So I am building a tidally locked world, but I want the shadow zone to vary a bit. One way to achieve this is through axial tilt. A planet with orbital period = day period, so tidally locked and 0 degree axial tilt will have the same area illuminated at all times. But a planet with the same parameters and say, 22.5 degrees axial tilt will have the shadow zone move by 22.5 degrees from the poles in both directions every year.
If we want to introduce another type of movement we can play with the eccentricity of the orbit. Look up libration of the moon to learn more. My question is this: given the orbital parameters of any planet, how can I calculate the libration in the east/west direction?
Starting at the bottom of the elliptical orbit, east and west are illuminated equally. A point on the globe just behind the terminator, so in the dark will experience a sunrise at some point between the bottom position and the right hand position. Then a sunset between right and top. Then this point will stay in the shade until the planet is at the bottom position again, after which a new orbit beings and it will experience another sunrise. So one sunrise and one sunset per orbit. What am I missing?