Computing osculating orbital elements

[cptolemy]

Good afternoon,

I wonder if someone can help me in a small doubt.

I'm trying to calculate the orbital parameters of some solar system bodies. It's quite easy knowing their positions and velocities.

But my question is this: these two components, position and velocity, must they be heliocentric or barycentric?

And as far the equinox and ecliptic of reference, must it be the J2000 or the mean of date?

I'm asking this, because I get different ascending nodes, for instance for Earth, compared to the NASA release values. Actually, their value is for J2000 about -11 degrees, which is strange; it should be a positive number (adding 360).

Does anyone has expertise in this field?

Cheers,

Kepler

 

[tony873004]

Position and velocity can be either heliocentric or barycentric. If you use heliocentric position and velocity, you'll get heliocentric orbital elements.

For computing Earth's orbital elements, it doesn't make much sense to use barycentric since Earth orbits inside the orbit of Jupiter, the Sun's biggest perturber.

-11 and 349 are just 2 ways of saying the same thing. Where is the NASA page that states -11 degrees? Using Horizons, I get 160 degrees.

Regardless, it's not surprising to get vastly different numbers when computing the ascending node of an orbit with no inclination. Since Earth's orbit defines the ecliptic plane, Earth has no inclination. Only the z-component tugs from the Moon and other planets barely give Earth an instantaneous non-zero inclination, but it changes all the time, causing Earth's calculated Longitude of Ascending Node to dance all over the place.

You'll get similar poorly-defined results if you try to compute Earth's argument of perihelion, since it's measured from the poorly-defined LAN.

To a lesser degree, Venus' argument of Perihelion dances all over the place too, since its orbit is very circular. A perfectly-circular orbit has no perihelion.

How do your computed values compare to NASA's values for other orbital elements?

 

[tfr000]

Good afternoon,
But my question is this: these two components, position and velocity, must they be heliocentric or barycentric?
And as far the equinox and ecliptic of reference, must it be the J2000 or the mean of date?

Depends on what you want out of it. If you start with heliocentric, J2000 pos/vel, you will get heliocentric, J2000 orbital elements. Just be careful in doing your comparisons with someone else's results (even NASA's) - if they started with, for instance, barycentric, J2000 pos/vel, their results will be different. Or, if they started with some other data set - pos/vel as measured by a spacecraft rather than pos/vel computed and published in an almanac - again, different results if you happen to be comparing yours to the almanac elements.

The best thing to do, if you're verifying a set of equations or something, is to find some output data with known input data and put that through your program.

 

[tfr000]

BTW, if you want to get deep into such things, may I recommend this author?
http://www.willbell.com/math/mc1.htm

 

[cptolemy]

Hi everyone,

Thanks for trying to help. Oh, and of course, thank you very much for mention the "great Jean Meeus" - one of my idols regarding time fit astronomical alghorythms. I have - I think - all his books. Willman Bell is a great provider of specific astronomy technical books that we do not find elsewhere...

I did some digging - and reversed the problem. Calculated the state vectors of Horizons from their orbital elements. Conclusion: they were diferent from mine... thus the difference.

Horizons calculates the simple vectors choice in barycentric coordinates. As for the orbital elements, it's calculation is made in heliocentric ones, referred to the equinox and equator plane of J2000, TDB scale (or similar - they use Coordinate Time), with true coordinates - no light effect, aberration or whatever. Not astrometric - just true.

I'm getting now very similar results since my state vectors differ only in some decimals (10^-9 aprox.). But the results are quite accurate, I must say :)

So, up until next time.

Cheers,

CPtolemy