You can also estimate the distance to the moon by knowing how long it takes for a lunar eclipse to occur, assuming the Sun is far away. Exercise to the reader: figure out the geometry behind this. This was done by Aristarchus in 270 BC.
The thing about the half moon measurement is that it sucks. You have cos(90° - x) for small degree x in the denominator, and so it’s close to 1⁄0, so tiny errors in the angle measurement will blow up.
Now here’s a fun one: Democritus in principle could’ve correctly estimated the size of atoms. Rayleigh did this in the 1800s, using only oil, ethanol, some flakey substance, and water. I also did this (using some graphite flakes from pencil lead), though my estimate (60 nm) was 10x bigger than his. It’s really simple: put a diluted drop on water with flakes floating in it, and there’ll be a single molecule thick layer that pushes the flakes. Eventually the oil runs out, so it makes a little circle whose radius you measure.
You can also measure the wavelength of light with some thin object whose width you can figure out, like an index card—but this requires having guessed that light should do interference. Once you guess that you can just shine some light at the object and see how far apart the diffraction pattern’s lines are. You can also see the patterns when you squint.
You can also estimate the distance to the moon by knowing how long it takes for a lunar eclipse to occur, assuming the Sun is far away. Exercise to the reader: figure out the geometry behind this. This was done by Aristarchus in 270 BC.
The thing about the half moon measurement is that it sucks. You have cos(90° - x) for small degree x in the denominator, and so it’s close to 1⁄0, so tiny errors in the angle measurement will blow up.
Now here’s a fun one: Democritus in principle could’ve correctly estimated the size of atoms. Rayleigh did this in the 1800s, using only oil, ethanol, some flakey substance, and water. I also did this (using some graphite flakes from pencil lead), though my estimate (60 nm) was 10x bigger than his. It’s really simple: put a diluted drop on water with flakes floating in it, and there’ll be a single molecule thick layer that pushes the flakes. Eventually the oil runs out, so it makes a little circle whose radius you measure.
You can also measure the wavelength of light with some thin object whose width you can figure out, like an index card—but this requires having guessed that light should do interference. Once you guess that you can just shine some light at the object and see how far apart the diffraction pattern’s lines are. You can also see the patterns when you squint.
Really cool!