Do moons experience periods of no sunlight when orbiting "behind" their planet? I'm writing a story that takes place on the Saturn moon Iapetusand I was thinking that especially since Iapetus only has an inclination of about 17 degrees from the ecliptic, wouldn't there be a point during its orbital period where it orbits &quot;behind&quot; Saturn — that is to say, Saturn is directly between Iapetus and the Sun — and doesn't get any direct sunlight?
Is that correct or am I missing a detail here?
If it is true that moons like Iapetus experience these periods of no sunlight, how difficult would it be to calculate roughly how long this period would be using the inclination and the orbital period?
This is basically a repeat of Aristarchus’ experiment of trying to figure out the distance between the Earth and the Moon from a lunar eclipse. See for example https://pwg.gsfc.nasa.gov/stargaze/Shipprc2.htm
So, we know that Iapetus orbits Saturn in 79.3215 days, at an average distance of 3,560,820 km. Saturn’s diameter is 116,464 km, and it orbits the Sun at an average distance of 1,433,530,000 km. The Sun’s diameter is 1,392,684 km.
Using this data, you can now use the formulas given on Wikipedia https://en.wikipedia.org/wiki/On_the_Sizes_and_Distances_(Aristarchus)#Lunar_eclipse to calculate the size of Saturn’s shadow at Iapetus’s distance. Knowing how long Iapetus spends in it is then only a matter of dividing the size of Saturn’s shadow by the circumference of its orbit, then multiplying by Iapetus’s orbital period.
I’ll let you do the math. We’re here to help find the answers, not give all the answers. ;-)