# Intro - The Moon's Phases When you stare up at the night sky, chances are that you've taken a good luck at the moon. After all, it's the brightest object in the night sky, so it's difficult to miss. If you give the moon around 27 days, you'll notice that the percentage of the moon's surface that's actually illuminated changes. We call this phenomenon a *phase*, and for the moon, we've actually got names for these! %%moon phase diagram%% Today, we'll be diving deeper into the maths behind these 'phases' and finding the **exact percentages** of the illuminated surfaces relative to us. Excited yet? # Types of Orbits and Phases ![[Pasted image 20240330235808.png]] ## Superior Orbits Superior orbits are orbits higher than that of our Earth (or any other body), such as those of Mars, Jupiter and Saturn. ![[Pasted image 20240331002504.png]] However, it's impossible to assign each point in a planet's orbit a 'phase name', given that they move around the sun at different speeds. Therefore, we've just taken 4 important points that serve as reference points for our orbits. ![[Pasted image 20240331004230.png]] For some reason, the cardinal directions are all opposite when it comes to the ## Inferior Orbits # A Case Study - The Moon's Phases When it comes to the moon, we've just got to calculate it's phase angle by taking its period and its radius. Most of the time, this data's also given, so it's not too much of a hassle! Before we hop straight into defining this, let's start with defining some angles! ![[Pasted image 20240331001754.png]] For our purposes, we define $\phi$ as the *angle of displacement along the orbit.* Once we get that, we just have to substitute the angle into $\frac{1+\cos\phi}{2}$ to get our answer! >[!Example]- Problem Taster - # Eclipses Solar eclipses. Some of the most beautiful things to occur - especially when totality hits! Unfortunately, Hong Kong's been struck with the terrible blow of having clouds. Lots and lots of them. Seems like every time the old telescope's out of the 'garage' (my living room), there's always a thick layer of cumulostratus clouds blocking the view up above. For an eclipse to occur, there's a set of very, *very* specific conditions we've got to match. For starters, the two objects have to be at the right distance to "overlap" relative to a distant light source - just imagine a sun further out from the top right corner of the diagram below: ![[Pasted image 20240331001347.png]] This diagram is a representation of the **maximum possible angle for an eclipse to occur**, *i*.