Is there an approximate way to calculate the distance to the Moon for any given day?

Well let me give you a very approximate formula based on the July-August orbit. The distance to the Moon is given by D = 6378/sin(theta) where at 5 day intervals:

Day.....Theta(arc minutes).....distance(km)  
July 1     61                    359460
July 5     59.9                  366000
July 10    55.9                  392200
July 15    54.0                  406000
July 20    54.6                  401590
July 25    57.9                  378700           
July 30    61.4                  357100
Aug   4    58.5                  374800
Aug   9    54.7                  400800
Aug  14    54.0                  406000
Aug  18    55.2                  397200
Aug  23    58.5                  374800
Aug  28    61.1                  358800
........................................

Example: on July 20, 1996 Theta = 54.6' = 0.91 degrees. sin(0.91) = 0.0159 and so D = 401590 km or 257,018 miles. Since the orbit is a periodic function with a period of 29 days, you should be able to create a simple periodic function of the form:

D = A + B cos( 360*(T/29) )
where T is the number of days since one of the days in the above table. A bit of trial and error will get you a solution for A and B when you plot the distance and dates above.
Copyright 1997 Dr. Sten Odenwald
Return to Ask the Astronomer.