# Converting a State Vector

1. Oct 8, 2004

### kepler

Hi,

I have sort of a problem: I have a routine to calculate the geometric place ( the state vector ) of the bodies in our solar system ( from Paul Heafner - you probably know it ). But the problem is that the results are referred to the J2000 epoch frame. I was trying to convert the vector [x,y,z,vx,vy,vz ] from the J2000 epoch to the TDB (UT is also fine) choosen epoch, correcting the values for precession and nutation, getting [ x',y',z',vx',vy',vz' ]; and then, convert the result vector to the ecliptic plane, obtaining a new vector [ x",y",z",vx",vy",vz" ]. Does someone knows the routines to make this calculation? Or, at least, this final conversion?

Kind regards,

Kepler

2. Oct 8, 2004

### tony873004

I'm just guessing here, but won't the state vectors automatically be in the same reference plane as the orbital elements that served as your input? Or are you using visual positions such as RA and DEC as your input rather than orbital elements? Although you'd also need distance if you were to it this way. Orbital elements are usually referred to in reference to the ecliptic where z is up and down, and x or y (I forget) points to the Vernal Equinox. So precession of Earth's axis won't play a role here.

Also, I don't know if this helps, but you can get x,y,z & xdot, ydot, zdot for any solar system object for any epoch from JPL Horizons system. If this solves your problem and you want me to show you how, let me know.

3. Oct 15, 2004

### Jenab

You're dealing here with coordinate transformations. I know how to do coordinate transformations - and so, probably, do you. What you need to know, first, is the specific angles by which to rotate from the unprimed coordinates to the primed coordinates (to account for precession and nutation), and then rotate again from the corrected celestial coordinates to the ecliptic coordinates at your epoch, then vector subtract to translate your coordinate origin from geocentric to heliocentric.

I don't have the numbers in front of me for precession and nutation. Indeed, I doubt those numbers are anywhere in my hillbilly cabin. But the Astronomical Almanac should have them.

Jerry Abbott

4. Oct 18, 2004

### kepler

The vectors and it's tranformation

Hi again,

I've solved basically all the problems I posted in this thread. Some information came in specific books, other was calculated with a piece of paper and a pencil from scratch...I now have several routines that work directly with State Vector, given the position [x,y,z], the velocity [vx,vy.vz], and the factor GM ( or Mu ). All the tests I've made are correct an consistent with other sources - except for the system Earth-Moon.
The value of the vectors are, for 1/1/2000, 12h00:

x = -0.0019490056;
y = -0.0018384464;
z = 0.0002424016;
vx = 0.0003717380;
vy = -0.0004221159;
vz = -0.0000066657;

In my main routine I used simplified values; for instance: the value of GM is taken to be equal to Mu = GaussK * GaussK * ( 1 + massp ) - simplified way - where GaussK is the Gaussian constant (0.01720209895) and massp is the mass of the planet divided by the mass of the sun ( for earth, massp = 1/328900.56, for example, as you know).

But for the Earth-Moon system, in proportion, GM should be equal to Mu = 0.07436680 * 0.07436680 * (1 + 0.012300034).

The problem is that certain values come ridiculous, like the eccentricity: 0.999...etc instead of ~0.0549!

Any ideas?

Kind regards,

Kepler

Last edited: Oct 18, 2004