Nineteen centuries elapsed between the death of Archimedes in 212 B.C. and the publication of Newton’s Principia in 1687. Given the philosophical implications of Newton’s theory, it’s interesting to speculate what might have happened had Archimedes discovered the universal nature of gravitation.
To do this, he would have had to suspect that attraction was universal, suggest an experiment to confirm this, and perform that experiment, with results validating the hypothesis. Here is information in Archimedes’ possession which might have suggested the universality of gravitation.
The main problem with this experiment for an eight year old is that one has to leave the room when it operates. That’s a big deal.
Now suppose you’re crouching down in order to move the test masses, with your centre of gravity one metre from the closer test mass, and that you weigh 65 kg. Plugging these numbers into the calculator shows that your own gravitational attraction on the nearer end of the beam is 0.000147 dynes, 1.7 times as great as that of the test mass. Your actual influence on the motion of the balance arm is less, however, since what matters is the difference in force exerted on the masses at the two ends of the balance arm. Since your centre of gravity is more distant than the test masses, the difference is less.
Let’s work it out. Assume the centres of gravity of the two masses on the balance arm are 25 cm apart, and that you’re crouching so the arm makes a 45° angle with your centre of gravity, one metre from the centre of the arm. The nearer mass is then 17.68 cm closer than the more distant one and the difference in gravitational attraction (or tidal force) on the two masses is the difference in attraction on a mass 91.16 cm distant and one 108.84 cm away. The calculator gives the attraction on the near end of the arm as 0.0001764 dynes and the far end as 0.0001238 dyne, with a difference of 0.0000527 dynes. Now recall that the force exerted by the test mass was 0.000085 dynes, only 1.6 times as large, so even taking into account the reduced tidal influence due to your greater distance, the force you exert on the balance cannot be neglected. This makes it essential to remotely monitor the experiment so your own mass doesn’t disrupt it.
In practice, air currents due to your motion and resulting from convection driven by your body’s temperature being above room temperature may exert greater forces on the balance arm than the gravitational field generated by your mass. In any case, it’s best to let the experiment evolve on its own, observed from elsewhere.
I love that write up for this:
The main problem with this experiment for an eight year old is that one has to leave the room when it operates. That’s a big deal.
It occurs to me that you could probably build a box around it with a plastic window, to isolate it from air currents.
That’s what I deserve for not rereading the page after a decade, sigh.