## Home Experiment: Deriving the Gravitational Constant

Posted on April 12, 2009  Comments (2)

Deriving the Gravitational Constant by Joe Marshall

In the summer of 1985 I was at home convalescing and being bored. It occurred to me one day that if Cavendish could determine the gravitational constant back in 1798, I ought to be able to do something similar

Cavendish cast a pair of 1.61 pound lead weights. I found a couple of 2-pound lead cylinders my dad had lying around. I used duct tape to attach them to a 3-foot wooden dowel. Cavendish used a wire to suspend the balance, I used nylon monofilament. To determine the torsion of the fiber, you wait until the balance stops moving (a day or two) and then you slightly perturb it. The balance will slowly oscillate back and forth. The restoring force is calculated from the period of oscillation. Cavendish had a 7-minute period. My balance had a 40 minute period (nylon is nowhere near as stiff as wire).

Cavendish used a pair of 350 pound lead balls to attract the ends of the balance from about 9 inches away. I put a couple of 8 pound jugs of water about an inch away. The next trick was to measure the rotation of the balance. Cavendish had a small telescope to read the Vernier scale on the balance. I used some modern technology. I borrowed a laser from Tom Knight (Thanks again!), and bounced it off a mirror that I mounted on the middle of the balance. This made a small red dot on the wall about 20 feet away. (I was hoping this would be enough to measure the displacement, but I was considering an interferometer if necessary.)

To my surprise, it all worked. After carefully putting the jugs of water in place, the dot on the wall started to visibly move. Within a few minutes, it had moved an inch or two. I carefully removed the jugs of water and sure enough, the dot on the wall drifted back to its starting position.

Very cool example of a home physics experiment.

2 Responses to “Home Experiment: Deriving the Gravitational Constant”

1. Bernd Jendrissek
January 21st, 2010 @ 5:53 pm

Excellent! I’ve been wondering myself if I could replicate Cavendish’s experiment, but everytime I ran the numbers I concluded it’d be disappointing. Maybe my estimates for the restoring force were wrong – probably, hopefully!

Are you able to exclude effects such as the jugs of water flexing the floor and that it is this causing the deflection of the laser dot instead of gravitational attraction? Also, if you’re worried about the floor / other setup “remembering” that you walked around while reconfiguring the water distribution, you could use a hosepipe to fill the jugs. Oh well, I suppose your goal was detection more than precision!

I think I need to try this next rainy weekend.

2. lin lee
March 30th, 2010 @ 1:04 am

Is it possible G depends on c and e?
G=G’^2 c^2 e^2

G’~=1.70106×10^5
e=electron charge
c=speed of light

If search 1.70106 in google, there are a lot of coincidences.