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jfribrg
2015-Oct-17, 11:51 PM
I have been reading a very interesting book from about 110 years ago, Sidlights in Astronomy and Kindrid Fields (http://www.amazon.com/Side-Lights-Astronomy-Kindred-Popular-Science-ebook/dp/B002RKT7GO) by Simon Newcomb. It is a fascinating look at what we knew about the universe in the early 1900's, but more interesting is everything that we knew that we didn't know about the universe, such as the source of the Sun's energy, and the anomoly in Mercury's orbit. Anyway, in this book there is a discussion of an apparent anomoly in the orbit of the Moon. A solar eclipse in 1900 was supposedly several seconds late. Of course the anomoly in Mercury's orbit was famously explained by Einstein's General Theory of Relativity 10 years later, but I don't think that it can explain an anomoly in the Moon's orbit, simply because the Earth is not nearly massive enough, but I may be wrong about that. Has anyone heard of this anomoly? I'm wondering if it is simply the result of inaccurate calculations (they were all done by hand after all).

Shaula
2015-Oct-18, 04:39 AM
You could try skimming https://en.wikipedia.org/wiki/Lunar_theory and https://en.wikipedia.org/wiki/Ernest_William_Brown and see if it answers your question - the précis is that there are actually quite a number of effects that affect precision estimates of the Moon's position and it wasn't until Brown's methods were accepted after 1908 that there was a really good set of tables for lunar motion.

A telling quote from Wikipedia:

The analysts of the mid-18th century expressed the perturbations of the Moon's position in longitude using about 25-30 trigonometrical terms. The number of terms needed to express the Moon's position with the accuracy sought at the beginning of the twentieth century was over 1400; and the number of terms needed to emulate the accuracy of modern numerical integrations based on laser-ranging observations is in the tens of thousands: there is no limit to the increase in number of terms needed as requirements of accuracy increase.

Jerry
2015-Oct-20, 10:03 PM
"The number of terms needed to express the Moon's position with the accuracy sought at the beginning of the twentieth century was over 1400; and the number of terms needed to emulate the accuracy of modern numerical integrations based on laser-ranging observations is in the tens of thousands: there is no limit to the increase in number of terms needed as requirements of accuracy increase."

Which is a nice way of saying we are still using epicycles to predict the future position of the moon; and we will not know its path with depthy accuracy. This isn't really a problem, just a realization that every nuance of motion in the Earth is in minute degrees transferred to the moon. If you sleep with an elephant, you move when he breaths.

Hornblower
2015-Oct-21, 05:54 PM
"The number of terms needed to express the Moon's position with the accuracy sought at the beginning of the twentieth century was over 1400; and the number of terms needed to emulate the accuracy of modern numerical integrations based on laser-ranging observations is in the tens of thousands: there is no limit to the increase in number of terms needed as requirements of accuracy increase."

Which is a nice way of saying we are still using epicycles to predict the future position of the moon; and we will not know its path with depthy accuracy. This isn't really a problem, just a realization that every nuance of motion in the Earth is in minute degrees transferred to the moon. If you sleep with an elephant, you move when he breaths.

That is similar to what my father did in tracking beacon satellites from the launch of Vanguard 1 in 1958 until his retirement in 1974. The lumpy figure of the Earth forced him to use something like 17 terms to keep predictions of the positions of U.S. Navy low orbit satellites in good agreement with radar observations for a few days. This was when the tolerances for the task at hand were far looser than what we need for GPS today. These terms were empirically derived kinematic sinusoidal terms whose periods formed a harmonic series, and were the functional equivalent of the epicycles used in ancient times before any dynamic theory of gravitation had been developed.

Reality Check
2015-Oct-21, 10:40 PM
"The number of terms needed to express the Moon's position with the accuracy sought at the beginning of the twentieth century was over 1400; and the number of terms needed to emulate the accuracy of modern numerical integrations based on laser-ranging observations is in the tens of thousands: there is no limit to the increase in number of terms needed as requirements of accuracy increase."

Which is a nice way of saying we are still using epicycles to predict the future position of the moon; ....
Which is actually saying what everyone should know - there are no realistic exact solutions to Newtonian gravitation, Jerry. The only exact solution is for a universe containing only 2 spherical bodies (ignoring the trivial case of a universe containing 1 body!). We have a real universe with a Moon interacting with a non-spherical Earth with perturbations from the Sun and want to get as accurate as practicable results. Thus Lunar theory (https://en.wikipedia.org/wiki/Lunar_theory).

Hornblower
2015-Oct-22, 01:33 AM
I have an old Funk and Wagnalls encyclopedia in which an article on the Moon asserted that its motion cannot be fully explained gravitationally. That of course is not the case. The motion is purely gravitational but is difficult to calculate with great accuracy. With screaming fast supercomputers we now can do numerical integrations with short steps that could not be done in a human lifetime on the equipment available in 1954, the date of the encyclopedia.

tony873004
2015-Oct-22, 04:57 AM
I have an old Funk and Wagnalls encyclopedia ...1954.No wonder you knew where Arcturus was in 150000 BC :)


With screaming fast supercomputers we now can do numerical integrations with short steps that could not be done in a human lifetime...
To demonstrate your point, see what your desktop computer can do by running the following simulation in a web browser while you've probably got a million other tabs and apps running in the background.

According to NASA's eclipse page, there will be a total solar eclipse of the Sun on August 12, 2045. It will be total in Redding, CA at 16:17 UTC. This simulation is started using JPL's solar system data for July, 2015. Depending on the speed of your computer, it takes about 5 seconds to propagate all the solar system's planets and Earth's moon 30 years from 2015 to 2045 and accurately reproduce this eclipse as viewed from Redding. Press "P" to begin the simulation.
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1445485644214_Propogate_to_2045.html

Jerry
2015-Oct-24, 07:13 PM
"Epicycles" is an appropriate description, because Fourier and other transforms used to simulate and predict planetary motion are periodic functions AND there are degeneracies between electrodynamic and 'gravitational' vectors. For example, a hurricane is clearly a electro-dynamic event that produces tidal shifts that effect the path of the moon.

The Nuisance Parameter Hypothesis states that there are always degeneracies between electro-dynamic and 'gravitational' effects; and these limit the precision and accuracy of every test of Relativity. It is interesting that in spite of Mercury's proximity to the highly volatile sun, the precession of Mercury's orbit is more accurately predicted by Relativity than that of any other planet.

George
2015-Oct-24, 10:03 PM
"Epicycles" is an appropriate description, because Fourier and other transforms used to simulate and predict planetary motion are periodic functions AND there are degeneracies between electrodynamic and 'gravitational' vectors. For example, a hurricane is clearly a electro-dynamic event that produces tidal shifts that effect the path of the moon. ... and the rotation rate of the Earth. Air mass changes cause the largest variations in our rate vs. tsunamis, etc. They use quasars to help measure the time variance.

Jeff Root
2015-Oct-25, 12:47 AM
... Nuisance Parameter ...
Okay so I never heard of this until today and here it
is for the second time in about 12 hours. I suspect a
causal connection!

-- Jeff, in Minneapolis

Jeff Root
2015-Oct-25, 01:22 AM
The number of terms needed to express the Moon's position
with the accuracy sought at the beginning of the twentieth
century was over 1400; and the number of terms needed to
emulate the accuracy of modern numerical integrations based
on laser-ranging observations is in the tens of thousands
I can't believe that. I can barely believe that they actually
used that many terms, but I can't believe that all of them
were actually needed.

I'm guessing that when they become this numerous, the
"terms" are mostly the orbital parameters of other bodies
that can perturb the Moon's orbit. After the Earth and Sun,
which obviously have major influence, I'd expect all other
influences to be very small. The planets, okay. But Ceres?
Pallas? Vesta? Could their gravitational effects on the
Moon's orbit ever be detectible? Could a body as small
as Apophis, passing near the Moon, affect its orbit enough
to detect?

-- Jeff, in Minneapolis

Jerry
2015-Oct-25, 03:15 PM
As the earth is warming and the water is being redistributed from locked ice in the polls to tidal lubricant centered at the equater; both the migration and the resulting higher tides become trackable lunar orbit influences; and it may take several dozen parameters to develop predicable periodic trends. Of course the computers don't know exactly where new trends come from, they only include them in the principle component analysis.

The Nuisance Parameter Hypothesis states that since gravitational and electromagnetic effect inertial components in exactly the same way; they are equivalent and ply from the same root force. Every careful test of relativity is bothered by nuisanced electromagnetic effects to limits and degeneracies.

For example, if you try to measure the relativistic curvature of light near the sun; the raw number will vary depending upon the observational frequency and absolute proximity. It takes a series of observations at different wave lengths, construction of atmospheric Rayleigh scattering and magnetic deflections; and a few baseline assumptions to extract an affirming Relativistic signature.

Reality Check
2015-Oct-27, 02:01 AM
"Epicycles" is an appropriate description, ....
Epicycles (https://en.wikipedia.org/wiki/Deferent_and_epicycle) have nothing to do with Fourier and other transforms.
Lunar theory (https://en.wikipedia.org/wiki/Lunar_theory) has little to do with Fourier and other transforms. This is the process of adding perturbations that are known to modify the orbit of the Moon. Newton started with the solar perturbation and later authors added more.
No citation to the "Nuisance Parameter Hypothesis" and its statement about gravitational and electromagnetic effects on the Moon (or in general) is a nuisance, Jerry.

Reality Check
2015-Oct-27, 02:19 AM
I can't believe that. I can barely believe that they actually
used that many terms, but I can't believe that all of them
were actually needed.
You are misunderstanding what these terms are, Jeff Root. The terms are not a term for every body in the Solar System (which would be billons!). The bodies considered are the Sun and major planets. The terms are an expansion of the perturbations. Restriction to principal terms (some are listed in that Lunar theory (https://en.wikipedia.org/wiki/Lunar_theory#Largest_or_named_lunar_inequalities) article) gives that "25-30 trigonometrical terms". Adding in more of the terms gives more accurate figures ("tens of thousands") which can be used to match observations.