Dance of the Planets appears to be written in Borland Pascal 7. While it worked well on my 486 66MHz DX2 PC, when I upgraded to a 400MHz Pentium II processor, it failed to run returning a Runtime error 200 at 0C7E:0091 message. Luckily this error is a well-known 'feature' of Borland Pascal 7 and work-arounds are possible.
ARC Science Simulations now has a patch with detailed instructions for applying it located at http://www.arcscience.com/downloads/DanceInstructions.doc or http://www.arcscience.com/downloads/DanceInstructions.txt