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Stacking Techniques - NEOCP Uncertainty Maps & Variant Orbits

Uncertainty maps

Newly discovered fast moving objects that are unconfirmed (i.e. those only reported by the discoverer) may have been observed for a short period of time, in many cases for less than an hour. The longer they go unobserved after discovery, the more uncertain the current prediction gets.

 

When such objects are posted on the NEO Confirmation Page they have extra information provided to help the observer gain an idea of the likely area on the sky that the object may lie in. This is given in the form of an uncertainty map and also the RA & Dec offsets used to draw the uncertainty map.

 

Fig. 1 Example Uncertainty Map

 

With this map an observer can try finding the object, often by starting at the most likely place where the  RA and Dec offsets are both zero (the nominal position) and then working outwards until the object is found.

 

However, each point on the uncertainty map is the representation of an orbit that has been calculated by the Minor Planet Center and each of these orbits fits the original discovery positions within the expected accuracy of the discovery observations. The spread of positions shows that the different orbits result in predicted positions (ephemerides) having different rates of motion on the sky.

 

If the new object is faint then the observer with a small telescope needs to take into account the differing rates of motion of the object, using track & stack techniques, so that the image of the new object is strengthened enough to be easily visible. The ephemeris provided directly from the NEO Confirmation Page are calculated for the nominal position only and the rate of motion at the extremities of the uncertainty map can be significantly different (faster or slower motion) and can make the detection very difficult or even impossible if the object is far from the nominal position.

 

Difficulties using Uncertainty Maps

An observer searching for an object using an uncertainty map faces a number of issues:

  • The area to be searched may be much larger than the field of view of the CCD camera, careful planning of the search area may be needed.

  • The object may be moving fast, making it difficult to ensure accurate coverage of the whole area. Offsetting from the nominal position can be prone to mistakes, especially as the distance away from the nominal position increases.

  • The uncertainty area expands with time, sometimes appreciably in just a few hours 

  • The difference in apparent speed from one side of the uncertainty area to the other may be significant, ideally the observer needs to take this into account when stacking if searching for faint fast moving objects.

Here is a 24h animated uncertainty map of an object discovered by LINEAR that appeared on the NEO Confirmation page in May 2004.

Discovered at about 05h UT on May 24th at mag +18.8, moving at 34"/min it was added to the NEOCP at 18:30 UT as a mag +19.3 object. By 21:00 UT the speed at the nominal position was 24"/min and the animation covers the 24 hours from then onwards.

The North-South spread of the uncertainty area at 21:00 UT on 24th is about 1.5 and 24h later has expanded to more than 7 long.

Each square in the grid represents a 20'x20' area, slightly smaller than the field of view of the CCD camera at Great Shefford (the size used during searches to ensure some overlap between adjacent search areas).

As can be seen, the area grows rapidly in size and demonstrates some of the issues described above. This particular object was lost, no other observatories managed to locate it before it faded from view.

Fig 2.

 

Variant Orbits

In January 2004 the Minor Planet Center started to provide ephemerides (including the speed and direction of motion) for each point on the uncertainty map, not just for the nominal position. These ephemerides, calculated for each of the 'variant' orbits used to create the uncertainty map are accessed by clicking on the Offsets link under the Uncertainty column of the NEOCP ephemeris (see Fig. 3). Note that if an object has been picked up and reported after the discovery then the orbit will be far better known and the uncertainty column will be removed by the Minor Planet Center, so not all objects on the NEO Confirmation Page will have uncertainty maps and offsets given.

 

As an example, the uncertainty map in Fig. 1 was provided by the MPC for an object assigned a temporary designation of AQ97025, discovered by LINEAR on 2004 Oct 12 at about 9h40m UT. This was first posted on the NEO Confirmation Page just over 12 hours later at 21h51m UT and the uncertainty map shows the likely range of positional uncertainty at midnight just over two hours after that.


As can be seen, the extent of the uncertainty area is about 2,500" in RA and 3,500" in Declination (or approximately 2/3 x 1), already quite a large area.

With the equipment at Great Shefford giving a field of view of slightly less than 1/2 square this area would already involve taking three or four different fields to cover the whole area adequately.

As mentioned earlier, each dot on the map represents an independent orbit and has its own associated speed and direction of motion. When stacking images these different speeds need to be taken into account. Depending on how quickly the numbers vary it may even be required to use different values to stack different parts of the image within a single field of view. Note: A position at coordinates 0,0 on the map is regarded as the most likely place to find the object (the nominal position), but there is a possibility that the object could be found anywhere on the map. Indeed, sometimes objects with unusual motion or with uncharacteristically poor discovery positions do lie completely outside the uncertainty map. See Major News About Minor Objects issued 2004 March 17th for an example when 2004 FH was found to be well outside its uncertainty area, 44 hours before passing by Earth just 4 Earth diameters away.
 Fig. 3 showing the ephemeris for the nominal position for AQ97025, which includes the uncertainty columns for Map/Offsets

NEO Confirmation Page: Query Results

Below are the results of your request from the Minor Planet Center's NEO Confirmation Page. Ephemerides are for observatory code J95.

AQ97025

 No comments so far!
  
Date       UT   *  R.A. (J2000) Decl.  Elong.  V        Motion     Object     Sun         Moon        Uncertainty
            h                                        "/min   P.A.  Azi. Alt.  Alt.  Phase Dist. Alt.
2004 10 12 20     08 21 57.6 +54 24 39  86.5  19.3   16.39  203.2  189  +16   -26    0.02  072  -26   Map/Offsets
2004 10 12 21     08 21 13.4 +54 09 38  86.5  19.3   16.31  203.3  198  +18   -34    0.02  072  -32   Map/Offsets
2004 10 12 22     08 20 29.5 +53 54 41  86.6  19.3   16.25  203.4  207  +22   -41    0.02  073  -37   Map/Offsets
2004 10 12 23     08 19 45.6 +53 39 49  86.7  19.3   16.21  203.7  215  +26   -45    0.02  073  -39   Map/Offsets
2004 10 13 00     08 19 01.6 +53 24 59  86.7  19.3   16.20  203.9  223  +32   -46    0.02  074  -37   Map/Offsets
2004 10 13 01     08 18 17.5 +53 10 10  86.8  19.3   16.22  204.1  231  +39   -44    0.01  074  -34   Map/Offsets
2004 10 13 02     08 17 33.2 +52 55 22  86.8  19.3   16.25  204.3  238  +47   -39    0.01  075  -28   Map/Offsets
2004 10 13 03     08 16 48.8 +52 40 32  86.9  19.3   16.30  204.4  244  +55   -32    0.01  075  -20   Map/Offsets
2004 10 13 04     08 16 04.3 +52 25 40  87.0  19.3   16.37  204.5  250  +64   -23    0.01  076  -12   Map/Offsets
2004 10 13 05     08 15 19.9 +52 10 44  87.1  19.3   16.43  204.4  256  +73   -14    0.01  076  -03   Map/Offsets
2004 10 13 06     08 14 35.8 +51 55 44  87.1  19.2   16.49  204.3  260  +82   -05    0.01  077  +06   Map/Offsets
2004 10 13 07     08 13 52.0 +51 40 40  87.2  19.2   16.55  204.0  106  +89   +04    0.01  077  +14   Map/Offsets
2004 10 13 08     08 13 08.8 +51 25 31  87.3  19.2   16.59  203.7  098  +79   +13    0.01  078  +22   Map/Offsets
2004 10 13 09     08 12 26.4 +51 10 18  87.3  19.2   16.61  203.3  103  +70   +20    0.01  078  +28   Map/Offsets
2004 10 13 10     08 11 44.9 +50 55 01  87.4  19.2   16.61  202.9  108  +60   +26    0.01  079  +33   Map/Offsets
2004 10 13 11     08 11 04.4 +50 39 42  87.5  19.2   16.59  202.4  115  +52   +30    0.01  079  +35   Map/Offsets
2004 10 13 12     08 10 25.1 +50 24 21  87.5  19.2   16.54  201.9  121  +43   +31    0.00  080  +35   Map/Offsets
2004 10 13 13     08 09 46.9 +50 09 01  87.6  19.2   16.47  201.4  129  +35   +29    0.00  080  +32   Map/Offsets
2004 10 13 14     08 09 09.9 +49 53 42  87.7  19.2   16.38  201.0  136  +28   +25    0.00  081  +26   Map/Offsets
2004 10 13 15     08 08 34.0 +49 38 26  87.7  19.2   16.28  200.6  145  +22   +18    0.00  081  +19   Map/Offsets
2004 10 13 16     08 07 59.1 +49 23 14  87.8  19.2   16.16  200.3  154  +17   +10    0.00  082  +11   Map/Offsets
2004 10 13 17     08 07 25.1 +49 08 07  87.9  19.2   16.04  200.1  163  +13   +02    0.00  083  +02   Map/Offsets
2004 10 13 18     08 06 51.7 +48 53 06  87.9  19.2   15.92  200.0  173  +11   -08    0.00  083  -08   Map/Offsets
2004 10 13 19     08 06 18.9 +48 38 11  88.0  19.2   15.81  199.9  183  +10   -17    0.00  084  -17   Map/Offsets
2004 10 13 20     08 05 46.4 +48 23 23  88.0  19.2   15.71  200.0  193  +11   -26    0.00  084  -25   Map/Offsets

This service has been made possible by Process Software Corporation, and their excellent OpenVMS Web server, Purveyor.

These calculations have been performed on the Tamkin Foundation Computing Network.

Note that the motion for the predicted nominal position for 2004 Oct 13 00h UT is 16.20"/min in p.a. 203.9 and the uncertainty map in Fig. 1 was generated by clicking on the Map link on the line for 2004 Oct 13 00h.

However, by clicking on the Offsets link on the same line a list of (999) uncertainty offsets, one for each dot on the uncertainty map is generated. Fig. 4 shows the start and end of that page, again for Oct 13 00h UT, with 980 intervening lines removed here for clarity (different objects have different numbers of orbits generated for their uncertainty maps, sometimes far fewer than 999 and sometimes even more):

Fig 4. Uncertainty Offsets

Uncertainty Offsets for AQ97025 (2004 10 13.000)

     -33     +34      Ephemeris #   1
     -99     -67      Ephemeris #   2
     -73     +27      Ephemeris #   3
     -19     +66      Ephemeris #   4
     +21     +44      Ephemeris #   5
     -85      +1      Ephemeris #   6
     +25    +114      Ephemeris #   7
     -48      +1      Ephemeris #   8
     +39     +85      Ephemeris #   9
    -111     -23      Ephemeris #  10
(Ephemerides #11 - #990 removed)
     -36    -991      Ephemeris # 991 !
    -927   -1756      Ephemeris # 992
    -813   -1646      Ephemeris # 993
    -890   -1737      Ephemeris # 994
   +1434   +1600      Ephemeris # 995 !
    -912   -1751      Ephemeris # 996
    -663   -1419      Ephemeris # 997
    -951   -1780      Ephemeris # 998
    -739   -1531      Ephemeris # 999

The extremities of the uncertainty map in Fig. 1 are represented by orbits #995 (top left, with offsets of +1434" in RA and +1600" in Dec) and #998 (bottom right, with offsets of -951" in RA and -1780" in Dec) as shown in Fig. 5.

Note that variant orbit #995 is coloured orange on the map and flagged with a '!' on the Uncertainty Offsets list indicating that it is close to Earth (between 0.01 and 0.05 AU) but orbit #998 is coloured green and has no flag on the Uncertainty Offsets list, indicating that it is further than 0.05 AU from Earth at that time. See the MPC's 'Comments and Notes on the NEOCP' page for full details of colours and flags used on the NEOCP ephemerides..

Fig. 5 Uncertainty map with variant orbits at extremities indicated.
Clicking on the links on the Uncertainty offsets page (Fig. 4) for Ephemeris # 995 and Ephemeris # 998 causes ephemerides for those specific orbits to be displayed and the wide range of motion represented by the uncertainty map can then be seen. In Fig. 6 three ephemeris positions for Oct 13 00h - 02h are listed for the two orbits:

Fig 6. Ephemerides for variant orbits #995 and #998

AQ97025 (Variant orbit #995)

Date       UT   *  R.A. (J2000) Decl.  Elong.  V        Motion     Object     Sun         Moon
            h                                        "/min   P.A.  Azi. Alt.  Alt.  Phase Dist. Alt.
2004 10 13 00     08 22 05.7 +53 48 37  86.4  19.6   10.16  200.4  222  +32   -46    0.02  073  -37   !
2004 10 13 01     08 21 41.1 +53 39 15  86.4  19.7    9.96  202.1  230  +39   -44    0.01  074  -34   !
2004 10 13 02     08 21 15.1 +53 30 08  86.5  19.7    9.84  203.7  236  +46   -39    0.01  074  -28   !

AQ97025 (Variant orbit #998)

Date       UT   *  R.A. (J2000) Decl.  Elong.  V        Motion     Object     Sun         Moon
            h                                        "/min   P.A.  Azi. Alt.  Alt.  Phase Dist. Alt.
2004 10 13 00     08 17 12.6 +52 55 43  86.8  19.0   21.87  204.1  224  +32   -46    0.02  074  -37
2004 10 13 01     08 16 12.8 +52 35 32  86.9  18.9   22.39  204.1  231  +39   -44    0.01  074  -34
2004 10 13 02     08 15 12.2 +52 14 51  87.0  18.9   22.93  204.1  239  +47   -39    0.01  075  -28

Note:
  • from one side of the uncertainty map to the other there is a doubling of apparent speed
  • the faster motion is from the orbit having the object further away from the Earth (#998)
  • the nearer orbit (#995) has the object fading while the further orbit (#998) has the object brightening

Therefore no assumptions should be made about the brightness or motion without checking the variant orbit ephemerides first. To stand any chance of finding this particular object with a small telescope, the appropriate ephemeris from the variant orbit applicable to the field or part of the field being examined would have been needed to be used.

See here for further details on how to conduct a search using Minor Planet Center variant orbits.


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