I want to know

How the value of $g$ was found and what experiments did Newton conduct to land upon the value that we use, which is 9.8 m/s^2.

I tried to search for it but I couldn't find much of a satisfactory answer, actually, I couldn't any answer.

And also, to what extend have scientists found the $g$ to vary on Earth's surface i.e; how low has it dropped and how much up has it jumped as per known and calculated magnitude ? I just need to know know an estimation and where those places are. And have we seen or noticed any drastic changes around those areas ? What if Olympics or any such even was to be held there ? What if Usain Bolt was to run there ? And also, how much can Gravity affect our health ? I was also wondering can we Punch in Space (Or in a place with very low to no gravity like Moon) and can we sprain ourselves by hasty haphazard movement of limbs etc. ?

And also, how did we come to know that Earth is tilted ? On seeing any photograph of earth, it looks straight to me. I have heard how it happened (due to some collision) and we know so due to the polar ends being away from the centre. But cannot it be that it was always like that ?

And one more thing, why doesn't Newton's Laws work on subatomic level ? Or Does it ? While I was studying Electricity, it was clearly mentioned that it complies with Newton's Law but it didn't seemed to be the case and when I consulted many people including teachers and students, I got mixed answers. Some said it does work but that the particles or so minutely small that all the force exerted becomes close to negligible and another one that I got was that it simply doesn't work at that small of a scale since those are fundamental or elementary particles.

While both of them seem good and true, the force cannot be negligible because then the electrical and other such forces should also be nullified (or it could be that when they sum up for a big particle, a big chunk, they become more identifiable and visible and less negligible (and so the electrical force must be the same or alike, that is that they should also act more prominently when occurring in greater amount (seems as if this is the case, but not sure)) and in case if it doesn't work at that level, then it shouldn't occur in bigger matters too because those small particles constitute up to being a big thing, I think.
I was about to say something else too but I can't recall right now because I was too delved in writing all that, but that is okay.

I am very much interested in knowing derivation of things (scientific, mostly) because it makes things easy for me to not only understand but to have it in head in a way that I could rephrase it instantly without much effort.

Please don't consider this to be a bogus, stupid and stubborn question like many other people around me do.

And also, please don't mark this as 'unclear' because I think I have explained in a simple and a neat way but if not, I will try to rephrase it (with letting this whole thing still being intact).

Additional Notes And Questions :-

Why do we say 'Per Second Square(d)' when that means 1 second only ? (Square of one second with always be one second, I think)

Is there or can there possibly be (I do think so) any relation between the square of value of pi to one decimal place and the value of speed of gravity (both are 9.8) ?

  • 1
    $\begingroup$ You may find this wiki article helpful: en.wikipedia.org/wiki/… $\endgroup$
    – Tim D
    Mar 12, 2016 at 23:53
  • 2
    $\begingroup$ Newton didn't know the value and didn't do the experiments to measure it. $\endgroup$ Mar 13, 2016 at 0:03
  • $\begingroup$ Thanks for the link Tim ! And I checked it dmckee, you are right, he did not, apparently. $\endgroup$
    – Raj
    Mar 13, 2016 at 2:12
  • $\begingroup$ When you have multiple questions you can ask each question in a separate post. $\endgroup$
    – Timaeus
    Mar 13, 2016 at 2:44
  • 1
    $\begingroup$ There are quite a lot of different questions here and it is difficult to decide what you are actually trying to ask. Please ask a single, focused question. $\endgroup$
    – ACuriousMind
    Mar 13, 2016 at 11:05

1 Answer 1


Considering only a two-body system of Earth-Ball where the mass of earth is given by M and the mass of Ball is given by m, using Newton's theory of gravity, F=GMm/r^2, try to find the gravitational force between two objects when Ball is simply sitting on Earth, e.g. the distance between two centers of masses is simply the radius of the Earth.

Then, try to find the weight of Ball as you normally do for any object in the gravitational field of Earth meaning (W=mg).

By definition, now you can set these two expressions equal to each other because weight is the force due to gravity between an object and Earth. From this equality, isolate the gravitational field of Earth near its surface, g.

It is only then that you will realize that this g has nothing to do with any mass whose weight is being meausred near the surface of the Earth.

Regarding your last question, please refer to the definition of acceleration in classical mechanics (kinematics) which says that acceleration is the rate of change of velocity. Now, knowing that velocity is the rate of change of displacement, you can see why there are two factors of seconds in the denominator. Always try dimensional analysis if you cannot memorize equations; you can at least get a sense of the relations up to some unitless prefactors. And the reason that g is nearly Pi^2 is 100% coincidence.

  • $\begingroup$ Your explanation is good Benjamin ! But there are many other simple and basic factors that bothers me. Apparently, there aren't just two objects but considering such a case, I still don't see an answer to my Actual Question, which was about Derivation Of 'g'. Even when I go for F = ma, I need to acceleration due to gravity which is g, which I want to know more about, as in how the value of it was found. Or do we just assume it to be 9.8 ? I am sorry if I misinterpreted your statement. And yes, I do understand it. It has speed or velocity of the moving object and g acting on it too. $\endgroup$
    – Raj
    Mar 13, 2016 at 2:08
  • $\begingroup$ The value of $g$, approximately $9.8 \,\,ms^{-2}$, can be derived from the statement of Newton's law, $mg = \frac{GmM_e}{r^2}$. $\endgroup$ Mar 13, 2016 at 2:52
  • $\begingroup$ Yes, I do see it and I did a little more research on it as in how 'G' was derived and surprisingly the device used was the same device used by Coulomb too ! Now it makes me wonder what G is ? And if it is constant, is it really constant throughout the universe and how was that derived was not mentioned in the article. I can figure out the formula or the expression for it but that is not what I am after. $\endgroup$
    – Raj
    Mar 13, 2016 at 3:34
  • $\begingroup$ There are current frontier research studying the hypothesis of G being constant both in small scales as well as large scales. I would like to keep silent and wait experts to speak and elaborate more on such topics as it is not my expertise. But, I thought that you actually meant little g which corresponds to Earth. Accept my apologize if got you wrong. $\endgroup$
    – Benjamin
    Mar 13, 2016 at 3:45
  • $\begingroup$ Benjamin, you were right. I was initially referring to 'g' but then I got concerned about 'G' too. Although I was feeling concerned internally (I was keeping it for more questions I have perhaps). User2505282's comment sparked more interest and so I asked it here. I am eagerly waiting to know the results. And recently, Gravitational Waves have been discovered and upon searching, the details I found (on what it is), I thought that I always felt that something like that always existed. I don't know why I think so, but I think many people also feel so or felt the same about it. $\endgroup$
    – Raj
    Mar 13, 2016 at 10:56

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