Direct Measurement of Gravitational Constant G: Cavendish Experiment

1. The Cavendish Experiment A Direct Measurement of The Gravitational Constant G Advanced Lab 2, Fall 2008 Joe Mitchell Brian Reed Johnny Sharp Leah Trafford

2. The Cavendish Experiment: Outline • Motivation • The Importance of The Gravitational Constant G • History • The Cavendish Apparatus and Measurement • Apparatus • Taking Measurements • Brief Description of Forces • Method 1: Equilibrium Positions • Theory and Procedure • Analyzed Data • Method 2: Constant Acceleration • Theory and Procedure • Show analyzed data • Demo • Summary Henry Cavendish Experimental Setup

3. Motivation University of Washington Big G Measurement • G determines the strength of gravitational force between two objects • Fundamental constant of nature • G is important in astrophysics and most any calculation involving gravity • Needed to determine the mass of the Earth and other planets and stars • Measurement of G still an active field • Striving to increase accuracy • Many current experiments to investigate the behavior of G http://lheawww.gsfc.nasa.gov/~merk/G/apparatus.JPG

4. Cavendish History Cavendish’s Experimental Setup Cavendish at Work • Cavendish’s results not improved until 100 years later • Density of earth first approximated by Newton using the density of rocks • Performed in 1797-1798 by Henry Cavendish • Intent of the experiment was to measure the density of the earth • “G” and the mass of the earth were derived by others after Cavendish’s death • Boys’ 1894 paper “On the Newtonian Constant of Gravitation”, introduced G

5. The Torsion Wire • A torsion wire acts very much like a spring • The torsion of the wire is equal to the twist in the wire

6. Apparatus: Inside and Outside the Box masses laser position after one period equilibrium position mirror Amplitude laser

7. Apparatus: Thinking of Forces Gravity and Torsion are equal and opposite Gravity and Torsionare equal and opposite Original Position: System is in equilibrium Final Position: System is in Equilibrium • Both forces are responsible for the acceleration that the small balls feel when the equilibrium positions are disturbed • Both forces are responsible for the final equilibrium position

8. Method 1: Equilibrium Position • Measure difference on screen ∆S between equilibrium positions • Equilibrium positions: States where lead balls are not moving • Measurement gives angular displacement between equilibrium positions • Combine with a measurement of the period to obtain G Actual Data

9. Method 1: Measurement of ∆S S1 ∆S =0.115 m S2 T= 395 s G = 6.9 ± 0.4 x10-11m3kg-1s-2- 4% deviation from accepted value

10. Method 2: Using Acceleration Gravity and Torsionare equal and opposite Gravity and Torsion are in the same direction Balls are moved: G can be described in terms of the initial acceleration felt by the small masses • Procedure: • Start with large balls in equilibrium position • Record Position • Flip large balls to final position • Record position every 15 seconds for approx. 45 seconds

11. Method 2: Measurement of a0 ΔX (m) This method gave the following value of G: G = 6.6 ± 0.8 X 10-11 m3kg-1s-2 - 1% deviation from the accepted value

12. Summary • G is the fundamental constant with the greatest uncertainty so accurate measurements of it are still important • The search for G began with Cavendish, using a similar method to the one we are implementing • This method uses a torsion balance to measure the gravitational interaction between small spherical weights • To analyze the data and calculate G we used two methods • The equilibrium method: measure the difference in angle of the equilibrium positions • This yields an accuracy of about 5% • The acceleration method: measure the initial acceleration of the masses and the period of oscillation • This yields an accuracy of about 15%