WEEKLY UPDATE FOR 15 JULY 2005:
GRAVITY PROBE B MISSION STATUS AT A GLANCE
|Mission Elapsed Time||451 days (64 weeks/14.79 months)|
|Science Data Collection||322 days (46 weeks/10.56 months)|
|Current Orbit #||6,655 as of 4:30 PM PST|
|Spacecraft General Health||Good|
|Roll Rate||Normal at 0.7742 rpm (77.5 seconds per revolution)|
|Gyro Suspension System (GSS)||All 4 gyros digitally suspended in science mode|
|Dewar Temperature||1.82 kelvin, holding steady|
|Global Positioning System (GPS) lock||Greater than 98.5%|
|Attitude & Translation Control (ATC)||
X-axis attitude error: 190.5 marcs rms
|Command & Data Handling (CDH)|| B-side (backup) computer in control
Multi-bit errors (MBE): 0
Single-bit errors (SBE): 8 (daily average)
|Telescope Readout (TRE)||Nominal|
|SQUID Readouts (SRE)||Nominal|
|Gyro #1 rotor potential||Before Discharge +3.6 mV; After Discharge: -2.6 mV|
|Gyro #2 rotor potential||Before Discharge +3.6 mV; After Discharge: +2.8 mV|
|Gyro #3 rotor potential||Before Discharge +9.3 mV; After Discharge: -4.5 mV|
|Gyro #4 rotor potential||Before Discharge +3.6 mV; After Discharge: -2.9 mV|
|Gyro #1 Drag-free Status||Backup Drag-free mode (normal)|
MISSION DIRECTOR'S SUMMARY
As of Mission Day 451, the Gravity Probe B vehicle and payload are in good health. All four gyros are digitally suspended in science mode. The spacecraft is flying drag-free around Gyro #1.
As reported last week, gyro #3 transitioned into analog backup suspension mode during the first phase of a calibration test that began on Thursday, 7 July 2005, that involves electrically "nudging" the gyro rotor to various pre-defined positions within its housing. We restored gyro #3 to digital suspension last Thursday evening and continued phase 2 of the test last Friday. We suspected that the root cause of the transition to analog mode was likely due to a known “race” condition, which occurs when the gyro rotor reaches a low threshold, set by the hardware. For this reason, we suspected that gyro #3 would transition to analog mode again during the second phase of the calibration test, and this was the case last Friday. We again returned gyro #3 to digital suspension and completed the test successfully.
The Poker Flats ground station in Alaska has been experiencing hardware problems, and for this reason, we have had to re-schedule some of our data telemetry sessions at other NASA TDRSS ground station facilities. We have recently run tests at the McMurdo station in Antarctica, and we successfully completed a data capture session from McMurdo this past Monday, 11 July 2005, after some last-minute scrambling to get the connection properly set up. We have also been using the Wallops ground station in Virginia.
On Wednesday, 12 July 2005, we completed a paper simulation of the calibration procedures we will be performing towards the very end of the mission, just before the helium runs out, to move our telescope from our guide star, IM Pegasi, to a nearby star and back to IM Pegasi.
Yesterday, 13 July 2005, marks the one-year anniversary of our full-speed gyro spin-up in space (gyro #4 was spun up to 105 Hz/6,300 rpm). That was a very tense and exciting time in the Mission Operations Center (MOC) here at GP-B. Also yesterday, we used ultraviolet light to reduce the electrostatic charge on all four gyros. Very small amounts of charge build continually build up on the gyro rotors throughout the mission. When the charge build-up reaches a sufficiently high level, we use ultraviolet light to reduce the charge. We last performed this procedure on during the week of 15 April 2005, and you can read a more detailed description of the process in the Weekly Highlights archive, here on our Web site: The results of the discharge are included in the Mission Status table, shown above.
In our Mission News story of 6 May 2005, we described the telescope dither and its important role in correlating the gyro spin axis orientation with the telescope orientation during the Guide Star Valid period of each orbit. In this week's Mission News, we describe the phenomena called “aberration of starlight” (or “stellar aberration”). As GP-B Principal Investigator, Francis Everitt, once put it: “Nature is very kind and injects a calibrating signal [the aberration of starlight] into GP-B for us.” This phenomenon actually provides two natural calibration signals in the relativity data that are absolutely essential for determining the precise spin axis orientation of the gyros over the life of the experiment. However, the word “aberration” typically refers to behavior that departs or deviates from what is normal, customary, or expected--and usually, such behavior is not welcome. So, what does aberration have to do with starlight? And, why would we want to use something aberrant as a calibration signal? To answer the first of these questions, we must first travel back in time to the 18th century.
At the beginning of the 18th century, astronomers were still seeking some form of direct proof of the Copernican theory that all the planets in our solar system orbit around the Sun. One such person was British Astronomer James Bradley, who in 1718 was recommended by the Astronomer Royal Edmund Halley to become a Fellow of the Royal Society, and who eventually succeeded Halley as British Astronomer Royal in 1742.
Starting on 3 December 1725, Bradley observed the star, Gamma Draconis, through his telescope and noted its position in the heavens. He was planning to observe the star's position periodically for a year, anticipating that in six months, he would be able to view a shift in the star's position due to stellar parallax caused by the Earth having moved around the Sun to the opposite extreme of its orbit. Parallax is the effect whereby the position or direction of an object appears to move when viewed from different positions. You can easily experience parallax by closing your right eye and viewing a finger at arm's length with your left eye. When you switch viewing eyes, closing your left eye and opening your right eye, your finger appears to have moved to the left.
In Bradley's time, the prevailing wisdom was that 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 of Bradley's day did not know is that even the closest star to our solar system is nearly 150,000 times further away than the distance across Earth's orbit, and thus the parallax effect between December and June observations of Gamma 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 would be another 100 years before stellar parallax was actually detected by Friedrich Bessel, director of the Konigsberg Observatory in Germany.
Out of curiosity, Bradley made a second observation of Gamma Draconis two weeks after his first one, and he was astonished to find that the star had already shifted position--but by a greater amount than he expected, and in the “wrong” direction for parallax. Bradley continued making observations of this star's position over the course of the following year. To his further surprise, he discovered that the pattern traced out by the star's motion was an ellipse. Moreover, the major axis of the ellipse coincided not with the long axis across Earth's orbit from December to June as would be expected for a parallax measurement, but rather with the short axis from March to September.
Bradley pondered these seemingly mysterious results for two more years, discovering that all other stars he observed also traced out identical elliptical patterns over the course of a year. One morning in 1728, he had an “aha” moment while sailing on a boat, watching the motion of a wind vane flying from a mast. He noticed that the vane kept changing directions as 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's direction had remained constant. At that point, he realized that the vane's direction was resulting from a coupling 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 to the 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. In his letter, he named the phenomenon “aberration of starlight,” because the stars appeared to be in a different position 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 the starlight to hit the eyepiece in the center of his telescope, he would have to tilt the telescope in the Earth's direction of motion, towards the apparent position of the star. He determined that the angle at which the telescope must be tilted represents the ratio of the speed at which the Earth is moving around the Sun divided by the speed of light. Nowadays, thanks to Einstein's special theory of relativity, we now know that a relativistic correction factor must be added to the speed of light in the denominator of the stellar aberration ratio.
From his observations of Gamma Draconis, Bradley knew that the maximum angle at which his telescope had to be tilted was tiny--approximately 20 arc-seconds. Using this angle, and the velocity of the Earth moving around the Sun, known in his day to be ~30 km/sec (~18.6 miles/sec), he calculated the speed of light to be about 10,000 times faster than the orbital velocity of Earth or ~300,000 km/sec (~186,000 miles/sec).
You can now see why the aberration of starlight plays a role in the GP-B experiment. While constantly tracking the guide star, IM Pegasi, the telescope on-board the spacecraft is always in motion--both orbiting the Earth once every 97.5 minutes and along with the Earth, the spacecraft and telescope are orbiting the Sun once a year. These motions result in two sources of aberration of the starlight from IM Pegasi. The first is an orbital aberration, which has a maximum angle of 5.1856 arcseconds, resulting from the spacecraft's orbital speed of approximately 7 km/sec, relative to the speed of light. (In the case of orbital aberration, the relativity correction is insignificant.). The second is the now familiar annual aberration due to the Earth's orbital velocity around the Sun, which when corrected for special relativity, amounts to an angle of 20.4958 arcseconds.
In the GP-B experiment, the signals representing the drift in the gyroscope spin axes over time are represented by voltages that have undergone a number of conversions and amplifications by the time they are telemetered to Earth. These conversions and amplifications impart a scale factor of unknown size into the data, and early on in the development of the GP-B experimental concept it was apparent that there needed to be a means of determining the size of this gyro scale factor in order to see the true relativity signal. Initially, it seemed that aberration of starlight was going to be a source of experimental error bundled into the scale factor. But upon examining this issue more closely, it suddenly became clear that, quite to the contrary, the orbital and annual aberration of light from the guide star actually provided two built-in calibration signals that would enable the gyro scale factor to be calculated with great accuracy.
To see how this works, let's first take a closer look at how the orbital aberration of the starlight from the guide star, IM Pegasi, is “seen” by GP-B spacecraft. As mentioned earlier, the spacecraft orbits the Earth once every 97.5 minutes. As the spacecraft emerges over the North Pole, the guide star comes into the field of view of the science telescope, and the telescope then locks onto the guide star. This begins what is called the “Guide Star Valid (GSV)” phase of the orbit. At this point in its orbit, the orientation of the spacecraft's velocity is directly towards the guide star, and thus, there is no aberration of the star's light-it travels straight down the center of the telescope. However, as the spacecraft moves down in front of the Earth, the orientation of its velocity shifts in the orbital direction until it becomes perpendicular to the direction of the light from the guide star, slightly above the equator. This is the point of maximum aberration since the telescope is now moving perpendicular to the guide star's light. As the spacecraft moves on towards the South Pole, the aberration recedes back to zero as the spacecraft moves under the Earth, directly away from the guide star. At this point, the telescope unlocks from the guide star, transitioning into what is called the “Guide Star Invalid (GSI)” phase of the orbit. The navigational rate gyros on the outside of the spacecraft maintain the telescope's orientation towards the guide star while the spacecraft is behind the Earth, but we do not use the science gyro data during the GSI phase.
During the GSV portion of each orbit, the telescope remains locked on the guide star, with the spacecraft's micro thrusters adjusting the telescope's pointing for the aberration of the guide star's light. This introduces a very distinct, half-sine wave pattern into the telescope orientation. This sinusoidal motion is also detected by the gyro pickup loops that are located in the gyro housings, along the main axis of the spacecraft and telescope. Thus, this very characteristic pattern, generated by the telescope and thrusters, appears as a calibration signal in the SQUID Readout Electronics (SRE) data for the gyros.
The annual aberration of the guide star's light works the same way as the orbital aberration signal, but it takes an entire year to generate one complete sine wave. Using the spacecraft's GPS system, we can determine the orbital velocity of the spacecraft to an accuracy of better than one part in 100,000 (0.00001). Likewise, using Earth ephemeris data from the Jet Propulsion Lab in Pasadena, CA, we can determine Earth's orbital velocity to equal or better accuracy. We then use these velocities to calculate the orbital and annual aberration values with extremely high precision, and in turn, we use these very precise aberration values to calibrate the gyro pointing signals. It is interesting to note that the amplitude of the sine wave generated by the annual aberration is four times as large as the orbital aberration amplitude, with peaks occurring is September and March. Because we launched GP-B in April and started collecting science data in September, the effect of the annual calibration signal did not become apparent in the data until this past February-March, six to seven months into the science phase of the mission. Thus, from March onward, both the annual and orbital aberration signals will be used in the ongoing analysis of the science data.
For more information about classical and relativistic aberration of light, see the Relativity Chapter on the Fourmilab Web site, maintained by John Walker.
Biographical Sources consulted on James Bradley and the aberration of starlight:
- BBC History on line.
- Oxford University Press. Oxford Dictionary of National Biography.
- Cambridge University Press. The Life and Science of Leon Foucault by William Tobin, University of Canterbury, 2003.
- NASA Web site: From Stargazers to Starships by David P. Stern.
- Encyclopedia Britannica, Online Edition.
UPDATED NASA/GP-B FACT SHEET AVAILABLE FOR DOWNLOADING
We recently updated our NASA Factsheet on the GP-B mission and experiment. You'll now find this 6-page document (Adobe Acrobat PDF format) listed as the last navigation link under "What is GP-B" in the upper left corner of this Web page. You can also click here to download a copy.
Drawings & Photos: The layered composite photo of the GP-B spacecraft orbiting the Earth and the orbital aberration diagrams were created by GP-B Public Affairs Coordinator, Bob Kahn using Adobe Photoshop and Adobe Illustrator. Mr. Kahn also took the photos of the Greenwich Observatory and Museum and the photo of the GP-B MOC during gyro spinup. The photos of the gyroscope housing and the UV lamp discharge system are from the GP-B Image Archive here at Stanford. The photo of the McMurdo ground station is courtesy of NASA. The portrain of James Bradley was painted by Thomas Hudson. Click on the thumbnails to view these images at full size.
MORE LINKS ON RECENT TOPICS
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- The GP-B Launch Companion in Adobe Acrobat PDF format. Please note: this file is 1.6 MB, so it may take awhile to download if you have a slow Internet connection.