How Can One Calculate the Gravitational Constant G by Combining Two Formulas?

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Discussion Overview

The discussion revolves around the calculation of the gravitational constant G by combining two formulas related to gravitational force and acceleration. Participants explore the implications of standing on the Earth's surface versus falling, and how these conditions affect the calculation of G. The scope includes theoretical reasoning and mathematical derivations.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Some participants propose that G can be calculated using the formulas Fg = G x (m1 x m2 / r^2) and Fz = m1 x g, particularly when standing on the Earth's surface.
  • Others argue that when standing still, the distance traveled (s) is zero, leading to complications in calculating G, as it results in a 0/0 scenario.
  • A later reply questions the assumption that acceleration is zero when standing still, clarifying that the net force acting on a person is zero due to the balance of forces, not that acceleration itself is zero.
  • Some participants emphasize the need to measure g through free-fall conditions rather than standing still, suggesting that the gravitational force formula applies primarily to falling objects.
  • There is a discussion about the relationship between acceleration and gravitational force, with some participants attempting to derive G from various forms of the equations.

Areas of Agreement / Disagreement

Participants express disagreement regarding the implications of standing still versus falling in relation to calculating G. There is no consensus on the correct interpretation of the formulas or the conditions under which G can be accurately calculated.

Contextual Notes

Limitations include unresolved assumptions about the conditions of measurement, the definitions of acceleration in different contexts, and the implications of using zero distance or time in calculations.

  • #31
it is not about measuring g
 
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  • #32
The first words of the thread are about calculating G with a formula containing g. How can you calculate it from g if you don't measure g at some stage? (I now see this has been mentioned at least once before).

Calculating G from g (and other things) is surely just a rearrangement of some formulae. Most of the arguments here seem to involve pulling yourself up by your own bootstraps. You can't do anything without measuring some mass, some forces, some times and some distances, in one form or another. You takes your pick as to which ones and how.
 
  • #33
Siebevp said:
to calculate g you ofcourse need the equation g=GM/r^2,

but every time on one side of the equation there is just one variable of time.
I don't know where you are getting that idea. The only variables are g, G, M, and r. There is no variable of time which would usually be denoted by the variable t.

The rest of your post seems to confuse a dimensional analysis of an equation with the variables of the equation.
 

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