I have a complicated watch face i am working on and having trouble getting the mechanics of the orbital rotation and latitudes just right.
Here is the draft watchface i am working on:
The earth orbits the sun properly, and the moon orbits the earth properly. The earth is supposed to be a replacement for the second hand, and that is working fine. The moon accurately shows the phase of the moon, and I’m happy with how that is working.
The problem is the rotation of the earth relative to the sun and the time of the day. There is a graphic for a red line that is supposed to overlay your latitude location accurately on the map, which isn’t working. Then the earth and the red line are supposed to rotate in sync with each other relative to the time of the day such that it is directly in front of the sun at noon, and directly opposite the sun at midnight, rotating counterclockwise. I can’t seem to get the rotation equations right…
If you look at this watchface that I have, it is similar in concept, except the sun and earth are stationary and not intended to orbit. Yet the earth and it’s longitudinal location properly have the latitude marked in red and rotate relative to the time of day to the sun.
Here are the current rotational equations that I am using, which are incorrect:
Where the difference between 6- & 50 is simply a constant to account for the different original earth and red line graphic differences.
Any astrophysicists or orbital mechanics engineers out there?
Thanks in advance!