Without any a priori knowledge of the mass, speed, distance, and size of local celestial bodies (aside from Earth's size), what can I calculate and how from my "backyard" through observation?
Edit:
My goal is to create a high-school level physics project that students can conduct over the course of a year/term as both a physics problem mixed with a bit of astrophysics history. Core concepts would include observation (within reason). This isn't meant to be extremely precise work (within an order of magnitude would be excellent), but to demonstrate the methods.
Given a bunch of knowns, it's trivial to find out one unknown, but I am unsure of how to start from square one like the early physicists and astronomers did in times past.
Best Answer
calculate the size of the earth e.g. through vertical sticks (what Erathostenes did) (or just assume it, this requires travelling)
measure the acceleration of gravity at the earth's surface and calculate the earth's mass (this is cheating by assuming newton's law of gravity, which was developed astronomically)
assume the moon's mass is small and calculate its distance from its orbital period. confirm the orbit is roughly circular by measuring the moons position at a specific time of day over 1 month (or so).
in principle the sun's distance can then be determined by measuring how much of the moon is lit on the night exactly between new and full moon, thus measuring the angles of the sun-moon-earth triangle (greeks did it, but this is probably pretty hard to get right)
sun's and moon's diameter can be determined through their viewing angle
sun's mass can be calculated through the earth's orbital period