Last updated 29 Apr 2024

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Stacking Techniques - Searching using NEOCP Variant Orbits

Keeping Track

The Minor Planet Center (MPC) posts details of newly discovered Near Earth Objects (NEOs) on the NEO Confirmation Page, so that other observers can attempt to confirm the existence of the objects and to help to refine their orbits. If only the discovery observations have been reported, or it has been seen for less than 24 hours, then the MPC will normally refer to the object as a '1 nighter' and will provide extra information to indicate the likely uncertainty in their prediction so that observers trying to find the object can search the right area of the sky.


The normal details given by the MPC consist of an ephemeris (a list of dates and corresponding positions) for the most likely place a new object is expected to be. The extra details for a 1-nighter consist of a map of the possible area in the sky that the object might be found (Fig. 1). Each dot on the uncertainty map is the result of a separate prediction by the MPC - a range of likely orbits is calculated, all of which fit the available observations within the limits of their expected errors and each separate orbit (or variant orbit) results in a dot on the uncertainty map. Using the NEO Confirmation page, ephemerides for any of the dots on the map can be generated to assist the observer trying to find the object. Each ephemeris will give a slightly different speed and direction of motion for the object. Sometimes there can be large differences in motion from one side of an uncertainty map to the other (see here).


Most NEOCP objects are relatively slow moving and often close to their predicted positions while others are fast moving with correspondingly larger uncertainties. Generally, only those with uncertainties larger than your field of view require special attention as described below.


Issues to overcome

Trying to find a fast moving object in an area of sky much larger than the field of view of your telescope & camera requires some care to ensure that the entire search area (the uncertainty map) is properly covered. In practice it is very easy to cover the same area more than once and to miss other areas completely, as the uncertainty area is moving with respect to the background stars and is also expanding as the hours go by (sometimes rapidly, see an animation here).


If the object itself is bright enough to be easily recorded by your equipment in single exposures, then the main benefit of the uncertainty maps is to help keep track of areas that have been searched. When the object is finally found, then the nearest variant orbit can be used to determine the speed and direction of motion reasonably close to reality so that stacking can be used to get a stronger image to report positions to the Minor Planet Center.


However, if the object is faint, either so that it would be difficult to notice on individual exposures, or so faint that it would only be recorded by stacking exposures together, then as well as helping keep track of the areas searched, the variant orbits also provide the likely speed and direction information critical to successful stacking. Sometimes there will be only small variations across the entire uncertainty map, but quite often there will be substantial differences, the speed varying by a factor of 2 or 3 or even more from one side to the other. Stacking with the appropriate values may make the difference between finding and not finding the object.


The method used at Great Shefford to conduct a search of a large uncertainty map is described below. Some elements are suitable for software automation but the basics are described here, using the NEO Confirmation page facilities and an Excel spreadsheet. 


Image capture, stacking (if required) and searching of the images is best done in real time, with the goal of trying to locate the object before the entire area has been searched.


Fig. 1 Example Uncertainty Map




Getting the raw uncertainty map data:

  • Generate the basic NEOCP ephemeris for the object to be searched for. Either enter your MPC observatory code or your observatory longitude/latitude/altitude and press the Get Ephemerides button. If present, the uncertainty information is available via links on the right hand of the page (Map/Offsets)

  • Display the NEOCP Uncertainty Offsets in a web browser for a time at or just before when the search is to start. This will be the starting time of any variant ephemerides generated.

  • Save the displayed list of offsets as a text file (e.g. File/Save As and Save as type 'Text File (*.txt)' in MS Internet Explorer). The file will be named similar to Uncertainty Offsets for object (yyyy mm dd_ddd).txt (where object is the temporary designation used on the NEOCP and yyyy mm dd_ddd is the date and time of the generated list of offsets)

  • Open a spreadsheet and import the text file (Data/Get External Data/Import text file from within MS Excel). The columns imported are the RA and Dec offsets (in seconds of arc), the variant orbit number and the distance indicator character (! = between 0.05-0.01 AU from Earth, !! = 0.01-0.0027 AU and *** = nearer than 0.0027 AU (= the distance of the Moon). 

Example 1 (Imported Uncertainty Offsets)

Columns 1 and 2 are the RA and Dec offsets in units of seconds of arc. The last column is the distance indicator (here showing '!', indicating the object is thought to be between 0.05-0.01 AU from Earth). Only the first 10 rows of the original 494 rows are shown here.

1223 -3044 Ephemeris # 1 !
250 -1204 Ephemeris # 2 !
462 -1624 Ephemeris # 3 !
972 -2547 Ephemeris # 4 !
725 -2056 Ephemeris # 5 !
40 -789 Ephemeris # 6 !
-167 -378 Ephemeris # 7 !
238 -1094 Ephemeris # 8 !
-373 29 Ephemeris # 9 !
480 -1572 Ephemeris # 10 !


Manipulating the list of uncertainty offsets and variant orbit numbers in the spreadsheet:

  • Copy the list and sort into either RA or Dec order (depending on which has the biggest range). Sorting allows you to find a point on the map quickly by its coordinates and then get the associated variant orbit number so that an ephemeris for the chosen point can be generated from the NEOCP and used to position the telescope.

Example 2 (Sorted Uncertainty Offsets)

Here the original columns have been sorted by RA" and then Dec". The most westerly variant orbit (#490) has been sorted to the top of the spreadsheet, with RA offset of 5513", or 92' or about 1.5 and Dec offset of 10,200" or 170' or nearly 3. Note that variant orbit #489 has a more extreme Dec offset of 10,305".

-5513 10200 Ephemeris # 490 !
-5450 10157 Ephemeris # 484 !
-5363 9833 Ephemeris # 453 !
-5337 9857 Ephemeris # 486 !
-5334 10014 Ephemeris # 494 !
-5286 10305 Ephemeris # 489 !
-5252 9771 Ephemeris # 467 !
-5252 10135 Ephemeris # 485 !
-5212 9959 Ephemeris # 460 !
-5207 9529 Ephemeris # 438 !


  • Plot the list of offsets as a chart (which should look very similar to the MPC's uncertainty map). Converting the points to arcminutes is more convenient to work with than the original units of arcseconds. It will also help to specify a horizontal and vertical grid size equivalent to the field of view of your CCD (with some allowance for overlap). e.g. With a field of view of 18'x18' a grid size of 15'x15' would be appropriate.

  • Choose field centres for the search. Starting from the nominal position, use the mouse to 'hover' over appropriate dots to find their co-ordinates. Boxes can be drawn using the spreadsheet as a visual aid to spacing out to ensure that areas are not missed.

Example 3 (Chart recreating Uncertainty Map, with field centres added)


Here the individual offsets have been divided by 60 to convert to arc minutes before being plotted on a chart. The mouse is hovering over the westernmost point and its co-ordinates are shown to be -92' (west) and +170' (north) of nominal. Field centres have been chosen and 24'x24' boxes drawn. The object (2005 NG56) was found within the field centred on +91, -171, over 3 degrees from nominal.

  • Start searching from the nominal position (offset = 0,0) and find the appropriate apparent motion from the NEO Confirmation page. Take a set of images with exposure length adjusted to match the apparent speed of the object, with the number of images chosen so that there is likely to be enough strength of signal for you to notice the new object.

  • Use the field centres chosen from the uncertainty map in the spreadsheet to ensure thorough coverage, including some field overlap. Start by searching the field centres on either side of the nominal position and work outwards from there. If the map has more dots on one side than the other then try and cover the more dense areas before the less dense - although the object could be found anywhere in the uncertainty area, the density of dots is a rough indication of the likelihood of finding the object.


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