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The meat of the question isn't about JPL Horizons precision at all, it's about compatibility of two forms of information given out for same bodies & date by 'Horizons'. (I also added a comment indicating where there might be a slip in the questioner's undisclosed calculations.)
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edit approved Mar 14, 2018 at 8:59
terry-s
edit approved Mar 14, 2018 at 8:59
terry-s
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Compatibility of osculating elements and cartesian vectors given by JPL Horizon orbit precisionHorizons?

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DBCL
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JPL Horizon orbit precision?

I'm facing a problem I can't explain and I would like to know if someone has more information about it.

I'm drawing a solar system and when I plot earth with the Horizon cartesian coordinates, it does not match the orbit plotted via the Horizon orbital elements.

Here is the query of the orbital elements Query of earth's orbital elements

Here is the answer

2458055.500000000 = A.D. 2017-Oct-29 00:00:00.0000 TDB 
 EC= 1.693936505240274E-02 QR= 9.828535727121969E-01 IN= 1.619499879517213E-03
 OM= 1.180185004251146E+02 W = 3.460022671282024E+02 Tp=  2458123.158659660257
 N = 9.859206292830410E-01 MA= 2.932939316914255E+02 TA= 2.914962922586066E+02
 A = 9.997893698231427E-01 AD= 1.016725166934089E+00 PR= 3.651409548675242E+02

I'm using EC and A to plot the ellipse. Here are my calculations : Center of ellipse X : -EC * A Center of ellipse Y : 0 Radius of ellipse X : A Radius of ellipse Y : A * sqrt(1 - EC^2)

Here is the query of the cartesian coordinates Query of earth's cartesian coordinates

And here is the answer :

2458055.500000000 = A.D. 2017-Oct-29 00:00:00.0000 TDB 
 X = 8.085189297377026E-01 Y = 5.770742450594002E-01 Z =-2.783714659030374E-05
 VX=-1.027876320855459E-02 VY= 1.393441165141858E-02 VZ= 7.146303246417249E-08
 LT= 5.737033579585715E-03 RG= 9.933365717771512E-01 RR=-2.711916121500719E-04

I'm plotting earth at the given X, Y, Z coordinates

And I don't understand the result. Earth is almost on its orbit but not exactly. It's off by 1,275... % and I don't understand why.

Wrong position of the orbit

Is it because the keplerian elements are approximations or is it because my drawing of the orbit is not very well made atm ? In other words, should the earth be exactly on its orbit when using the Horizon data or is this error expected ?

Thank you very much