Transforming Orbital Elements from J2000 to Ecliptic Plane

[kepler]

Hi,

since the previous conversion I needed doesn't seem to be of the common sense, let's try this: I have the orbital elements of a body referred to the equinox J2000 and to the equatorial plane. I need to transform the argument of the Perihélion, the inclination and the ascending node to the ecliptic plane and apply the precession to another epoch.

Any ideas?



Kepler

 

[BobG]

It's hard to give a short answer.

The ECI coordinates need to be translated (by the Sun-Earth distance), then rotated.

Try the IERS or the US Naval Observatory to get the ECI to Barycentric rotation coefficients.

 

[kepler]

First step

I was able to reduce the orbital elements for precession and nutation. Now, it leaves me the work of refer the inclination, arg. of perihelion and asc. node from the equatorial plane to the ecliptic one.

Kepler

 

[Chronos]

Why look for a more complex way to explain orbital motions when Newton's [and the original Kepler's] laws work as well they do? Relativity adds a few tweaks, but, you are adding more than a few tweaks. While that does not make you wrong, it makes your theory very suspect. Once you show the math and predictions supported by observational evidence, physicists will fight to fall in line to endorse your theories.

 

[BobG]

No, he's talking about transforming coordinates from one frame of reference (with the center of the Earth as the origin) to another (with the center of the Sun as the origin). Once you move far enough out that the Sun's gravity has more effect on an object's motion than the Earth, using the Sun as your reference frame makes description of the motion a lot simpler than the using the Earth's.

If you have an Astronomical Almanac, I'm pretty sure you could piece together the info you need. Unfortunately, I have a lot more experience with Earth satellite orbits and it would take a bit of work to figure out the transformation to a Barycentric reference frame.

I'm thinking the Right Ascension of Ascending Node would use the same reference, the First Point of Aries, but I wouldn't want to guarantee it. The difference between the equatorial plane and the ecliptic plane is about 23.4 degrees (an astronomical almanac should show the exact value, adjusted for nutation).