Hi,
Here is the Gravity Probe B report of the events of this past week.
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GRAVITY PROBE B MISSION UPDATE FOR 03 MARCH 2005
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GP-B STATUS AT A GLANCE
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Mission Elapsed Time: 318 days (45 weeks/10.5 months)
Science Data Collection: 189 days (27 weeks/6.25 months)
Current Orbit #: 4,694 as of 2:00PM 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 98.7%
Attitude & Translation Control (ATC): X-axis attitude error: 206.7 marcs rms
Y-axis attitude error: 385.6 marcs rms
Command & Data Handling (CDH): Multi-bit errors (MBE): 0
Single-bit errors (SBE): 8,198 (daily avg.)
Telescope Readout (TRE): Nominal
SQUID Readouts (SRE): Nominal
Gyro #1 rotor potential: -1.4 mV
Gyro #2 rotor potential: +7.5 mV
Gyro #4 rotor potential: -6.6 mV
Gyro #3 Drag-free Status: Backup Drag-free mode (normal)
MISSION DIRECTOR'S SUMMARY
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As of Mission Day 318, the Gravity Probe B vehicle and payload are in good health, with all systems functioning nominally and more than six months of science data collected. All four gyros are digitally suspended in science mode. The spacecraft is flying drag-free around Gyro #3.
One activity occupied our attention this past week:
(1) Guide star capture times have improved to the one-minute range after gyro biases were updated on all three axes. This is a typical adjustment of the positioning gyroscopes on the satellite (which are different than the science gyros) that is required due to the influence of the Sun as GP-B orbits the Earth. These adjustments allow the satellite to more quickly re-focus, or "capture", the guide star as it emerges from the Earth's eclipse on each orbit.
MISSION NEWS -- Do Variations in Earth's Shape and Gravity Affect GP-B?
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For the sake of simplicity, when describing GP-B’s mission, we show its polar orbit as a circle around a spherical Earth. But, as several astute readers have pointed out, this is not truly the case. The Earth is not perfectly spherical in two ways: one, it has a slight bulge around its waistline, called “oblateness”. Two, its gravitational field differs from place to place around the globe due to varying distributions of the Earth’s mass.
GP-B Mission Diagram
http://einstein.stanford.edu/highlights/sb1-030405-GP-B_ExperimentDiagram.jpgHow then do these factors affect GP-B’s orbit, and more importantly, affect the geodetic and frame-dragging predictions? If GP-B’s predictions for the drift of a gyroscope (6.614 arcsecs - geodetic; 0.0409 arcsecs – frame-dragging) assumed a perfectly spherical Earth and a perfectly circular orbit, wouldn’t these numbers be wrong?
The answer is, ‘Yes…and no.’ Leonard Schiff’s original “relativity gyroscope” predictions did have to take into account these two aspects of the Earth – but not as much as you might think. Schiff’s original calculations, based on a spherical Earth and a corresponding circular orbit, came within 0.1% of the final calculation for gyroscopic drift.
Leonard Schiff (1915-1971)
http://einstein.stanford.edu/highlights/sb5-030405-schiff.jpgOBLATENESS
By far, the oblateness, or bulging, of the Earth is the more significant factor of the two that had to be taken into account. The Earth’s rotation causes its center, or equator, to bulge out slightly due to rotational momentum. At present, the equatorial radius is about 21 km longer than the Earth’s polar radius (a difference of 0.33%), meaning the Earth has a slightly oblong shape when viewed from space. Consequently, a polar orbiting satellite will not follow a perfectly circular path; its orbit will be slightly elliptical as it goes from pole to equator to pole. In regards to Schiff’s calculations and the predictions for GP-B, the Earth’s oblateness altered the final number by about 0.1%. See this NASA article for more info on the Earth’s changing shape.
GRAVITATIONAL VARIATIONS
The second aspect, variations in Earth’s gravitational field, has an even smaller effect on an orbiting satellite. The strength of Earth’s gravitational field varies with the amount of mass in the Earth at a given location. Mountain ranges like the Himalayas, which comprise of an enormous amount of mass in a given area, exert a stronger gravitational pull than do areas like the Indian Ocean, where most of the mass is in the form of water (less dense, so less mass in a given area).
In theory, these variations in gravity could effect the GP-B satellite. A stronger or weaker gravitational area could change the position of the satellite, ever so slightly. In reality, however, these variations are far too miniscule to affect the GP-B gyroscopes and satellite. Any possible changes in the satellite’s orbit ahve been calculated to be well below the tolerances of the SQUID (device that monitors gyroscopic drift) and of the experiment as a whole.
For more information about mapping the Earth’s gravity field, check out the GRACE experiment, including its incredible models of Earth’s gravity!
So the answer to the initial question is both ‘Yes’ and ‘No’. GP-B scientists did have to account for the Earth’s oblateness to make an accurate prediction of a gyroscope’s drift. But since the gravitational variations around the Earth are so small, GP-B scientists did not need to take them into account. Just in case, GP-B is carefully monitoring the orbit of the satellite and its gyroscopes and will compare these orbit paths with the predicted path after the completion of the mission.
FACTOID OF THE WEEK
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Did you know that the Earth has been experiencing “post-glacial rebound”? During the most recent ice age, tens of thousands of years ago, the massive weight of the ice caps was flattening the Earth. Since then, as the ice caps melt, the Earth has been regaining its spherical figure slowly but surely. As of today, the Earth is nearly spherical – less 0.5% from perfectly round!
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PREVIOUS GP-B UPDATES
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If you wish to read any of our previous updates, our GP-B Web site includes a chronological archive of all the updates/highlights (with photos and drawings) that we have posted over the past 8 years:
http://einstein.stanford.edu/highlights/hlindexmain.html=============================
OTHER LINKS THAT MAY INTEREST YOU
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Our GP-B Web site,
http://einstein.stanford.edu contains lots of information about the Gravity Probe B experiment, general relativity, and the amazing technologies that were developed to carry out this experiment.
Visual tour of the GP-B spacecraft and payload from our GP-B Web site:
http://einstein.stanford.edu/content/vehicle_tour/index.htmlPDF file containing a 1/20 scale, paper model of the GP-B spacecraft that you can download print out, and assemble:
http://einstein.stanford.edu/content/paper_model.
NASA's Marshall Space Flight Center also has a series of Web pages devoted to GP-B: (http://www.gravityprobeb.com )
Photo, taken through a telescope by Swiss physics teacher and amateur astronomer Stefano Sposetti, of GP-B spacecraft in orbit, passing near IM Pegasi: http://aida.astronomie.info/sposetti.
The Harvard-Smithsonian Center for Astrophysics (Cambridge) and York University (Toronto), with contributions from the Observatoire de Paris, have been studying the motions of the guide star, IM Pegasi for over a decade. To find out more, visit: http://www.yorku.ca/bartel/guidestar/
In addition, you'll find information in the Guide Star FAQ on our Web site: http://einstein.stanford.edu/content/faqs/faqs.html#guidestar and on pages 18-20 of the Gravity Probe B Launch Companion: http://einstein.stanford.edu/highlights/GP-B_Launch_Companion.pdf.
Track the GP-B satellite on the Web using NASA's Java-based J-Pass satellite tracking application at: http://science.nasa.gov/realtime/JPass/ Also, you can track the GP-B satellite on Personal Digital Assistants (PDAs) using either the Palm OS or Pocket PC operating systems with software from Big Fat Tail Productions: http://www.bigfattail.com.
The Einstein Exhibition at the Skirball Cultural Center in Los Angeles through May 2005: Information about the Einstein exhibition is available on the Skirball Center Web site: http://www.skirball.org/index.asp?s=exhibit&p=einstein.asp. If you can't make it to Los Angeles, you can visit the AMNH's virtual Einstein exhibit on the Web at: http://www.skirball.org/exhibit/amnh_frame.html.
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NASA - Stanford - Lockheed Martin
Gravity Probe B Program
"Testing Einstein's Universe"
http://einstein.stanford.edu
Bob Kahn
Public Affairs Coordinator
Phone: 650-723-2540
Fax: 650-723-3494
Email: kahn@relgyro.stanford.edu
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Regards,
LelandJ
