I know that I'm getting in over my head, but the thread is sounding a lot like statistical filtering, orbit determination, and tracking.
Filtering is estimation into the future based on mathematically redundant observations subject to minimizing a cost function. Think least squares. (I just know that I am selling ice to the Eskimos.) It is finding the best fit to the observations of a hypothesis with free parameters. Smoothing is going backwards with the same process -- perhaps with an improved hypothesis from filtering. (Think, perhaps, prolepsis.) I am sure that many have applied these principles to estimating the "state" of the Earth, where the state vector includes things such as nutation and the deceleration of the Earth's rotation. So much for teaching astronomers algebra. Most such estimations are the outcome of series expansions of governing independent variables, dependent variables, or similarity parameters. Think Fourier series -- actually, Jacobi Polynomials, but who is keeping track. Think also of the moments of an assumed statistical distribution. The lowest order (DC component, if you will) is called the mean. In Fourier series, it would be the state averaged over the period of the trigonometric functions. For an assumed Gaussian, it is really the Mean. (If the statistics are Gaussian, the first two moments specify the distribution completely.) Otherwise, that is not really a time averaged mean -- partly because the independent variable isn't always time. In optics expanded in Zernike Polynomials (a complete, orthonormal series over the unit circle), it is called "PISTON," translating a lens back and forth. The result in orbit determination is called the "mean orbit," but that doesn't imply that it is averaged over time. It is usually the Keplerian, two-body orbit, which is certainly time varying. The second order (linear terms) are called "secular," or in optics "tilt." The quadratic terms in optics are called focus (the cross product term is -- guess what -- astigmatism.) Now that I've exposed my lack of understanding, the conclusion is that the "mean" solar second is the outcome of a statistical estimation of governing state variables fitted against observations. Which "means" that it is really not necessarily an average over time. Now, attack!!! Dave Finkleman Senior Scientist Center for Space Standards and Innovation Analytical Graphics, Inc. 7150 Campus Drive Colorado Springs, CO 80920 Phone: 719-510-8282 or 719-321-4780 Fax: 719-573-9079 Discover CSSI data downloads, technical webinars, publications, and outreach events at www.CenterForSpace.com. _______________________________________________ LEAPSECS mailing list LEAPSECS@leapsecond.com http://six.pairlist.net/mailman/listinfo/leapsecs