Gravitational Charge - Equivalence between Gravitational and Inertial Mass

[neutrino]

Gravitational "Charge" - Equivalence between Gravitational and Inertial Mass

My mind is currently in a mess regarding the equivalence of gravitational mass and inertial mass. Yes, I know which comes in which equation and that they have been experimentally observed to be equal, etc., but I'm trying to understand why the gravitational 'charge' is considered a mass in the first place. Essentially, I want to know how Newton came up with the equation for the gravitational force and why the dimensions of mass is assigned to the M's in it. To find that out, I was reading this page in which I came across a (translation) statement by Newton.

In simple pendulums whose centers of oscillation are equally distant from the center of suspension, the quantities of matter are in a ratio compounded of the ratio of the weights and the squared ratio of the times of oscillation in a vacuum.

I would like to know what exactly he is referring to. There are two pendulums, but only one point of suspension?

If anyone knows the answer to my original questions, then please enlighten me, so that I can avoid reading the Principia and do something useful.

EDIT: And that's my first Golden post.

 

[Andrew Mason]

My mind is currently in a mess regarding the equivalence of gravitational mass and inertial mass. Yes, I know which comes in which equation and that they have been experimentally observed to be equal, etc., but I'm trying to understand why the gravitational 'charge' is considered a mass in the first place. Essentially, I want to know how Newton came up with the equation for the gravitational force and why the dimensions of mass is assigned to the M's in it. To find that out, I was reading this page in which I came across a (translation) statement by Newton.



I would like to know what exactly he is referring to. There are two pendulums, but only one point of suspension?

If anyone knows the answer to my original questions, then please enlighten me, so that I can avoid reading the Principia and do something useful.

The full explanation is found in the link you provided.

Newton was referring to two pendulums of equal length but with different masses. They would be suspended from the same 'axle'. [In three dimensional space (x,y,z with y being the vertical axis), the pendulums would oscillate in different z planes but with centres of suspension at the same x y position]. The pendulums are started from the same angular displacement. If there is a different in the ratio of mass to weight, the pendulums will have differing periods of oscillation. Newton tried it with different masses of all kinds of material and found the periods of the two pendulums to be identical over long times.

AM

 

[neutrino]

Ah. Much clearer. So two pendulums with same lengths suspended from the same height above the ground. Thank you very much.