>surface using just a sextant.

In practice, if you need accuracy, I suspect you are better off working
with star sightings than with Earth sightings, because that takes the
Moon's orbit almost entirely out of the picture.  The Moon's rotation is
much simpler.

Rather than taking a sextant, take a Clementine star tracker with a bubble
level and a small electronics pack.  (The whole assembly shouldn't weigh
any more than the sextant and a book of tables, perhaps less.)  Put it on
the ground, level it with the bubble level, and then switch it on and
stand back to give it a clear view of the sky.  Within a few seconds, it
can tell you exactly which way it is pointing.  The bubble level and a
battery-backed clock turn that into a position on the lunar surface.  The
limiting factor would probably be the leveling; you should be able to get
within a degree or so.  Add a couple of little electronic tiltmeters to
improve that by an order of magnitude.
--
The good old days                   |  Henry Spencer   henry@spsystems.net
weren't.                            |      (aka henry@zoo.toronto.edu)

From: henry@spsystems.net (Henry Spencer)
Newsgroups: sci.astro,sci.space.science
Subject: Re: Lunar-equatorial coordinate systeem
Date: Sat, 6 Nov 1999 01:46:38 GMT

In article <3822732C.A1C9321@gte.net>,
Michael M. Martinez <mmm9343@gte.net> wrote:
>Could someone point me to a reference that defines / provides the
>elements of the coordinate transformation matrix to go from
>geocentric-ecliptic or geocentric-equatorial to lunarcentric
>(selenocentric?)-equatorial coordinate systeem?

Well, you can start with the low-precision lunar-position algorithm in
Jean Meeus's "Astronomical Algorithms".  It only needs three or four pages
of description and three pages of coefficient tables.  *High*-precision
algorithms for determining the Moon's position are at least an order of
magnitude more complex.

Precise prediction of the Moon's position is one of the most horribly
difficult problems in all of orbital dynamics.  The Moon is close enough
to the Earth that Earth's nonspherical shape is quite significant, but far
enough away that the Sun's gravity cannot be ignored either.  When Isaac
Newton says that a problem makes his head ache -- which he did, about this
one -- that is a hint that you are not going to find a one-page solution!
--
The space program reminds me        |  Henry Spencer   henry@spsystems.net
of a government agency.  -Jim Baen  |      (aka henry@zoo.toronto.edu)