Definition of constellation boundaries by the IAU
The celestial sphere is conventionally divided into 88 regions, called constellations, whose boundaries have been standardized in 1930 on behalf of the International Astronomical Union by the Belgian astronomer Eugène Delporte.
The edges of each constellation boundary are segments of meridians of right ascension and parallels of declination in the equatorial coordinate system relative to the equinox B1875.0. Delporte's book Délimitation Scientifique des Constellations [2] provides coordinates for the edges of every constellation boundary. It is still the reference source for these coordinates.
There are interesting sites covering the topic of constellation boundaries, for instance Ian Ridpath's and Andrew James's (which contains an English translation of the introduction to Delporte's book). Felice Stoppa's site, mainly in Italian, has reproductions of Delporte's book, including the pages that specify the coordinates of the constellation boundaries.
Available constellation boundary data
The constellation boundary data is available through the VizieR service in catalogue VI/49. The file of interest is bound_18.dat, which seems to be the closest version of Delporte's original data available in electronic form.
However, the data it contains differs from the original in several respects.
- The coordinates have been converted from sexagesimal to decimal format and rounded, so that many of the values are only approximations of the original ones. In a couple of instances, the value was truncated rather than rounded (declination value of +86.16666 instead of +86.16667).
-
In order to facilitate plotting (as stated in
the documentation), some vertices
were added to the original set:
1.00000 +88.0000 CEP 0.00000 -90.0000 OCT 24.00000 -90.0000 OCT 12.00000 -90.0000 OCT
Also, the right ascension of24.00000 -75.0000 OCT
was set to 24 instead of 0.
Catalogue VI/49 is adequate for practical purposes, but it seems unsatisfactory that such standard data shouldn't be available in a form closer to the original.
Data available on this page
This is why I have compiled the constellation boundary data directly from Delporte's book and made it available on this page, along with various potentially useful derived data sets. The following files are available.
| File name | Explanation |
|---|---|
| ReadMe | File descriptions |
| bound_ed.dat | Boundary data from E. Delporte's book |
| verts_18.txt | Vertices (B1875, sex) |
| edges_18.txt | Edges (B1875, sex) |
| bound_verts_18.txt | Boundary vertices (B1875, ccw, sex) |
| bound_edges_18.txt | Boundary edges (B1875, ccw, sex) |
| bound_18.txt | Boundaries (B1875, ccw, dec) |
| bound_in_18.txt | Interpolated boundaries (B1875, ccw, dec) |
| bound_in_20.txt | Interpolated boundaries (J2000, ccw, dec) |
| lines_18.txt | Merged edges (B1875, decimal) |
| lines_in_18.txt | Interpolated merged edges (B1875, dec) |
| lines_in_20.txt | Interpolated merged edges (J2000, dec) |
| centers_18.txt | Constellation centers (B1875, dec) |
| centers_20.txt | Constellation centers (J2000, dec) |
The files are described informally below. Their formal descriptions are gathered in the ReadMe file in a format compatible with the conventions for catalogue descriptions of the VizieR service, which allows them to be validated automatically using the Anafile package.
Original boundary data
The original constellation boundary data compiled from Delporte's book is contained in the file bound_ed.dat. The format of this file is similar to that of bound_18.dat. Each constellation boundary is represented by a sequence of vertices, one vertex per line keyed by the constellation abbreviation, according to the following format.
| Bytes | Format | Unit | Explanation |
|---|---|---|---|
| 1- 2 | I2 | hrs | Right ascension B1875 (hours) |
| 4- 5 | I2 | min | Right ascension B1875 (minutes) |
| 7- 8 | I2 | sec | Right ascension B1875 (seconds) |
| 10 | A1 | Declination B1875 (sign) | |
| 11-12 | I2 | deg | Declination B1875 (degrees) |
| 14-15 | I2 | arcmin | Declination B1875 (minutes) |
| 17-18 | I2 | arcsec | Declination B1875 (seconds) |
| 20-23 | A4 | Constellation abbreviation |
The last field contains the abbreviation of the constellation corresponding to the current boundary. All the constellation abbreviations consist of 3 letters, or 3 letters followed by a digit for SER1 and SER2, the two parts of Serpens, treated as distinct constellations in most places on this page.
Delporte's book describes boundary edges rather than vertices (see this example), and therefore contains much redundancy. The vertices description is more compact and lends itself better to automatic processing. In bound_ed.dat, the vertices are enumerated in the order in which they appear in the book.
For verification, among other things, I converted the VizieR file bound_18.dat to sexagesimal format (rounding to the nearest second), removed the additional vertices mentioned above and normalized right ascensions. The resulting file is identical to bound_ed.dat except for the position of the vertex 00:00:00 -75:00:00 OCT which, in the book, appears first instead of last in the constellation Octans.
Derived data
The constellation boundary edges in Delporte's data set have been designed so that every edge is shared by exactly two constellations. Say that three points P, Q, R lie on the same segment of meridian or parallel, with Q between P and R, and that PR borders constellation C on one side, while PQ and QR border different constellations D and E on the other side. Even though the edge PR could be used in C's boundary, the data set will enumerate PQ and QR separately in C's boundary in order to satisfy this requirement.
A desirable feature of the constellation boundaries data set would be that all the boundaries be enumerated in the same direction, say counterclockwise (looking at the celestial sphere from inside), so that every edge would appear twice, once in each direction. This was apparently not a concern of the author. The following constellations are enumerated clockwise: ANT, APS, CAE, CAP, CAR, CEN, CHA, CIR, CRT, CRU, CRV, DOR, GRU, IND, LEP, LIB, LUP, MUS, NOR, PAV, PHE, PIC, PSA, PUP, RET, SCT, SGR, TEL, TUC, UMI, VEL, VOL. The rest of the datasets described on this page consistently use the counterclockwise orientation when applicable.
Vertices in sexagesimal B1875.0 coordinates
The file verts_18.txt enumerates the boundary vertices in the order of their appearance in Delporte's book and assigns them a unique key. Each line describes one vertex, according to the following format.
| Bytes | Format | Unit | Explanation |
|---|---|---|---|
| 1- 3 | A3 | Vertex key | |
| 5- 6 | I2 | hrs | Right ascension B1875 (hours) |
| 8- 9 | I2 | min | Right ascension B1875 (minutes) |
| 11-12 | I2 | sec | Right ascension B1875 (seconds) |
| 14 | A1 | Declination B1875 (sign) | |
| 15-16 | I2 | deg | Declination B1875 (degrees) |
| 18-19 | I2 | arcmin | Declination B1875 (minutes) |
| 21-22 | I2 | arcsec | Declination B1875 (seconds) |
| 24-38 | A15 | Constellation abbreviations |
The last field contains the space-delimited abbreviations of the constellations whose boundaries contain the vertex. A vertex can belong to two, three, or four constellations.
Edges in sexagesimal B1875.0 coordinates
The file edges_18.txt enumerates the boundary edges. Each edge appears only once, oriented in the direction of increasing right ascensions (for parallels) or declinations (for meridians). Each line describes one edge, according to the following format.
| Bytes | Format | Unit | Explanation |
|---|---|---|---|
| 1- 3 | A3 | Key of 1st vertex | |
| 5- 7 | A3 | Key of 2nd vertex | |
| 9 | A1 | Edge type: [M]eridian or [P]arallel | |
| 10 | A1 | Edge direction: + increasing or - decreasing | |
| 12-13 | I2 | hrs | Right ascension B1875 (hours) of 1st vertex |
| 15-16 | I2 | min | Right ascension B1875 (minutes) of 1st vertex |
| 18-19 | I2 | sec | Right ascension B1875 (seconds) of 1st vertex |
| 21 | A1 | Declination B1875 (sign) of 1st vertex | |
| 22-23 | I2 | deg | Declination B1875 (degrees) of 1st vertex |
| 25-26 | I2 | arcmin | Declination B1875 (minutes) of 1st vertex |
| 28-29 | I2 | arcsec | Declination B1875 (seconds) of 1st vertex |
| 31-32 | I2 | hrs | Right ascension B1875 (hours) of 2nd vertex |
| 34-35 | I2 | min | Right ascension B1875 (minutes) of 2nd vertex |
| 37-38 | I2 | sec | Right ascension B1875 (seconds) of 2nd vertex |
| 40 | A1 | Declination B1875 (sign) of 2nd vertex | |
| 41-42 | I2 | deg | Declination B1875 (degrees) of 2nd vertex |
| 44-45 | I2 | arcmin | Declination B1875 (minutes) of 2nd vertex |
| 47-48 | I2 | arcsec | Declination B1875 (seconds) of 2nd vertex |
| 50-57 | A8 | Constellation abbreviations |
All the edges in this dataset have the + direction, meaning that their end points are listed in the order of increasing coordinates (right ascensions for parallels, declinations for meridians).
The last field contains the space-delimited abbreviations of the two constellations adjacent to the edge. The constellation for which the edge appears counterclockwise figures first.
Boundary vertices counterclockwise in sexagesimal B1875.0 coordinates
Every vertex can belong to two, three, or four constellations. The file bound_verts_18.txt enumerates the boundary vertices, just like bound_ed.dat, but all the boundaries are enumerated counterclockwise, the vertex keys are specified, and all the constellations to which the vertex belongs are given. Each boundary is represented by a sequence of vertices, one vertex per line, according to the same format as verts_18.txt.
In the last field, the constellation corresponding to the current boundary appears first.
Boundary edges counterclockwise in sexagesimal B1875.0 coordinates
The file bound_edges_18.txt enumerates the boundary edges, much like Delporte's book, but all the boundaries are enumerated counterclockwise. Each boundary is represented by a sequence of edges, one edge per line, according to the same format as edges_18.txt.
In the last field, the constellation corresponding to the current boundary, and for which the edge appears counterclockwise, figures first.
Boundaries counterclockwise in decimal B1875.0 coordinates
The file bound_18.txt is the counterclockwise and decimal version of bound_ed.dat. The right ascensions and declinations of the boundary vertices are respectively given in decimal hours and decimal degrees, more convenient than sexagesimal values for practical purposes. Its format is as follows.
| Bytes | Format | Unit | Explanation |
|---|---|---|---|
| 1-10 | F10.7 | hrs | Right ascension B1875 (decimal hours) |
| 12 | A1 | Declination B1875 (sign) | |
| 13-21 | F9.6 | deg | Declination B1875 (decimal degrees) |
| 23-26 | A4 | Constellation abbreviation |
Interpolated boundaries counterclockwise in decimal B1875.0 coordinates
Even though the edges of the constellation boundaries align with meridians and parallels of the B1875.0 equatorial coordinate system, they can take the form of complex curves in an arbitrary projection. It is probably more convenient to draw them as sufficiently smooth polygons. In the file bound_in_18.txt, the boundary edges have been interpolated by adding points with whole degree declinations (along meridians) or whole degree right ascensions (along parallels) between vertices. This granularity seems sufficient for many applications. The imprecision becomes apparent only in regions of extreme distortion in some projections. The format of bound_in_18.txt is identical to the format of bound_18.txt.
Interpolated boundaries counterclockwise in decimal J2000.0 coordinates
In order to draw constellation boundaries in the current J2000.0 equatorial system, the coordinate transformation corresponding to the precession of the equinoxes between B1875.0 and J2000.0 needs to be applied. In that coordinate system, the constellation boundaries are not aligned with meridians and parallels any more, and an interpolated data set is even more necessary. The file bound_in_20.txt contains the same points as bound_in_18.txt, but represented in the J2000.0 coordinate system. The transformation has been effected according to the Explanatory Supplement to the Astronomical Almanac [1, pp 103-104], and using the Besselian to Julian epoch conversion as implemented by the SOFA software library. The format of bound_in_20.txt is identical to that of bound_in_18.txt and bound_18.txt, except that the coordinates are relative to the J2000.0 equatorial system.
| Bytes | Format | Unit | Explanation |
|---|---|---|---|
| 1-10 | F10.7 | hrs | Right ascension J2000 (decimal hours) |
| 12 | A1 | Declination J2000 (sign) | |
| 13-21 | F9.6 | deg | Declination J2000 (decimal degrees) |
| 23-26 | A4 | Constellation abbreviation |
Merged edges in decimal B1875.0 coordinates
The data sets bound_18.txt and its variants are appropriate when drawing the boundary of a single constellation. However, when drawing all the constellations boundaries, they cause every edge to be drawn twice (once in each direction, since all the boundaries are oriented counterclockwise). This can be undesirable when using a dotted or dashed line pattern, or for efficiency reasons.
In such a situation, a data set such as a decimal version of edges_18.txt, where every edge is mentioned only once, is preferable. Better yet, contiguous edges along the same direction can be merged into a single segment, providing an additional optimization. The data set lines_18.txt contains the segments obtained by merging contiguous edges as much as possible. Each segment is represented by two vertices, one per line, tagged with a unique key for the segment, made from the vertex keys assigned by verts_18.txt. The format is as follows.
| Bytes | Format | Unit | Explanation |
|---|---|---|---|
| 1-10 | F10.7 | hrs | Right ascension B1875 (decimal hours) |
| 12 | A1 | Declination B1875 (sign) | |
| 13-21 | F9.6 | deg | Declination B1875 (decimal degrees) |
| 23-29 | A7 | Segment key |
Interpolated merged edges in decimal B1875.0 coordinates
In order to draw the merged edges in an arbitrary projection, interpolated segments are useful. The dataset lines_in_18.txt provides this data. All the interpolated points along a segment are tagged with the segment's key. The format of this file is identical the format of lines_18.txt.
Interpolated merged edges in decimal J2000.0 coordinates
The file lines_in_20.txt is the J2000.0 version of lines_in_18.txt, and its format is similar, as follows.
| Bytes | Format | Unit | Explanation |
|---|---|---|---|
| 1-10 | F10.7 | hrs | Right ascension J2000 (decimal hours) |
| 12 | A1 | Declination J2000 (sign) | |
| 13-21 | F9.6 | deg | Declination J2000 (decimal degrees) |
| 23-29 | A7 | Segment key |
Constellation centers in decimal B1875.0 coordinates
The file centers_18.txt contains the coordinates of constellation center points in B1875.0 coordinates, as well as the constellation areas in square degrees and the constellation ranks in order of decreasing area. The centers are useful when drawing maps. They can serve as default positions for constellation names, for instance.
The constellation areas were computed by subdividing the constellation into coordinate rectangles and adding the rectangle areas. The area of a coordinate rectangle between right ascensions α0, α1 and declinations δ0, δ1 on the celestial sphere of radius 1, obtained by integrating the element of surface dS = cos δ dα dδ over the rectangle, is given by
S = (α1 - α0) (sin δ1 - sin δ0)
(in square radians if all the angles are expressed in radians; the proper conversion factor should be applied to obtain the area in square degrees as in centers_18.txt and centers_20.txt).
The constellation centers are defined as their barycenters on the sphere. Their coordinates are given by the integrals of α dS = α cos δ dα dδ and δ dS = δ cos δ dα dδ over the constellation, divided by the area of the constellation. They can be obtained as weighted averages of the barycenters of the coordinate rectangles mentioned above. The barycenter of the coordinate rectangle between right ascensions α0, α1 and declinations δ0, δ1 is given by
αc = (α0 + α1) / 2
δc =
(δ1 sin δ1 - δ0 sin δ0 + cos
δ1 - cos δ0) / (sin δ1 - sin δ0).
The ranks represent the positions of the constellations in their order of decreasing area. To compute the rank, the two parts of Serpens have been merged, their individual areas added, and the rank of Serpens assigned to both SER1 and SER2.
Reassuringly, the areas and ranks computed here agree with those found on Ian Ridpath's site (here and here). The format of centers_18.txt is as follows.
| Bytes | Format | Unit | Explanation |
|---|---|---|---|
| 1-10 | F10.7 | hrs | Right ascension B1875 (decimal hours) of center |
| 12 | A1 | Declination B1875 (sign) of center | |
| 13-21 | F9.6 | deg | Declination B1875 (decimal degrees) of center |
| 23-29 | F7.2 | deg2 | Constellation area (square degrees) |
| 31-32 | I2 | Constellation rank in area | |
| 34-37 | A4 | Constellation abbreviation |
Constellation centers in decimal J2000.0 coordinates
The file centers_20.txt is the J2000.0 version of centers_18.txt and follows a similar format.
| Bytes | Format | Unit | Explanation |
|---|---|---|---|
| 1-10 | F10.7 | hrs | Right ascension J2000 (decimal hours) of center |
| 12 | A1 | Declination J2000 (sign) of center | |
| 13-21 | F9.6 | deg | Declination J2000 (decimal degrees) of center |
| 23-29 | F7.2 | deg2 | Constellation area (square degrees) |
| 31-32 | I2 | Constellation rank in area | |
| 34-37 | A4 | Constellation abbreviation |
Maps
The celestial maps gathered here illustrate the constellation boundaries. The constellation boundaries were drawn using the lines_in_18.txt data set. Individual constellations were traced using the bound_in_18.txt data set for coloring.
I hope that this page will be useful or interesting to someone. Don't hesitate to drop me a note for comments, questions, or suggestions for improvements. While I have taken great care to ensure the accuracy of the data, errors are always possible. I would be grateful, if you find any, that you let me know about it.
References
[1] P. Kenneth Seidelmann (ed.), Explanatory Supplement to the Astronomical Almanac, 2nd edition, Sausalito: University Science Books, 1992.
[2] Eugène Delporte, Délimitation Scientifique des Constellations, Cambridge University Press, 1930.