Lightcurves of Hildas and Trojans

I published a short paper on the following info in vol. 40, page 7, 2013 of The Minor Planet Bulletin. A pdf version of the paper is here. Complete issues of The Minor Planet Bulletin can be downloaded here.

A lightcurve of a minor solar system body can give its rotational period. Lightcurves obtained over a sufficient period of time when as an object orbits the Sun can yield information on the shape and rotational axis orientation of the object.

I was wondering how many Hildas and Trojans had good lightcurves, so I compared lists of Hildas and Trojans with lists of objects with known lightcurves. There are thousands of Hildas and Trojans cataloged. To make lists of more practicable size, I essentially listed the 100 largest Hildas and the 100 largest Trojans.

Of the Trojan100 objects, 96 have lightcurves, although only about half of these are of the best quality (3 or 3-). For the Hilda100 objects, only about half have published lightcurves, and less than half of these are of the best quality.

Clearly, much more work is needed to get excellent quality lightcurves of even the 100 largest Trojans and especially the 100 largest Hildas.

Another reason I made these lists is to have an unbiased list of objects for rotational period study. To do, say, a proper statistical comparison of rotational periods of different classes of objects, or a comparison of rotational periods with some theoretical model, one must have a list of objects defined by some property other than period. If you took just the objects that had measured periods you might lead astray. The lists of objects with measured lightcurves may be systematically lacking in some types of lightcurves. Perhaps very long rotational period objects have been under-observed, simply because of the amount of time needed to get lightcurves of very long period objects. Perhaps nearly spherical objects have been under-observed as they have very uninteresting lightcurves. By defining a list of objects by some property other than rotation, then measuring the rotational periods of all the objects in the list, you would have a much better idea of the true distribution of rotational periods than if you just went to a list of measured objects and took the observed periods.

Hilda100 and Trojan100 Lists

The following 2 lists are the 100 Hildas and 100 Trojans with the lowest H magnitude values. If all objects have the same albedo, then the lower H mag objects are larger, so the lists are arranged from larger to smaller bodies. The H mag values are taken from the JPL HORIZONS system database. These only include objects observed astrometrically at 2 or more oppositions.

I searched for lightcurve information for the objects in these lists using the latest Asteroid Lightcurve Database (LCDB) (Warner, Harris, and Pravec). I plan to update the lightcurve information as updates of the LCDB become available.

The objects are listed in increasing H magnitude. These tables were made utilizing the JPL Small Body Search Engine. The first column is simply a sequence number, 1 to 100. The second and third columns give the asteroid number and name (if available). The fourth column gives the rotational period in hours from the LCDB, if available. The last column gives the quality code of the lightcurve, as taken from the LCDB. If the SAM flag is set to "Y", a "Y" is shown. If no lightcurve has been published, but a period has been, an "N" is listed.

The Hilda100 list

The Trojan100 list

Upcoming Oppositions of Hildas

To most efficiently observe lightcurves, one targets objects that can be observed for a long portion of each night. That means targeting objects that are near opposition, so that they can be observed for many hours on either side of the middle of the night, and objects that have a declination that allows a long period of time with low airmass as seen from your observatory.

To help observers make initial plans to observe lightcurves of Hildas, I have made tables listing some basic information about the upcoming oppositions of objects in the Hilda100 list. For each Hilda in the Hilda100 list, I computed a table showing the dates of opposition until the end of 2019. These tables should provide a guide as to objects that are observable from your observatory.

For example, here is the table for 1911 Schubart:

1911 Schubart (1973 UD)
  2012-Sep-24   Dec= +02  apmag= 15.7  elong= 177.9  r= 4.1
  2013-Nov-21   Dec= +21  apmag= 14.9  elong= 178.3  r= 3.5
  2015-Feb-04   Dec= +15  apmag= 14.7  elong= 178.8  r= 3.4
  2016-Apr-09   Dec= -09  apmag= 15.5  elong= 177.8  r= 3.9
  2017-May-26   Dec= -22  apmag= 16.1  elong= 178.5  r= 4.4
  2018-Jul-05   Dec= -22  apmag= 16.3  elong= 179.9  r= 4.6
  2019-Aug-13   Dec= -13  apmag= 16.2  elong= 178.8  r= 4.5

The first column is the date when the object has a maximum in its solar elongation angle. This is very close to the time of opposition. The remainder of each line refers to values on that date.

The second column gives the declination.

The third column gives an estimate of the object's visual magnitude.

The fourth column gives the maximum solar elongation angle.

The last column gives the heliocentric distance.

These tables were made utilizing the JPL HORIZONS Ephemeris Generator. Values for position, magnitude, solar elongation and heliocentric distance were requested for each day from 2012 to 2019. A FORTRAN program was written to go through these files, find the times of local maxima of the solar elongation, then output the information in the table format.

The information on oppositions is given in several different formats. First, the oppositions are arranged in a chronological format for each year, then as a single file for the 8 years 2012 to 2019:

Hildas at oppostion in 2012

Hildas at opposition in 2013

Hildas at opposition in 2014

Hildas at opposition in 2015

Hildas at opposition in 2016

Hildas at opposition in 2017

Hildas at opposition in 2018

Hildas at opposition in 2019

Hildas opposition 2012-2019

This link gives a single file that has information for all 100 Hildas. The same information is given for groups of 5 Hildas below.

All 100 Hildas, ordered as in Hilda100 list

Each page below shows the information for 5 Hildas. The objects are listed in the same order as in the Hilda100 list. (These are simple ASCII files. Some browsers may automatically download these instead of displaying them- check your browser settings if you wish to change this behavior.)

Hildas 153, 190, 334, 361, 1269

Hildas 748, 1268, 1180, 499, 1162

Hildas 1902, 1212, 1512, 1256, 1345

Hildas 1754, 1746, 2760, 1529, 5661

Hildas 1911, 2312, 1578, 3694, 3577

Hildas 3990, 4317, 1439, 2067, 3843

Hildas 5603, 2246, 1202, 1748, 3202

Hildas 3134, 1877, 2624, 4196, 3561

Hildas 958, 3415, 3557, 6984, 8551

Hildas 2483, 1038, 23301, 3655, 15638

Hildas 5368, 7027, 3254, 7394, 23186

Hildas 12920, 5711, 3571, 4446, 17428

Hildas 2959, 8721, 8130, 4495, 11388

Hildas 11542, 9121, 9661, 19752, 10331

Hildas 7284, 3923, 14669, 5928, 1941

Hildas 10889, 8743, 8376, 8086, 25869

Hildas 6237, 38613, 15540, 31817, 15505

Hildas 13504, 13035, 7174, 11410, 11249

Hildas 15278, 5439, 32460, 4230, 3514

Hildas 15231, 15417, 38701, 3290, 16970