Equations for the first exam:
Motion:
Kepler's laws: 1) all orbits are ellipses with the Sun at one focus.
2) Orbits sweep out equal area in equal time.
(Within a given orbit, the planet slows down as it gets farther from the Sun.)
3) P² = a³
(P is the time the planet takes to complete an orbit, and a is the semimajor axis of the orbit. This formula means that the large orbits take a very long time to get around, so the planets on large orbits must be moving more slowly.)

Newton's laws:
A=F/m
(A is acceleration, F is total force, usually gravity, and m is the mass of the object that is accelerating.)
force of gravity F = GMm/d² (where G is a constant that is of no consequence to our purposes, M is one of the masses, m is the other mass, and d is the distance between the centers of the two masses involved in the action/reaction pair force of gravity we are talking about)

Rules of light:
Thermal emission depends only on temperature T, and the total rate that energy is emitted into light (also called "radiation") is proportional to T⁴. The average energy per photon, which is also the average frequency of the light waves, is proportional to T. For T=6000 K like the surface of the Sun, this means the average frequency is visible light. For T=300 K, like in this room, the average frequence is infrared.

Spectral lines:
Atoms absorb and emit light only at the special energies where a photon can have a frequency (equal to the photon energy divided by Planck's constant h) that "resonates" (experiences constructive interference, like the note on a guitar string) inside the atom. This is different energies for different types of atoms, so the "lines" they absorb and emit provide a signature of the type of atom. That's how we know the Sun is mostly hydrogen with about 25% helium by mass.

Wave mechanics:
Waves are governed by interference, and they appear to in some sense "tell the photons where to go." Interference can produce refraction and reflection, both useful in focusing light and creating images, and it can produce diffraction, which is a blurring of images that come through an aperture. But diffraction is not all bad, because by carefully creating tiny slits, we can control diffraction so that it sends different colors (frequencies) of light to different places, creating a "spectrum." Such careful slits are called a "diffraction grating," and they work better than prisms (which us refraction like how raindrops create rainbows) for creating spectra.