Finding The Gravitational Constant “big G”

The value of the fundamental constant G has been of great interest for physicists for over 300 years and it has the longest history of

measurements after the speed of light. In spite of the central importance of the universal gravitational constant, it is the least

well defined of all the fundamental constants.

Henry Cavendish (1731-1810)

• Henry Cavendish set about to “weigh the earth”

• In order for him to accomplish this Cavendish needed to first find “big G”

• Rev. John Michell helped Cavendish devise an experiment using torsion balance to detect the tiny gravitational attraction between metal spheres

Inside the Gravitation Torsion Balance Housing

• Torsion Fiber• Concave mirror• Dumbbell-shaped

pendulum body, consisting of 2 lead balls on metal rod

Method For Analyzing Gravitational Interactions

• Shine a laser beam at the mirror, reflecting onto a screen.

• The location of the laser spot on the screen allows us to determine the twist of the dumbbell.

• By placing the screen at a reasonable distance away, we can detect even a small twist.

Obtaining Equilibrium position at start

• The big lead spheres are placed next to the smaller lead spheres.

• The gravitational force attracts the smaller lead spheres causing the balance arm to twist, thus shifting the laser beam to one side

• Eventually the torque of the gravitational force come to equilibrium with the torque fiber

Obtaining the New Equilibrium

• The big lead balls are then switched to the other side where a new equilibrium is obtained

• The measurements for 3 periods of oscillation takes about 30 minutes

• This prompts the use of averaging the equilibrium positions and using the period of oscillation in the calculation of big G

Computing the Gravitational constant

• The equation f =(pi2*b2*d*S)/(m1*T2*L)

• b is the distance between the center point of large ball (when touching housing) and the small ball (in equilibrium position) = 0.047mm

• d is the distance between ball center point and axis of rotation = 0.05m

• S is is the difference between light pointer position for initial and final pendulum equilibrium states = x00 - x0

• m1 is the mass of the large lead ball =1.5kg

• T is the oscillation period

• L is the distance between the mirror and to the scale on wall

Our measurements

• For Run 1

• L = 5.7

• T = 658.3s

• xo =0

• x00 =22.46

• f = 6.48 E-11 m

• For Run 2

• L = 5.721m

• T = 631 s

• x0 = set to 0

• x00 = 20.3cm

• f = 6.75E -11

The First Runtime (s) displacement (cm) xeq to 20 sec

0 0.0 320 3.040 6.260 9.580 13.1

345 32.1765 11.0

1020 31.2860 20.1

1006 26.0880 21.4900 22.8920 23.8

1080 23.21100 22.01120 20.81140 18.91160 17.51180 16.01200 15.61220 13.81240 12.61260 12.0 13.152651280 11.3

Position

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Series1

Second run

time (s) displacement (cm)0 0

20 0.740 2.260 4.480 6.6

100 9.7120 12.1140 16.1160 22.4180 25.6200 28.3220 31240 33.1260 34.7280 36300 36.7320 36.6340 36.4360 35.4380 33.9400 32.3420 30440 27.7460 25.3 distance to x00 = 20.31188

Position

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0 500 1000 1500 2000 2500

Displacement (cm)

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