Quote:
Originally Posted by a humble lich
The perpendicular component of each moon's displacement is given by x= A cos(2 pi t/T +phi). We could solve for where those all intersect, but that will get messy because you have to define how close they need to get to count as an intersection. Simpler, just look at the function x=cos(2 pi t/T_1) + cos(2 pi t/T_2) + cos(2 pi t/T_3). When this function approaches 3, then all three moons are aligned behind the planet. We will ignore the phases because they hold the information of when the next full moon will occur and we are only interested in the frequency of full moons.
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It's been a long time since I've had to graph trigonometric functions, and I'm a little unfamiliar with your notation. I'd greatly appreciate a bit more in-depth explanation of your variables. I'd love to be able to calculate this kind of thing myself in the future.
Jinumon