An A/CC Special Topic:

Residuals

Info updated: 1 June 2003

"Astrometry" is the measurement of the positions of celestial objects such as asteroids and comets, as well as bigger things, like stars. It is from these measurements that orbits are calculated and then progressively refined with new observations. A large part of astrometry for minor objects, especially NEOs, is performed by a few very serious and well-equipped amateur astronomers who report their data to the International Astronomical Union's Minor Planet Center (MPC) in Cambridge, Mass.
"Residuals" are the difference between where an object was reported to be and where it should have been according to the current orbit solution based on all observations. The difference is reported in arc seconds (") of right ascension (R.A.), multiplied by the cosine of declination, and in arc seconds of declination (dec.).
Right ascension and declination are similar to longitude and latitude on the sky dome. When not decimalized, R.A. is shown in hours (h), minutes (m), and seconds (s), while dec. is given in degrees (°), arc minutes ('), and arc seconds ("). One second (1s) equals 15 arc seconds (15"). Genny Sansaturio, of NEODyS and the University of Valladolid, explains that, "Residuals for both quantities are always given in seconds of arc ("), but the factor cos(dec.) must be included in the R.A. residuals to account for the fact that the sky is not a plane, but a sphere."
Observers need to see their residuals to monitor how well they are performing, as Reiner Stoss explains at right.

More about residuals

MPC Residuals page

Where to get residuals

The primary way to get residuals is to enter a query at the Minor Planet Center's Minor Planet & Comet Ephemeris Service page (enable "MPC 8-line" and "Show residual blocks"), and in monthly batch reports by paid subscription to the Minor Planet Circulars.
Residuals for asteroids can be viewed on the Web at NEODyS for near-Earth objects, and at AstDyS, the NEODyS counterpart for other asteroids. Just look up the object you want and scroll down to a link to "Optical observations." Residuals for comets can be viewed on the Web in the Nakano Notes.

Reiner Stoss writes: Nothing is more useless and time wasting than reporting bad astrometry over a long period of time only because one doesn't know that there is some error source in the observing process.
As with every physical measurement, astrometric measurements have errors. These "residuals" are due to

1. time error
2. centroiding error
3. error in the reference star catalog

The time error should be less than one second (1s) with today's time keeping by atomic clocks. So this will result in no significant error for slow movers like Main Belters and even trans-Neptunian objects. But, for fast moving near-Earth objects, even a 0.5s timing error can result in large residuals of over one arc second (1") in R.A./Dec.
An asteroid is a point of light that spreads into an irregular blob of pixels in the CCD image according to its brightness, observing conditions, and exposure details. It is the centroid (center) of this blob that is reported to the MPC. Centroiding errors are sometimes due to a too low signal-to-noise ratio (SNR), and imaging faint objects means working at low SNR. Today's software is quite good at determining the centroid of a point source, to maybe 1/20th of a pixel. Another error source within the centroiding problem are errors in tracking the object or in making too long an exposure. Both will trail the object's image and thus lower the SNR, making precise centroiding harder for the software. Of course, comet comas and tails present additional centroiding problems.
Minor object positions are calculated in software by reference to the background stars using a star catalog. Every star has a certain error within a catalog. This error can come from the star's "proper motion" (if a catalog is used with an outdated epoch and no proper motion data), or from centroiding errors in making the catalog, when positions were taken from plates or reduced from CCD images. But these are random errors that are almost eliminated by using many reference stars. What is more of a problem is the systematic error in a catalog, where the entire reference frame is shifted, and also because the proper motion of stars can be mostly in the same direction within small areas of the sky.
Astrometry today has improved significantly, by almost a whole digit in accuracy from where it used to be, but even so there will always be residuals.