Plotting a planisphere

Contents

• Overview
• QBASIC program
• Contributed code
• Checks

Overview

This page provides a QBASIC program that generates DXF files that draw the base plate and moveable horizon window for a planisphere of given latitude. The base plate is produced in three parts (the RA and DEC scale, the star map, and the constellation lines) to allow flexibility in labelling and style of presentation.

If you need a 'ready made' planisphere template try the page by M. S. Pettersen at Otterbein College.

A planisphere consists of two discs of plastic with a common central pivot allowing them to rotate. The base plate has a star map and lines of right ascension and declination, and there is a scale of months and days drawn around the edge with March 21st corresponding to RA = 0 hours. The moveable horizon plate has a window showing the visible horizon for the latitude at which the planisphere is plotted and a scale of hours of time around the circumference, arranged so that 0h is in the same direction as the North horizon. In use, if we want to know what stars are visible at 22h on November 26th, we rotate the horizon plate so the 22h mark co-incides with the Nov 26th date, and the horizon window shows the stars visible.

DXF Files will import into many drawing and painting programs to allow for printing and re-sizing. I use CorelDRAW version 6, Paint Shop Pro and AutoSketch 2.2 and all will import the files fine.

The method used here is a direct implementation of a suggestion in Brian Tung's page about the Planisphere, and you should read that page if you are not familiar with the planisphere. The program here is based around the following ideas:

• General: The centre of the planisphere is the North Celestial Pole, so it is probably sensible to work in terms of the polar angle (90 - dec) when plotting. Using the simplest possible projection, the 'azimuthal', gives declination circles that are concentric and evenly spaced. I'm plotting polar angles to 145 degrees from the NCP (corresponding to a declination of -55 degrees)in the program given here. The RA lines are straight radial lines. The basic formulas to convert from polar coordinates to X,Y coordinates in the plane are (x = pa.cos(alpha), y = pa.sin(alpha)) where pa stands for the polar angle of the point you are plotting, and alpha is the RA.
• The base plate: A set of concentric circles every 10 degrees of polar angle down to 150, and RA lines every hour. The star map is plotted by reading in the RA and DEC of each star, converting these to the appropriate X and Y coordinates and then plotting a small circle of radius that depends on the magnitude of the star.
• The base plate day scale: This simply consists of a scale of 365.25 divisions. The scale runs clockwise round the planisphere base, starting with March 21st on the Oh RA line.
• The horizon plate window: using the formula that Brian Tung gives to find the 'declination of the horizon' for any given RA...
  
  tan d = cot l cos a, so d = atan(cos a / tan l)
  
  where d is the required declination, l is latitude and a is the RA line we are calculating for. Treating the resulting ra and dec point as a star, just find the X, Y coordinates, and join a line from the last point on the horizon. Plotting points at each degree of ra results in a smooth horizon window curve.
• The horizon plate hours scale: A scale of 24 hours runs anti-clockwise around the circumference of the moveable horizon plate, with 0h (24h) on North. The Horizon window is symetrical about the North South line. North is the direction on this line with the smallest gap between the NCP and the horizon.

QBASIC program

The QBASIC program below produces four DXF files, three associated with the base plate and one that plots the moveable horizon window. The horizon window is the part of the planisphere that depends on the latitude - just change the value of phi to match your latitude (above 37.5 degrees).

You can download the program and the data file with star coordinates and visual magnitudes using the links below. Both files should be copied to the same directory. Load planastr.bas into QBASIC and run the file. You should see four DXF files appear in the directory.

• QBASIC program PLANASTR.BAS to make the 4 unlabelled DXF files
• Star coordinate file for the program (must be called YALE.DAT) - the data in this file is used to plot the stars on the star map.
• Constellation figure coordinates(must be called CONLINES.DAT) - the data in this file is used to plot the lines making the constellation figures on the conline.dxf file. The current file was pinched from the conline.csv file that forms part of John Walker's excellent Home Planet star chart program.

Below are examples of the three output files, rendered as GIF files by Paint Shop Pro:

• GRID.DXF: The RA and DEC grid with a scale of days in the year, part of the base plate.
• STARS.DXF: A plot of some stars in the Northern hemisphere, a second part of the base plate.
• CONLINE.DXF: A the constellation figures for the Northern hemisphere, a second part of the base plate.
• HORIZON.DXF: The horizon window [ samples: latitude 52.5 | latitude 37.5 ] with a scale of hours - this is the bit that turns around the NCP. You need to print this one onto acetate.

Contributed code

A number of people have generously contributed code or links by e-mail.

• C version of DXF program Contributed by Barberra Ande. Barberra is thinking of developing a planisphere showing the 'alignment stars' for the NextStar telescopes.

• Basic PostScript routines from Robert Lane. Robert is working in MS Excel VBA, and is completing a neater version at present. I have minimally modified the routines and added them to the end of the original QBASIC program.

• Very nice online resource signposted by the entity known as Keoeeit. Look especially at the 'download template' section - this is a CGI program that can make 'astrolabes' for any latitude or longitude. These do not appear to be classical stereographic projection astrolabes, the device looks more like an enhanced planisphere to me.

Thanks to these people for their encouragement, feedback and enthusiasm!

Checks

I checked the shape of the horizon window by printing out a copy the same size as my Phillips 5 inch planisphere for 51.5 degrees north and comparing the shape of the horizon window with a tracing of the window from the Phillips planisphere. The two matched in shape to a satisfyingly good degree. I then made a working planisphere using two printouts with the horizon window cut out with a scalpel and the days and hours scales added by hand. The resulting star view matches that in the commercial planisphere well.

Following a suggestion from Robert Lane, it turns out that the horizon window and ecliptic curves may well be ellipses - and this will make plotting them much easier (and the DXF files smaller). More on this soon - but I checked the horizon window by folding the window along the N-S axis and along the E-W axis with promising results. I then superimposed an ellipse in CorelDRAW and, by trial and error, managed to produce a curve that matched the horizon curve very closely...

Another reality check is to remember that the North horizon has a declination equal to 90 - latitude, and the Southern horizon has a declination equal to -(90 - latitude), so you can check two points on the horizon directly.

[ Root ]

Last Modified 2nd December 2000
Keith Burnett