(HP-67/97) Planetary Ephemeris II

[Josef]

There are not many astronomical programs for the HP-67 calculator, or they are limited by the date 31.12.1999 because in 1977, it was far in the future. Therefore, they are no longer usable today.

I decided to write my own program that simplistically calculates the positions of the planets for the selected date. I used the simplified equations because the calculator is limited to 24 memory registers and 224 program steps, which is woefully short and would require about 70 registers and, ideally, 800 program steps for more accurate calculations.

The program first calculates Julian date and the number of days since 1.1.2010 (the chosen epoch). It then calculates the heliocentric longitude of the planet being calculated and then the Earth. Then it calculates the geocentric latitude of the planet. The formula is different for inner planets (Mercury and Venus) and different for outer planets. Finally, it calculates RA and DEC. I split the program into two because the calculations would fit into 260 steps, which the calculator does not have. I also did some optimizations, but still the calculations didn't fit in 224 steps. Due to the small number of registers, only the positions of two planets can be calculated at a time. Thus, there are two programs and 4 data sets that are loaded into the calculator (Mercury-Venus, Mars-Jupiter, Saturn-Uranus, Neptune-Pluto). Although Pluto is no longer in the planets, I left it in. I have also attached a complete annotated listing of the program and a listing of the registries.

Program Instructions.
1. Upload the data for the selected set of planets and program for the inner or outer planets, e.g. specifically the Mercury-Venus data and the program labelled Inner, or the Mars-Jupiter data and the program labelled Outer.
2. Enter the date by typing the day and pressing A, then the month and pressing B, and finally the year by pressing C. Once entered, the number of days elapsed since the epoch will appear (the past is marked with a - sign).
3. pressing f and then A. The RA coordinates appear on the display in the format HH.MM (h,m).
4. R/S and the display shows the coordinates DEC again in the format DD.MM (°,').
5. After pressing R/S, we can select the second planet by pressing f and then B.

Below are the calculated positions of the planets to compare the accuracy of the calculations and the accuracy of the calculator.

For calculations, you can use any emulator for Mac OSX, e.g. LXVII or for iPad RPN-67 NP. This is what the LXVII program looks like.