2021-10-11, 05:35 PM
Hi Greg,
Sorry I wasn't clear. I didn't mean to interpolate the individual component values of the elements, then calculate a position. What I intended was, assuming we call the preapproach element set E(1), close approach E(2) & postapproach E(3), to calculate a position using E(1) then E(2) and do a time interpolation between those positions before close approach. After close approach, switch to E(2) & E(3) & again interpolate between the calculated positions.
This seems like a possible way to find a good position without the effort of solving the n-body problem. At least one good enough to find the object. If the epochs of the elements aren't too far apart the path of the MP should be close to the line between the positions calculated using E(1) & E(2) for example. If things don't work that way, I stand corrected.
If the described approach is workable, the question becomes, how close do the epochs of osculation need to be to be good enough? It would be interesting to plot the positions calculated by several sets of osculating elements for a time t(x) to see where they appear on the sky. What kind of curvature would the plot of positions show?
BMD are you aware of software that could perform this type of calculation & plotting? SkyTools would be great for the plotting, but I'm not sure how to get it to calculate a position using a particular epoch for the elements. It picks the elements internally.
Just some spitballing here. It seems like we might be close to something useful.
Phil S.
Sorry I wasn't clear. I didn't mean to interpolate the individual component values of the elements, then calculate a position. What I intended was, assuming we call the preapproach element set E(1), close approach E(2) & postapproach E(3), to calculate a position using E(1) then E(2) and do a time interpolation between those positions before close approach. After close approach, switch to E(2) & E(3) & again interpolate between the calculated positions.
This seems like a possible way to find a good position without the effort of solving the n-body problem. At least one good enough to find the object. If the epochs of the elements aren't too far apart the path of the MP should be close to the line between the positions calculated using E(1) & E(2) for example. If things don't work that way, I stand corrected.
If the described approach is workable, the question becomes, how close do the epochs of osculation need to be to be good enough? It would be interesting to plot the positions calculated by several sets of osculating elements for a time t(x) to see where they appear on the sky. What kind of curvature would the plot of positions show?
BMD are you aware of software that could perform this type of calculation & plotting? SkyTools would be great for the plotting, but I'm not sure how to get it to calculate a position using a particular epoch for the elements. It picks the elements internally.
Just some spitballing here. It seems like we might be close to something useful.
Phil S.