Letting \ boldsymbol { \ rho } be the radius vector of the osculating orbit, \ mathbf { r } the radius vector of the perturbed orbit, and \ delta \ mathbf { r } the variation from the osculating orbit,
2.
Letting \ boldsymbol { \ rho } be the radius vector of the osculating orbit, \ mathbf { r } the radius vector of the perturbed orbit, and \ delta \ mathbf { r } the variation from the osculating orbit,
3.
I realize that these stem in part from osculating orbits, different epochs, etc ., etc . Correctly interpreting the JPL-Horizon's output isn't easy, either ( a guideline for that might be useful, by the way ).
4.
An osculating orbit and the object's position upon it can be fully described by the six standard Keplerian orbital elements ( "'osculating elements "'), which are easy to calculate as long as one knows the object's position and velocity relative to the central body.
5.
Its use in this context derives from the fact that, at any point in time, an object's osculating orbit is precisely tangent to its actual orbit, with the tangent point being the object's location and has the same curvature as the orbit would have in the absence of perturbing forces.
6.
The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an JPL Horizons, the barycentric orbital elements for epoch 2010-Jan-01 generate a semi-major axis of 700 AU, an aphelion distance of 1400 AU, and a period of approximately 18, 700 years.
7.
The orbit of a long-period comet is properly obtained when the osculating orbit is computed at an JPL Horizons, the barycentric orbital elements for epoch 2020-Jan-01 generate a semi-major axis of 1, 100 AU, an apoapsis distance of 2, 230 AU, and a period of approximately 37, 000 years.
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