Dear Frank, I do enjoy your puzzles!!
> ... a question appeared of the form: > > "Find a day on which the sun sets (altitude 0 deg.) at > the same moment in London and Paris (positions given)." Conceptually this is trivial. Mathematically it gets a little messy but I think I can get a closed form of the solution. CONCEPT I assume that at any instant half the Earth is in sunlight and half is in darkness. A great circle separates the two halves. Any place on this great circle is experiencing the moment of (mathematical) sunset or sunrise. The solution to your problem is to draw a great circle from London to Paris and extend it until it reaches the Equator. The angle this great circle makes to the plane of the Equator is the complement of the solar declination (subject to a minus sign). MATHEMATICS Let t1 = tangent of the latitude of place 1 Let t2 = tangent of the latitude of place 2 Let d = their difference in longitude We then have: tan(dec) = -sin(d)/sqrt(t1^2 - 2.t1.t2.cos(d) + t2^2) Where dec is the required solar declination. EXAMPLE You cite London and Paris. I take the latitudes as being 51 deg 30' and 48 deg 52' and the difference in longitude as being 2 deg 23'. This gives the solar declination as -18.7 degrees. I expect I have goofed. Some bright youngster can now tidy up my efforts!!! Best wishes Frank King Cambridge, U.K. --------------------------------------------------- https://lists.uni-koeln.de/mailman/listinfo/sundial
