Mike Kretlow
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Solar System - Occultations

On prediction uncertainties

The most reliable (and straight forward) way computing the ephemeris uncertainty would be to compute a new/improved orbit for the asteroid. From this least-squares fit the formal error of the solution (covariance matrix) can be propagated to the time of occultation. And out of that we got the uncertainty ellipse (RA/DE) in the sky plane. Other methods to estimate the ephemeris uncertainty are nicely summarized in a mail list message by Steve Chesley (JPL).

While this could be done (and in case of selected updates it is) for single asteroids or special events this approach is not suitable (or at least not easy) in an automatic way necessary to feed the occultation search engine with a large bunch of asteroids. Beside of performance reasons these orbit improvements would have to be done automatically, including weighting and rejecting bad observations. Especially for low-numbered objects (and these are the main candidates for occultations because they are the larger ones), over decades (and more) observed, an automated observation selection procedure could be worse then a comprehenshive, manually examination of the orbit solution and the observational data.

One practical way is to use the daily updated astorb.dat database of orbital elements. The database gives also a current ephemeris uncertainty and the daily change for it. These values can be used to get an ephemeris uncertainty for the time of occultation (plus a formal error of the star position).

NB: in my point of view the automated process of computing the orbits (i.e. rejecting, weighting of the observations) can lead to lower quality solutions compared to the orbits given in mpcorb.dat, especially for low-numbered objects etc.. Thus I would basically prefer mpcorb.dat for prediction purposes, but the individual computed (low-numbered) orbits here might not consider the latest observations (or even latest oppositions). In conclusion it is sometimes recommendable to take both data sets into account (or to compute an individual/updated orbit).

The following table gives you an idea how the prediction uncertainty in arcs (ephemeris + star position) together with the geocentrical distance yields to the path uncertainty on Earth (better: on the Bessel plane). The left column gives the assumed uncertainty in arcs (0.05, 0.1, 0.5,...), the top row the geocentric distance of the object in AU (1.0, 1.5,...,30.0). Then you can pick up the uncertainty on Earth in km.

 

-- 1.0 1.5 2.0 2.5 3.0 3.5 4.0 5.0 10.0 20.0 30.0
0.05 36 54 72 90 108 126 145 181 362 725 1087
0.1 72 108 145 181 217 253 290 362 725 1450 2175
0.5 362 543 725 906 1087 1269 1450 1813 3626 7252 10878
1.0 725 1087 1450 1813 2175 2538 2901 3626 7252 14505 21757
1.5 1087 1631 2175 2719 3263 3807 4351 5439 10878 21757 32636
2.0 1450 2175 2901 3626 4351 5076 5802 7252 14505 29010 43515
5.0 3626 5439 7252 9065 10878 12691 14505 18131 36262 72525 108788

 

Note 2016/2017: A more recent discussion on this topic is given in this talk.


Reference Frames / Star Catalogs

A good introduction/overview to the ICRS including further reading (links/papers) is given by George Kaplan (USNO).
Comprehenshive informations and recommendations on star catalogs are given by Norbert Zacharias et al. (USNO).
You might also take a look here on some personal comments concerning star catalogs for occultation work.


Credits

In general all individuals / institutes are acknowledged for providing the community with data and/or services for free !

The U.S. Naval Observatory (George H. Kaplan) is acknowledged for the superb NOVAS library which I am using in my programs (Fortran and Python)  since many years.

Last edited: February 11, 2017, 11:05

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