General > General Technical Chat
Physics Question - ma = mg
CatalinaWOW:
After following many pages of this I think I have finally realized another of the problems. It is akin to the pound mass pound force problem. Two different things with the same name. g has even more definitions for the same symbol.
Some practitioners use g to refer to gravitational acceleration at the surface of the earth. It has a formal value, traceable to the defined value of G, and can be used for many calculations that don't require corrections for centripetal acceleration, mascons and the like.
Other practitioners uses the same symbol to refer to the local corrected acceleration (somewhere on or very near the Earth) including all of the correction factors.
And still another group uses it it refer to the nominal acceleration due to the dominant local mass, the earth, moon or mars for example.
I personally assume that the first usage is intended unless context suggests otherwise. That works in the vast majority of cases, especially if you use the sub rule to check the context more carefully the more decimal places matter.
The third usage is uncomfortable to me, but made more palatable by flagging and identifying with a subscript identifying the reference mass. Something which I haven't noticed happening in this thread.
RJSV:
I vote for a lable of:
'REGIONALLY STABLE VOLITILE'
to use 'g' in a C code and defined as Volitile to C compiler.
but that's a bit snarky / infantile. Hey, some classic jokes provide a sort-of structure, for framing difficult / frustrating problems. (I'd rather that irk, over a direct, energetic encounter with gravity...Oops, I meant 'rapid deceleration (w ground).
bostonman:
While I agree that 'g' should not be called a constant, a few errors have taken place throughout this thread.
The whole topic is based around ma = mg. If this were a topic of C code and someone used 'g' as a variable, then 'g' would be known as a variable, however, it began (and continued) around ma = mg.
Somewhere along the way someone (or at least how I interpreted) needed to state that 'g' is the acceleration of gravity on Earth and 'G' is the Gravitational constant. I was a bit baffled why someone assumed the contributors of this thread were confused over g and G when we clearly separated the lower and upper case.
In any case, I feel some began reading the thread halfway and therefore felt 'g' was improperly used. Much like if I began reading halfway through about a programming thread involving 'g' as a variable, I may ask: why are you using the gravity on Earth as a variable.
I'll ask the philosophical question though: is anything really a "constant"?
If science is always polishing the apple per se, then every 'constant' we know will change. Pi is a constant, but it's a never ending value that hasn't been fully carried out (nor may never). G is the gravitational constant, however, it must have some error margin.
If all these numbers are constantly being worked on to be more precise, then are they truly constants? By saying (little) 'g' is a constant may not be completely incorrect.
TimFox:
If you define g as the acceleration of gravity at the surface of the earth, where exactly on that surface is that to be measured? It is slightly different at the peak of Everest, in the city of Denver, and at whatever they are calling mean sea level now. I prefer g as a parameter measured within a region of interest where the gravitational field is uniform, whether that be on Earth or on the moon, which should be stated or made obvious in context.
The importance of g is that all objects within this region of interest experience the same value of gravitational acceleration, independent of mass. This is different from Aristotle's theory that predates Newton.
(Of course, all of this neglects air resistance, as in freshman physics discussions. When there is serious resistance, the force is proportional to velocity, and dependent on the object's shape. If you drop an object far enough through a medium, the fall approaches "terminal velocity", where the resistance force equals the gravitational force and the object stops accelerating.)
CatalinaWOW:
In a practical sense g and G are constants. By agreement of international standards bodies. While the values may change over time, in these two cases, and over human time scales these changes will be within the error bars of the existing definition, somewhat akin to computing more digits of pi.
I'll leave the philosophical questions of whether these matter on some cosmic sense, and programming style questions to others.
As always, when doing something that has real consequences it is important to thoroughly understand the problem at hand. A programmer who uses a standard constant library which includes g better not use that for a Mars lander. A student taking a test needs to understand what the teacher is asking. Don't give a spherical geometry answer in a course in Euclidean geometry unless you are willing to do a great deal of possibly unsuccessful explaining
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