Last updated 20 Mar 2018

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Determining the absolute timing accuracy of an astrometric system

Measuring the positions of very fast moving near-Earth objects using a telescope and CCD requires the start time of exposures to be accurately known. With modern star catalogues and a strongly recorded target, the errors in the positional measurements of RA and Dec can be as small as +/- 0.1 arc-seconds, but for an object moving at e.g. 300 arc-seconds per minute, to match that precision the exposure start time needs to be known in absolute terms to 0.1 / (300 / 60) seconds = 0.02 seconds.

 

There are plenty of ways of trying to ensure the clock timing of a system is good (GPS hardware, NTP synchronisation over the internet etc.), but it is much more difficult to determine the absolute accuracy of the end result, i.e. the accuracy of the start time of an exposure.

 

A post on the Minor Planet Mailing List by Bill Gray (message #32821) titled "New on-line tool to help detect/measure timing errors in astrometry" has given astrometrists the means to test their systems and determine their absolute timing accuracy relatively simply. The steps I have taken to measure my system are given below and I would recommend that observers try Bill's approach to measure their own equipment. It does not help in identifying which components may be causing problems but does provide an absolute measure of accuracy which is otherwise very difficult to obtain.

Overview

Bill's approach is to take images of GPS and GLONASS (the Russian equivalent of GPS) satellites and measure their astrometric positions. The orbits of these objects are very well known, from the  early 1990's to about 24 hours into the future and to an accuracy of just a few centimetres. As these satellites are generally moving at apparent speeds of 2,000 - 2,400 arc seconds per minute, or 30 - 40 arc seconds per second, they can be used as a very sensitive gauge of the absolute timing accuracy of an astrometric imaging system, with all the delays and errors from CCD camera shutter, imaging software, operating system, timing source and even observatory topocentric coordinates combining to affect the final measurement. The positional accuracy in RA & Dec can be expected to be of the order of 1 arc-second or better but a timing error of 1 second in the clock will manifest itself as a 30-40 arc-second discrepancy with the ephemeris, so allowing a very sensitive measure of timing accuracy.

 

Selecting a satellite to observe

The on-line tool provided by Bill now includes the following pages:

GPS and GLONASS satellites available for astrometry testing

This link allows the observer to display those satellites that are higher than a selected altitude at a given time.

GPS and GLONASS satellites ephems

Here an ephemeris can be generated for a previously selected satellite.

 

Taking images

Trying to measure long trails accurately is notoriously difficult and so I have kept exposures very short, experimenting between 0.2 and 1 second and settling on 0.3 second exposures which allows Astrometrica to determine a good centroid in the standard 3-pixel radius aperture I normally use with a trail length of about 10-12 arc-seconds.

 

 

You will need:

Web pages provided by Bill Gray giving GPS and GLONASS satellite positions and ephemerides

FindOrb orbit determination software by Bill Gray

Images of GPS and GLONASS satellites suitable for astrometric measurement

Start times and exposure lengths for the images recorded ideally with better than 1 second precision

Spreadsheet program e.g. Excel

 

Select a GPS/GLONASS satellite to observe

The on-line tool(s) provided by Bill Gray include the following pages:

GPS and GLONASS satellites available for astrometry testing

Displays those satellites that are higher than a selected altitude at a given time at the observer's location.

GPS and GLONASS satellites ephems

Generates an ephemeris for a previously selected satellite.

 

Take images

Satellites are generally 12th to 14th magnitude, moving at 2,000 - 2,400 arc-seconds per minute, or 30 - 40 arc-seconds per second.

Ideally use exposure times short enough to limit trailing so that the entire trail fits within the measurement annulus during measurement, allowing automatic centroiding of the target.

At Great Shefford, with a 2.2"/pixel scale and a 3-pixel radius aperture in Astrometrica, a 0.3 second exposure allows the 10-12 arc-second trails to be easily measured.

 

Measure astrometric satellite positions

As an example, with a 2.2"/pixel scale and a 3-pixel radius aperture in Astrometrica, a 0.3 second exposure allows the 10-12 arc-second trails to be easily measured. Make sure that the exposure mid-time in the resulting MPC formatted astrometry output is written out to 6 decimal places (in Astrometrica, use the Time precision value in the CCD settings).

Example

     GPSG07   C2017 09 05.84367420 58 30.75 +31 46 08.9          13.6 G      J95
     GPSG07   C2017 09 05.84374220 58 42.50 +31 48 38.2          13.7 G      J95
     GPSG07   C2017 09 05.84376820 58 47.03 +31 49 35.5          13.4 G      J95
     GPSG07   C2017 09 05.84378720 58 50.31 +31 50 17.6          13.8 G      J95
     GPSG07   C2017 09 05.84382920 58 57.70 +31 51 51.4          13.7 G      J95
     GPSG07   C2017 09 05.84385520 59 02.14 +31 52 47.2          13.6 G      J95
     GPSG07   C2017 09 05.84387520 59 05.60 +31 53 31.5          13.4 G      J95
     GPSG07   C2017 09 05.84392820 59 14.80 +31 55 27.5          13.7 G      J95
     GPSG07   C2017 09 05.84395420 59 19.32 +31 56 25.0          13.9 G      J95
     GPSG07   C2017 09 05.84397320 59 22.69 +31 57 07.3          13.7 G      J95
     GPSG07   C2017 09 05.84401520 59 30.07 +31 58 40.4          13.4 G      J95
 

Generate an ephemeris for the period observed

The observations in the example above cover the period 2017 September 05 from 20:14:53 - 20:15:23 UT.

Using the GPS and GLONASS satellites ephems page generate a 1-minute interval ephemeris covering about 10 minutes before and 10 minutes after, for the same observatory location, e.g. from 20:04 - 20:26 UT for observatory code J95. This gives:

GPS positions for JD 2458002.336111 = 2017 Sep  5 20:04:00 UTC
Observatory (J95) Great Shefford
Longitude 358.553000, latitude 51.474659
Target object: G07
HH:MM:SS  RA     (J2000)     dec     dist (km)     Azim  Alt  Elo
20:04:00 20 37 50.441 +27 00 56.332  21179.61572  132.8  59.2 132
20:05:00 20 39 38.682 +27 27 38.332  21166.33125  132.0  59.5 132
20:06:00 20 41 28.001 +27 54 14.737  21153.44726  131.3  59.8 132
20:07:00 20 43 18.420 +28 20 45.340  21140.96502  130.5  60.0 132
20:08:00 20 45 09.959 +28 47 09.929  21128.88575  129.7  60.3 132
20:09:00 20 47 02.640 +29 13 28.288  21117.21060  128.9  60.6 132
20:10:00 20 48 56.483 +29 39 40.200  21105.94067  128.0  60.8 132
20:11:00 20 50 51.510 +30 05 45.438  21095.07702  127.2  61.1 132
20:12:00 20 52 47.741 +30 31 43.776  21084.62061  126.3  61.3 132
20:13:00 20 54 45.200 +30 57 34.982  21074.57239  125.4  61.5 132
20:14:00 20 56 43.907 +31 23 18.818  21064.93321  124.6  61.7 132
20:15:00 20 58 43.885 +31 48 55.043  21055.70389  123.6  62.0 132
20:16:00 21 00 45.156 +32 14 23.412  21046.88517  122.7  62.2 132
20:17:00 21 02 47.741 +32 39 43.676  21038.47776  121.8  62.4 132
20:18:00 21 04 51.664 +33 04 55.578  21030.48228  120.8  62.5 132
20:19:00 21 06 56.947 +33 29 58.861  21022.89931  119.9  62.7 132
20:20:00 21 09 03.611 +33 54 53.259  21015.72936  118.9  62.9 132
20:21:00 21 11 11.681 +34 19 38.506  21008.97289  117.9  63.0 132
20:22:00 21 13 21.177 +34 44 14.327  21002.63031  116.9  63.2 132
20:23:00 21 15 32.122 +35 08 40.443  20996.70195  115.9  63.3 132
20:24:00 21 17 44.540 +35 32 56.572  20991.18809  114.9  63.4 132
20:25:00 21 19 58.451 +35 57 02.426  20986.08895  113.9  63.5 132
20:26:00 21 22 13.879 +36 20 57.714  20981.40470  112.8  63.7 132

Reformat the ephemeris into MPC format astrometry lines

The above ephemeris converts to:

     GPSG07   C2017 09 05.83611120 37 50.441+27 00 56.33                     J95
     GPSG07   C2017 09 05.83680620 39 38.682+27 27 38.33                     J95
     GPSG07   C2017 09 05.83750020 41 28.001+27 54 14.74                     J95
     GPSG07   C2017 09 05.83819420 43 18.420+28 20 45.34                     J95
     GPSG07   C2017 09 05.83888920 45 09.959+28 47 09.93                     J95
     GPSG07   C2017 09 05.83958320 47 02.640+29 13 28.29                     J95
     GPSG07   C2017 09 05.84027820 48 56.483+29 39 40.20                     J95
     GPSG07   C2017 09 05.84097220 50 51.510+30 05 45.44                     J95
     GPSG07   C2017 09 05.84166720 52 47.741+30 31 43.78                     J95
     GPSG07   C2017 09 05.84236120 54 45.200+30 57 34.98                     J95
     GPSG07   C2017 09 05.84305620 56 43.907+31 23 18.82                     J95
     GPSG07   C2017 09 05.84375020 58 43.885+31 48 55.04                     J95
     GPSG07   C2017 09 05.84444421 00 45.156+32 14 23.41                     J95
     GPSG07   C2017 09 05.84513921 02 47.741+32 39 43.68                     J95
     GPSG07   C2017 09 05.84583321 04 51.664+33 04 55.58                     J95
     GPSG07   C2017 09 05.84652821 06 56.947+33 29 58.86                     J95
     GPSG07   C2017 09 05.84722221 09 03.611+33 54 53.26                     J95
     GPSG07   C2017 09 05.84791721 11 11.681+34 19 38.51                     J95
     GPSG07   C2017 09 05.84861121 13 21.177+34 44 14.33                     J95
     GPSG07   C2017 09 05.84930621 15 32.122+35 08 40.44                     J95
     GPSG07   C2017 09 05.85000021 17 44.540+35 32 56.57                     J95
     GPSG07   C2017 09 05.85069421 19 58.451+35 57 02.43                     J95
     GPSG07   C2017 09 05.85138921 22 13.879+36 20 57.72                     J95

Combine both sets of astrometry into a single list

Combine the astrometry from CCD image measurement with the lines converted from the ephemeris (these can be recognised by an extra digit of precision in the RA and Dec values and no magnitude before the observatory code):

     GPSG07   C2017 09 05.84367420 58 30.75 +31 46 08.9          13.6 G      J95
     GPSG07   C2017 09 05.84374220 58 42.55 +31 48 38.4          13.7 G      J95
     GPSG07   C2017 09 05.84376820 58 47.03 +31 49 35.5          13.4 G      J95
     GPSG07   C2017 09 05.84378720 58 50.31 +31 50 17.6          13.8 G      J95
     GPSG07   C2017 09 05.84382920 58 57.70 +31 51 51.4          13.7 G      J95
     GPSG07   C2017 09 05.84385520 59 02.14 +31 52 47.2          13.6 G      J95
     GPSG07   C2017 09 05.84387520 59 05.60 +31 53 31.5          13.4 G      J95
     GPSG07   C2017 09 05.84392820 59 14.80 +31 55 27.5          13.7 G      J95
     GPSG07   C2017 09 05.84395420 59 19.32 +31 56 25.0          13.9 G      J95
     GPSG07   C2017 09 05.84397320 59 22.69 +31 57 07.3          13.7 G      J95
     GPSG07   C2017 09 05.84401520 59 30.07 +31 58 40.4          13.4 G      J95

     GPSG07   C2017 09 05.83611120 37 50.441+27 00 56.33                     J95
     GPSG07   C2017 09 05.83680620 39 38.682+27 27 38.33                     J95
     GPSG07   C2017 09 05.83750020 41 28.001+27 54 14.74                     J95
     GPSG07   C2017 09 05.83819420 43 18.420+28 20 45.34                     J95
     GPSG07   C2017 09 05.83888920 45 09.959+28 47 09.93                     J95
     GPSG07   C2017 09 05.83958320 47 02.640+29 13 28.29                     J95
     GPSG07   C2017 09 05.84027820 48 56.483+29 39 40.20                     J95
     GPSG07   C2017 09 05.84097220 50 51.510+30 05 45.44                     J95
     GPSG07   C2017 09 05.84166720 52 47.741+30 31 43.78                     J95
     GPSG07   C2017 09 05.84236120 54 45.200+30 57 34.98                     J95
     GPSG07   C2017 09 05.84305620 56 43.907+31 23 18.82                     J95
     GPSG07   C2017 09 05.84375020 58 43.885+31 48 55.04                     J95
     GPSG07   C2017 09 05.84444421 00 45.156+32 14 23.41                     J95
     GPSG07   C2017 09 05.84513921 02 47.741+32 39 43.68                     J95
     GPSG07   C2017 09 05.84583321 04 51.664+33 04 55.58                     J95
     GPSG07   C2017 09 05.84652821 06 56.947+33 29 58.86                     J95
     GPSG07   C2017 09 05.84722221 09 03.611+33 54 53.26                     J95
     GPSG07   C2017 09 05.84791721 11 11.681+34 19 38.51                     J95
     GPSG07   C2017 09 05.84861121 13 21.177+34 44 14.33                     J95
     GPSG07   C2017 09 05.84930621 15 32.122+35 08 40.44                     J95
     GPSG07   C2017 09 05.85000021 17 44.540+35 32 56.57                     J95
     GPSG07   C2017 09 05.85069421 19 58.451+35 57 02.43                     J95
     GPSG07   C2017 09 05.85138921 22 13.879+36 20 57.72                     J95

Open combined astrometry with FindOrb

Open the combined astrometry with FindOrb and toggle all the astrometry from CCD image measurement off, so that it will NOT be used in any orbit calculation. In the screenshot below the blue lines are all now unselected (an "X" after time and before observatory code). Full step has been pressed a few times and the orbit is generated from the ephemeris data only

by clicking on an individual line selects it and causes FindOrb to display the timing error for that individual measurement at the bottom of the window. Here the first of the measured lines of astrometry is selected:

The residuals in RA and Dec are 0.94" and 1.4", but these, translated to timing error and cross track residual are +0.046 seconds and 0.33", i.e. assuming the time of observation is late by 0.046 seconds causes the overall residual to be reduced from about 1.7" to 0.33".

Generate an ephemeris for the period observed

Generate an ephemeris for the period observed

Generate an ephemeris for the period observed


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