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)

Index Home About Blog