I'm currently working on doing the cavendish experiment to determine G and I'm done with most derivations so have reached the point of corrections. One of the major corrections I have to make has to do with the gravitational force supplied by the other mass. Image for clarification: enter image description here

Where $F_g$ is the main force working on the smaller masses, $F'_g$ is probably quite significant (I'm estimating aproximately 5%) so I'd like to calculate $F'_{g,||}$ but have yet been unable to derive a formula for it. Is anyone here able to help?


1 Answer 1


The distance $D$ between the left smaller mass and the right larger mass is given by Pythagoras:


Thus for $F_g'$ we get:



$$F'_{g,||}=F_g'\sin \theta,$$





Because $F_g=G\frac{mM}{d^2}$ we can even determine $\frac{F'_{g,||}}{F_g}$:



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