GP-B Post-Flight Analysis—Final Report - Gravity Probe B - Stanford ...

Starting on 3 December 1725, Bradley observed the star, Gamma Draconis, through his telescope and noted itsposition in the heavens. He was planning to observe the star's position periodically for a year, anticipating thatin six months, he would be able to view a shift in the star's position due to stellar parallax caused by the Earthhaving moved around the Sun to the opposite extreme of its orbit. In Bradley's time, the prevailing wisdom wasthat the distance across the long axis of the Earth's orbit—approximately 300,000,000 km (186,000,000 miles)—would provide a sufficient baseline to view a parallax shift in the star’s position. What the astronomers ofBradley's day did not know is that even the closest star to our solar system is nearly 150,000 times further awaythan the distance across Earth's orbit, and thus the parallax effect between December and June observations ofGamma Draconis only amounts to about 1.5 arcseconds (0.00042 degrees). This is an angle about the size a pea,viewed from one kilometer away—much too small to be measured with instruments of Bradley's day. It wouldbe another 100 years before stellar parallax was actually detected by Friedrich Bessel, director of the KonigsbergObservatory in Germany.As a result of a year’s worth of periodic observations of the star, Gamma Draconis, Bradley was surprised todiscover that the pattern traced out by the star’s motion was an ellipse. Moreover, the major axis of the ellipsecoincided not with the long axis across Earth's orbit from December to June as would be expected for a parallaxmeasurement, but rather with the short axis from March to September. Bradley pondered these seeminglymysterious results for two more years, discovering that all other stars he observed also traced out identicalelliptical patterns over the course of a year. One morning in 1728, he had an “aha” moment while sailing on aboat, watching the motion of a wind vane flying from a mast. He noticed that the vane kept changing directionsas the boat turned to and fro, and that it did not necessarily point directly opposite the boat’s direction of travel.He thought this might be due to a shifting wind, but upon querying the boat's captain, he learned that the wind'sdirection had remained constant. At that point, he realized that the vane's direction was resulting from acoupling of the boat's motion with the wind direction.At this point, Bradley made a profound connection: he likened the Earth to the boat and the light from a star tothe wind. He then realized that the apparent position of the star was changing as the Earth moved in its orbit.Bradley described this phenomenon in a letter to Halley, which was read to the Royal Society in January 1729. Inhis letter, he named the phenomenon “aberration of starlight,” because the stars appeared to be in a differentposition that they actually were, due to the fact that they were being observed from a moving body.Bradley further realized that since his telescope was moving through space along with the Earth, in order for thestarlight to hit the eyepiece in the center of his telescope, he would have to tilt the telescope in the Earth’sdirection of motion, towards the apparent position of the star. He determined that the angle at which thetelescope must be tilted represents the ratio of the speed at which the Earth is moving around the Sun divided bythe speed of light. Nowadays, thanks to Einstein's special theory of relativity, we now know that a relativisticcorrection factor must be added to the speed of light in the denominator of the stellar aberration ratio.410 March 2007 Chapter 14 — Data Collection, Processing & Analysis