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I think this is what you want: Simon et al. 1994 You can find Meeus formula in it.

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Perhaps you are looking for Lagrange’s planetary equations? Given some perturbation $H_1$ to the Hamiltonian, they give six equations to calculate the change of the orbital elements over time; a thorough discussion is given in Goldstein’s textbook on classical mechanics. The equation for $\Omega$ is $$\frac{d\Omega}{dt}=\frac{1}{\sqrt{GMm^2(1-e^2)\sin i}}\... 16 Both ellipticity f (also called flattening) and eccentricity e are measures of how elongated an ellipse is, based on the semi-major axis a and the semi-minor axis b (figure from wikipedia). They are defined respectively as$$f=\frac{a-b}{a}$$and$$e=\sqrt{1-\frac{b^2}{a^2}} For a circle, $a=b$, which implies that $f=e=0$. In modern orbital ...

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Ellipses have a "long radius" called the "semi-major-axis" which is the length from the centre to the ellipse measured along the long axis. And a "semi-minor-axis" which is measured along the short axis. Call the semi-major-axis "a" and the semi-minor-axis "b". Ellipses also have foci: which is where the ...

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What Kepler (and others before and after him) wanted to do is predict where a planet would be. To do this we need some set up: First we want a coordinate system. This is a system of axes: x, y and z, at right angles to each other. And it should be an inertial coordinate system, so Newton's laws work. This means that the axes should not be rotating. And we ...

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Thanks folks for helping. I knew about SPK files but from Horizon's telnet inteface there is a limit of 200 bodies per request. Making over 5000 request might be possible but not very productive. I also looked at the DE421 file from ftp://ssd.jpl.nasa.gov/pub/eph/planets/bsp/ but it looks like the corrections for the 8+1 planets here is the output from ...

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This is a common problem with ephemeris or TLEs. They change over time and one might want to know the values after the times that are given. Most folks use an interpolation scheme to estimate values at a certain time. I would suggest starting with linear interpolation. If this doesn't give you good enough fidelity, you could move on to a more complicated ...

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