1. Outline of the Lectures Lecture 1: The Einstein Equivalence Principle Lecture 2: Post-Newtonian Limit of GR Lecture 3: The Parametrized Post-Newtonian Framework Lecture 4: Tests of the PPN Parameters

2. Outline of the Lectures Lecture 1: The Einstein Equivalence Principle Lecture 2: Post-Newtonian Limit of GR Lecture 3: The Parametrized Post-Newtonian Framework Lecture 4: Tests of the PPN Parameters  Deflection of light  Shapiro time delay  Perihelion advance  Nordtvedt effect and lunar laser ranging  Gyroscope precession & Gravity Probe B  LAGEOS tracking  Tests of the Strong Equivalence Principle  Summary of bounds on the PPN Parameters

3. Light Bending and Alternative Gravitation Theories Deflection = Space Curvature GR  =1  Cavendish 1784  von Soldner 1803  Einstein 1911 a b’c’ b c

4. The parameter (1+  )/2

5. Measuring light deflection using VLBI 541 quasars 1977-1999 87 VLBI sites 1.7 million measurement S. S. Shapiro et al (2004)

6. PPN Equation of motion for a binary system

7. Mercury’s Perihelion: from Trouble to Triumph 1687 Newtonian triumph 1859 Leverrier’s conundrum 1900 A turn-of-the century crisis 575 “ per century CauseRate (per century) Venus278 ‘’ Earth 90 ‘’ Jupiter154 ‘’ Others 10 ‘’ Total532 ‘’ Discrepancy 43 ‘’ Modern value 42.98 + 0.04 ‘’ GR Prediction 42.98 ‘’

8. Tests of the Weak Equivalence Principle

9. GRAVITY PROBE B Goal 0.4 mas/yr Launch April 20, 2004 Mission ended Sept 2005

10. Gravity Probe B: The Experiment -- Payload

11. Gravity Probe B: The Experiment -- Gyroscopes

13. ParameterEffect or ExperimentBoundRemarks  - 1 Time delay2.3 X 10 -5 Cassini tracking Light deflection4 X 10 -4 VLBI  - 1 Perihelion shift3 X 10 -3 J 2 = 2 X 10 -7 Nordtvedt effect2.3 X 10 -4 LLR,  < 3 X 10 -4  Earth tides10 -3 gravimeters  Orbit polarization 10 -4 LLR 2 X 10 -4 J2317+1439  Spin precession4 X 10 -7 Sun axis  Self-acceleration4 X 10 -20 Pulsar spindown  --2 X 10 -2 Combined bounds  Binary acceleration4 X 10 -5 PSR 1913+16  Newton’s 3rd law10 -8 Lunar acceleration  --Not independent Bounds on the PPN Parameters  =4  -y-3-10  /3-  1 +2  2 /3-2  1 /3-  2 /3 Bound on scalar-tensor gravity:  > 40,000