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For a scientific work for school I decided to measure the gravity constant with the Cavendish experiment.

I set up a structure like the one suggested on this website: http://www.school-for-champions.com/science/gravitation_cavendish_experiment.htm

I actually know there will be some inaccuracy, because I did not build a case for the experiment. It is standing in the basement of a house so vibrations have nearly no influence. The small masses are wrapped lead sheets, that weigh each about 120 g. The bigger masses are weighing 2 kg.

Today I measured all the needed values ($L, \theta, R_e, M$, like described on the site; $T$ was only measured quite inaccurate yet[+-50 secs possible])

My values are: $L=0.23 m, \theta = 7.44° = 0.13 rad, R_e = 0.09m, M=2kg, T=100s\pm50s$

But when inserting this into the equation I get an inaccuracy of 1000 to 10000 (depending on values for $T$):

$$G=\frac{2*\pi^2*L*\theta*R_e^2}{T^2*M}=2.4*10^{-7}$$

Where does this huge inaccuracy come from or how can I make the experiment more accurate (20% accuracy would be the best)?

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  • $\begingroup$ What is the propagated error on $G$? I guess it is pretty large, too, so your "huge inaccuracy" is really from the error on your measured values. $\endgroup$
    – ACuriousMind ♦
    Commented Oct 3, 2015 at 18:53
  • $\begingroup$ It is quite obvious that there is some error in the measured values, but even if I adjust them a bit in terms of correct measure errors I dont come near the $6*10^{-11}$. $\endgroup$
    – BlobbyBob
    Commented Oct 3, 2015 at 19:00
  • $\begingroup$ Newton's constant is the least well measure fundamental constant. This is simply a hard measurement. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Oct 3, 2015 at 19:01
  • $\begingroup$ That said your uncertainty on $T$ is killing you. Because of the square it leads to 100% relative uncertainty on the result (applying the usual rule for small errors way out side their realm of applicability). $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Oct 3, 2015 at 19:04
  • $\begingroup$ @dmckee - "This is simply a hard measurement" true. But four orders of magnitude error is a lot. Not explained by a 50% error in T. $\endgroup$
    – Floris
    Commented Oct 3, 2015 at 19:04

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The displacement of 7.44° is clearly wrong. It is inconceivable that a torsion pendulum with a period of around 50 - 100 seconds could be displaced by such a large amount through the attraction of a couple of 2 kg masses.

I have to conclude that other factors (air currents?), not gravity, were the cause of the displacement you observed. You really need to build a box, and be much more patient in your measurement. You should observe many oscillations of the pendulum in order to determine both the very small displacement, and the period of oscillation. Since the result scales with $T^2$, a 10 % error in $T$ results in a 20% error in $G$...

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  • $\begingroup$ Another, obvious, possibility is that in moving one or both of the large spheres into place a static charge is being induced, which will overshadow the gravitational effects. $\endgroup$
    – WhatRoughBeast
    Commented Oct 4, 2015 at 2:29
  • $\begingroup$ @WhatRoughBeast quite possible. It is a hard experiment. Looking at the motion over time will show if there is drift (charge would leak, air currents would settle) or a constant offset. Only the latter can be gravitational. $\endgroup$
    – Floris
    Commented Oct 4, 2015 at 2:30
  • $\begingroup$ Air currents don't necessarily settle. $\endgroup$
    – WhatRoughBeast
    Commented Oct 4, 2015 at 3:37
  • $\begingroup$ @Floris Because I'm only on weekends in the house where I built up this experiment the pendulum had 5 days to stop rotating. After putting the large spheres in place I waited about 90 mins before measured. Is this enough or should I wait much longer? $\endgroup$
    – BlobbyBob
    Commented Oct 4, 2015 at 5:07
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    $\begingroup$ @BlobbyBob there are many possible sources of drift in an experiment like this - including the torsion wire itself which can "unwind". It is imperative that you eliminate air currents and effects of static electricity, and that you observe the drift in the setup over many cycles - preferably automatically. A web cam looking at the reflection of a laser pointer produces an image that can be trivially analyzed to give you the deflection curve over many days. $\endgroup$
    – Floris
    Commented Oct 4, 2015 at 13:35
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Well, there are strong sources of error from the surrounding masses: furniture, walls, peoples around. To reduce them, you should ensure that everything has rectangular symmetry with respct to the two axis of the experiment up to a distance of few metres from the pendulum, and remove/symetrise large masses beyond that distance up to twice that distance.

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  • $\begingroup$ Try to rotate the pendulum. If the sources of errors are in the unsymmetrised surrounding masses, the result of the measurement should change considerably. $\endgroup$
    – Gherardo
    Commented Jan 4, 2018 at 11:43

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