# Help me with coordinates and orbits

1. Nov 21, 2009

### mattrix

Epoch J2000.0 refers coordinate systems to the mean equinox and mean ecliptic of January 1, 2000, noon TT.
I have the following mean orbital elements for Earth with element date January 1, 2000 and refered to j2000.0 epoch.

a := 1.00000011 - 0.00000005 *cy
e := 0.01671022 - 0.00003804 *cy
p := 102.94719 + 1198.28/3600 *cy
L := 100.46435 + 129597740.63/3600 *cy
i := 0.00005 - 46.94/3600 *cy
O := -11.26064 - 18228.25/3600 *cy

a - semi-major axis
e - eccentricity
p - longitude of perihelion
L - longitude of planet
O - longitude of ascending node, of the intersection of the orbital plane and the plane of the ecliptic
i - inclination, angle between the plane of the ecliptic and the plane of orbit

as I understand it,
the earths orbital plane is synonomous with the ecliptic and
as these planes do not intersect the zero direction is taken to be the vernal equinox

I realize that these references move over time, hense epoch.

However I'm confused about how at the time of epoch the last 2 elements can have a value, not equal to zero?
Where is "O" measured from, and to?
I'm not sure about the use of "longitude" either, is this figurative or literal for these 3 elements?

thanks matt

PS does anyone have the Osculating elements for the solar system plants at January 1, 2000.

2. Nov 21, 2009

### tony873004

Earth's inclination is not fixed. Like the other planets, its inclination changes. The j2000.0 epoch will define the ecliptical plane as the inclination of the Earth/Moon barycenter on January 1, 2000 at noon. Here's a graph I made with Gravity Simulator showing the inclination of the Earth for a few decades surrounding 2000. Note that it doesn't completely zero-out at j2000. My guesses are that this graph is Earth's instantaneous inclination, rather than the inclination of the EM barycenter. And it's the inclination with respect to the Sun rather than with respect to the SS barycenter. But those are just my guesses.

If inclination is exactly 0, longitude of ascending node is undefined. I believe that in this instance, it's specifically defined as the vernal equinox. In the real universe, there's no such thing as an inclination of exactly 0, except for the instantaneous moment when you define the plane. As the graph shows, it immediately drifts.

"Longitude" means degrees from the vernal equinox. "Argument" means degrees away from the longitude of longitude of ascending node.

You can use JPL's Horizons system to generate the orbital elements for any solar system object.
http://ssd.jpl.nasa.gov/?horizons

3. Nov 21, 2009

### mattrix

Hi Tony,

Thats my point, these data are for the exact same moment as when the J2000 plane is defined, and they are both "mean" values.

So if there is an inclination at this time, what is the plane its inclined to?

Interesting graph, if your guesses are right, then over these few decades the average inclination of the earth is always greater than its mean!

matt

4. Nov 21, 2009

### D H

Staff Emeritus
5. Mar 31, 2011

### WildEnergy

I think the OP's confusion stems from a typo:

O - longitude of ascending node, of the intersection of the ORBITAL plane and the plane of the ecliptic