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Physics Question - ma = mg
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CatalinaWOW:

--- Quote from: bostonman on June 28, 2021, 01:15:21 pm ---Without getting too deep with math, or an explanation, how do we know an object has X kg of mass, and gravity (rounding off) is 9.8m/s^2 based on the beginning of time?

We know a 100kg mass is 100kg, but that's based off 9.8m/s^2, but gravity is derived from a Force, and the Force is derived from a known mass and gravity.

If we went back hundreds of years (or a twenty-six-hundred year journey as with TBBT - and I'm not trying to be funny), scientists needed a known gravity to calculate mass; or a known mass to calculate gravity.

I'm sure the math has been worked out several times over hundreds of years, but it seems because each factor is derived from the other, any one can be wrong throwing off the other.

Same with calculating the mass of planets. I believe it's done by looking at how gravity pulls on surrounding stars (?) and thus mass is calculated, however, we needed to start off with the mass of one planet which would be Earth (I should say I assume we started with Earth). If we got the mass of Earth wrong based off using a mass we thought was X kg, then everything derived since is wrong.

--- End quote ---

While you are sort of conceptually correct, there are literally hundreds of different observations that have to be reconciled and they all converge to the answer we use today.  Including even direct measurements of the gravitational attraction between spheres in a laboratory.  Some truly elegant experimental work to sort out all of the forces and get the precision required.  The problem you are describing is one of the things physicists since Kepler have worked on, even in the last few decades.  Polishing the apple so to speak and adding decimal places to the g constant.
bostonman:
I assumed (to use your term) we've been polishing the apple for years.

At my level, and the level of many on here, I imagine it doesn't make much difference if we use 9.81 or 9.80999, or if a 100kg mass is really 100.00001kg.

It still amazes me that hundreds/thousands of years ago, all these "constants" were discovered without computers, calculators, and just a pencil and paper. If I'm not wrong, many constants were quite close to what we have now.
TimFox:
With respect to the mass of planets, Cavendish is credited with "weighing the earth" in 1797 to 1798.
The modern interpretation of his work was to calculate the gravitational constant G by directly measuring the force between two objects in the laboratory, using a torsion balance.  See https://en.wikipedia.org/wiki/Cavendish_experiment
Once G is known, the mass of the earth follows from inserting g (measured at the surface of the earth) and R (radius of the earth, originally calculated by the ancients) into the gravitational force equation.
Orbital mechanics is another interesting field.  When calculating other masses in the Solar System, one needs the dimensions of the orbits.  Early astronomers were able to calculate orbital dimensions in terms of the "astronomical unit" (a.u.), the mean radius of the Earth's orbit, but a precise value for the a.u. waited until radar ranging of the actual distance between the Earth and Venus around 1964.   Since the Sun is continuously losing mass, the a.u. changes slowly with time.
David Hess:

--- Quote from: bostonman on June 28, 2021, 03:01:14 am ---Little 'g' being a constant in the sense that it's understood we are talking about gravity on Earth. Now 9.8m/s^2 is a general rule for physics 101, but, if I dug a five-mile deep hole, gravity would be less because it becomes negligible (???) at the center of Earth. Also, if I stood on a five-mile high mountain, it would be less because I'm further from the surface of Earth.

This means that to argue gravity on Earth is 9.8m/s^2 would be wrong because it can change depending on your height on Earth. Unfortunately, little 'g' can also mean gravity on Mars (or anywhere in the universe) because if I want to know my Weight on mars, I need to use W=mg. To call little 'g' a constant would be wrong, but, I hate to critique TBBT, but I think saying ma = mg is taken out of context.
--- End quote ---

Commercial load cells are good enough that the variation of surface gravity on Earth is a measurable error term in calibration.
TimFox:
Also, inertial navigation systems for guided missiles need to correct for local variations in the gravitational field due to geological effects.
Notes: 
1.  Please stop calling g a physical constant, in the sense that G (universal gravitational constant) is a constant.  Within a limited region where the change in distance to the center of gravity is negligible, g has a constant value (uniform gravitational field), but it changes by a large amount when you go to the moon, and by a small amount when you ascent to the top of Everest.
2.  You do not need to know the mass to determine g, use a pendulum.
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