The Law of Universal Gravitation
(SU ch. 6, OM ch. 4)
By Henry Cavendish - Cavendish,H.(1798), 'Experiments to determine the Density of the Earth' in McKenzie, A.S. ed. Scientific Memoirs Vol.9: The Laws of Gravitation, American Book Co. 1900, p.62 on Google Books., Public Domain, Wikimedia Commons
DAY 1: The Law of Universal Gravitation
From "beginning of chapter" to "...6 septillion kilograms."
Mr. Fleisher does not give the value of the gravitational constant. It is a pretty intimidating number, but I have included it here for those who might be curious. Just note how small it is: 10^-11. That is why we only seem to see the effects of the Law of Universal Gravitation between really big objects.
Gravitational Constant, Wikipedia
DAY 2: The Law of Universal Gravitation
From "In the Principia..." to "...of mass in either place."
The take-away is to not confuse weight and mass.
There is an interesting change in the newer edition of the book because of its being written for a British audience. OM p. 47 states, "If you weigh 45 kilograms on the Earth, you will weigh only about 8 kilograms on the Moon." In SI units, and when dealing with science, kilograms is the unit for mass (which does not change) and not for weight (which, depending on your location, as we will see below, can change). Mr. Fleisher correctly states in the last sentence of this paragraph, "However, your body still has the same amount of mass in either place."
A common confusion between weight and mass has been introduced here. Weight is our force due to gravity determined by Newton's second law: F=ma. In this case, F = weight (measured in pounds (english) or newtons (metric)); m = mass (measured in slugs (english) or kilograms (metric); and a = acceleration due to gravity which is dependent on our location. Often, when we are talking about acceleration due to gravity, the symbol g is used. Here is another version of Newton's second law, which, although it is identical to F=ma, is often seen when speaking about weight.
Since g is dependent on our location, our weight changes as we move. Your weight will be different if you are at sea level than when you are standing on top of Mt. Everest because g is actually smaller on Mt. Everest. Weight will also be different on the moon as g is even smaller there.
Sea level: g = 9.81 m/s^2
Mt. Everest: g = 9.77 m/s^2
Moon: g = 1.62 m/s^2
Mass or m, which we learned about when we studied Archimede's Principle, does not change. It is a measure of how much stuff is in an object, and the amount of stuff in an object doesn't change as one moves to different locations.
For Americans, it would have been better for Mr. Fleisher to have left what was in the original edition (p. 51):
"If you weigh 100 pounds on Earth, you will only weigh about 18 pounds on the moon." (though is actually closer to 16 pounds)
After a lengthy conversation with a British friend today, she assured me that Brits do indeed use kilograms for weight and would never use newtons when talking about a human's weight or anything outside of a scientific setting for that matter. Therefore, it would not have made sense for Mr. Fleisher to write:
"If you weigh 450 newtons on Earth, you will only weigh about 75 newtons on the moon."
DAY 3: The Law of Universal Gravitation
From "When he wrote the Principia..." to "end of chapter"