Finding The Gravitational Constant big G The value

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 =(pi 2*b 2*d*S)/(m 1*T 2*L) • b is the distance between the center point of large ball (when touching housing) and the small ball (in equilibrium position) = 0. 047 mm • d is the distance between ball center point and axis of rotation = 0. 05 m • S is is the difference between light pointer position for initial and final pendulum equilibrium states = x 00 - x 0 • m 1 is the mass of the large lead ball =1. 5 kg • 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. 3 s xo =0 x 00 =22. 46 f = 6. 48 E-11 m For Run 2 L = 5. 721 m T = 631 s x 0 = set to 0 x 00 = 20. 3 cm f = 6. 75 E -11

The First Run

Second run