Physics for Flerfs 4, "Motion Under the Action of Gravity"

By the time of Newton it was already known that the planets revolve around the sun, with measurements, and it was possible to predict where they would be in the future (flerfs just say "nuh-uh" but can't predict the location of planets, even if they are just "lights on the dome"). What Newton added was an explanation of why it works like that.

Starting with the First Law of Motion, since objects move in straight lines unless acted upon by a force, there must be a force acting on the planets, directed towards the Sun. The same is true of the Moon orbiting around the Earth. Newton tried various models for this force, the only one that could produce results consistent with observations was proportional to the masses of the two bodies and inversely proportional to the square of the distance between them. The equation for this is F = Gm₁m₂/r², where the m's are the masses of the two object, r is the distance between them, and G is measured by experiment, not predicted.

As it's always been measured to be the same, it's known as the gravitational constant and was first measured by Henry Cavendish in 1798 in an experiment that is often discussed in this group. Since gravity is a very weak force, it's necessary to use heavy weights as the two masses and eliminate air movement and vibrations. The book gives a measurement of G from 1942 as 6.673E-11 N m² / kg². That N stands for newton, the measurement of force in the metric system

(You've really made it in science if they don't just name the law after you, but also one of the variables in that law is measured in you's. This reminds me of how in Jewish sources, authors are sometimes referred to by the name of their book, rather than their own name, and a story about a professor who said that you may use the textbook on the final name, but he said the name of the author instead of the textbook, so one student got help from the author. For example, I've got a copy of "Bueche" in front of me right now, but if someone said you could consult Bueche (before 2015, when he passed away) it could be understood to mean either his textbook or the agent, settler, or even the person. I couldn't find that story, but I did find one of a student who was allowed to bring notes on a 3x5 card, and he did, only it was measured in feet rather than inches. I had a roommate in college who was allowed a single piece of paper, so he used a piece cut from a roll of paper that was intended for a computer plotter, which may have displayed less ingenuity than the friend in highschool who owned a photo enlarger and would make really tiny cheat-sheets. I'm not going to name you, even though I think the statute of limitations has run out)

Back to physics, once we have measured G, we can calculate the mass of the Earth. Without putting it on a scale in front of your eyes. The other values we need are the acceleration of falling objects and the radius of the Earth (thanks Eratosthenes).

Next is a section on how the laws of motion apply on an incline, but that's just trigonometry so I'm going to skip it.

Finally, projectile motion. This is for trajectories short enough for the curve of the Earth not to be noticeable. I suppose we should be glad that flerfs aren't trying to lob projectiles many miles and see where they land ...

For example, a baseball player (this reminds me of an exam I was one involved with in college, the had set up one of those "Physics for Poets" (in this school it was probably pre-laws and pre-MBAs, as pre-meds had to take standard science courses, and I didn't get an A in inorganic chemistry and the associated lab just to mess with the curve, that was just lagniappe) and there was a probability question involving playing cards and some students who got the wrong answers tried to blame it on that they didn't know how many cards were in a deck or suit) throws a ball, it is accelerated downward, and travels horizontally at a constant speed (these calculations will be simpler if the wind isn't blowing, and we can ignore friction from the air over the distances baseballs can be thrown, and this is why Superman should umpire rather than play) until it hits something.

So we use linear horizontal motion to compute the horizontal motion, and uniformly accelerated motion for the vertical part and can compute things such as how fast the ball is moving at any point, where it hits the ground, and how much time it takes until that happens.