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Projects: Pioneer Anomaly

Project Update: Thermal Modeling Accounts for Some, But Not All, of the Pioneer Anomaly

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Click to enlarge > The Pioneer Anomaly: April 13, 2008 presentation Slava Turyshev reported on the progress of thermal modeling of the Pioneer 10 spacecraft at the American Physical Society Meeting in St. Louis, Missouri on April 13, 2008. The complete presentation may be downloaded here (PDF format, 7.2 MB). Turyshev wishes to credit many collaborators who were responsible for the actual thermal modeling work, especially Gary Kinsella, of NASA's Jet Propulsion Laboratory, and Siu-Chan Lee and Daniel S. Lok of the Applied Science Laboratories.

by Emily Lakdawalla
May 19, 2008

This article is an extended version of an update posted on April 17 at The Planetary Society Weblog.

Researchers are attempting to understand the nature of the Pioneer Anomaly through two separate lines of inquiry: careful analysis of Doppler tracking data, and the development of a high-fidelity thermal model of the spacecraft.  The Planetary Society and its members have provided partial funding for the Pioneer data recovery, validation, and analyses.  On April 13 Pioneer Anomaly Project Director Slava Turyshev presented preliminary results of the thermal modeling efforts at a meeting of the American Physical Society.

Making a Model

Why is thermal modeling important? The magnitude of the Pioneer Anomaly is so very tiny that it could conceivably result from the uneven radiation of heat from the spacecraft. The Pioneers, like all spacecraft, were made from a wide variety of materials: aluminum, Teflon, Kapton, Mylar, aluminum-based paints, and so forth, all of which absorb, reflect, or emit radiation in different ways; and some materials, notably the plutonium in the spacecraft power supply, generate heat on their own. To figure out in which directions the spacecraft radiates how much heat, Turyshev and his colleagues needed to start from scratch, building a computer model of the spacecraft, covering the model with surfaces with the correct thermal properties, plugging in the recovered spacecraft data on the temperatures measured at various points within the spacecraft, and then solving a difficult set of differential equations to determine how heat conducts and radiates around within the spacecraft, and then in what direction it radiates once it exits the surface.

If Turyshev had wanted to create such a model for a modern mission, like Cassini, it would have been easy, as the computer models already exist. But there was no such model for the Pioneers.  Turyshev had to begin by performing a treasure hunt for any and all information that could help him understand the design and construction of the spacecraft, including piles of aging project documents (some of which he rescued from NASA's Ames research center in 2006 just before they were to be disposed of, thanks in part to funding provided by The Planetary Society and its members to recover Pioneer data) and archival photographs found online and at the Smithsonian Institution.  He also tracked down a few retired engineers who had actually built the Pioneers.  Some of the most useful photographs that Turyshev used came from the personal photo albums of the retirees.

Click to enlarge > Replica of Pioneer 10 A full-scale replica of Pioneer 10 hangs in the Milestones of Flight Gallery at the Smithsonian Institution in Washington, D.C. The replica was assembled by TRW in 1977 from spare parts provided by JPL, TRW, and Teledyne Energy Systems. Credit: Smithsonian Institution photography by D. Hrabak

Click to enlarge > Geometric model of the Pioneer 10 spacecraft This computer model of the Pioneer 10 spacecraft was built by Slava Turyshev and his coworkers to model the direction and intensity with which thermal radiation is emitted from the spacecraft. Some parts, such as the booms that hold the magnetometer and power supplies and the struts that hold the radio transmitter above the dish antenna, are "thermally inconsequential" and so not included in the model. Credit: Courtesy Slava Turyshev

To begin with, Turyshev decided to attempt to account for the thermal behavior of just one spacecraft (Pioneer 10) at just one point in time: July of 1981, when Pioneer 10 crossed through 25 Astronomical Units (AU) from the Sun. An Astronomical Unit is the average distance between Earth and the Sun; 25 AU is midway between the orbits of Uranus and Neptune.  Starting at 25 AU allowed Turyshev to make some simplifying assumptions. At that distance, Turyshev explained, the pressure from solar radiation is negligible; the temperature from the Sun is not enough to change the state of the spacecraft; and it is so cold that the louver system (designed to radiate excessive heat away from the interior of the spacecraft) is closed.

Adding Real-World Data

In addition to the idealized model of the spacecraft, Turyshev also had actual data to plug in to the model: information from temperature and other sensors built into the spacecraft.  These sensors reported a description of the spacecraft state at regular intervals through radio telemetry to Earth.  These temperature readings provided boundary conditions fixing the temperature of the spacecraft at certain points.  With the computer model constructed and boundary conditions set, Turyshev and his colleagues could run a computer simulation that determined the temperature at all points on the spacecraft.  The computer simulation solved differential equations that described how heat conducted between different parts of the interior of the spacecraft, and how heat radiated both within the spacecraft and from the surface of the spacecraft out into space.  The computer model included 3.4 million individual radiation conductors and took more than two days to run. 

Click to enlarge > Temperature sensors within Pioneer 10 Inside Pioneer 10's equipment and instrument compartments were six sensors that measured the temperature of the spacecraft through time. The temperature readings were reported back to Earth as a part of Pioneer 10's regular radio transmissions throughout the mission. These temperature readings provided boundary conditions for the thermal model of the spacecraft. Credit: NASA / JPL / Slava Turyshev

Click to enlarge > Predicted temperatures for Pioneer 10 at 25 AU The thermal model developed by Slava Turyshev and colleagues predicted a range of temperatures for the surface of the Pioneer 10 equipment and instrument compartments, from a low of -2.3 degrees Celsius (28 degrees Fahrenheit) to a high of 8.6 degrees Celsius (47 degrees Fahrenheit). The compartment is insulated from space by a blanket of multi-layer insulation (MLI), whose surface temperatures are much colder, from -161.8 to -119.1 degrees Celsius (-259.2 to -182.4 degrees Fahrenheit). These temperatures only hold for when Pioneer 10 was 25 Astronomical Units from the Sun, in July of 1981. Credit: NASA / JPL / Slava Turyshev

Click to enlarge > Anisotropic thermal emission from Pioneer 10 This graph represents the direction and power of thermal emission from Pioneer 10 at a distance of 25 AU from the Sun. The spacecraft's antenna points toward the top of the graph; the direction of spacecraft motion is toward the bottom of the graph. If Pioneer 10 radiated heat away in all directions equally, the plot would look like a circle (dark blue line). But Pioneer 10 does not radiate heat isotropically; the thermal model predicts that most of the power comes out the sides of the spacecraft, with almost none radiating directly along the spacecraft's direction of motion (magenta line). Credit: NASA / JPL / Slava Turyshev

The thermal model predicted a range of temperatures for different components of the spacecraft.  With the thermal model at hand, they then needed to figure out what that model really meant: would the uneven radiation of heat from the spacecraft result in a measurable acceleration, and, if so, what would its magnitude and direction be?  The fact that the spacecraft spins constantly simplifies this calculation. The model predicted what Turyshev said he had been expecting all along: the thermal radiation is not isotropic (the spacecraft doesn't radiate evenly in all directions).  Most of the radiation goes out the sides of the spacecraft, in a direction perpendicular to its direction of motion. And because the spacecraft spins, most of those sideways radiation effects cancel each other out. But a small component of the radiation does go in a direction parallel to the spacecraft's direction of motion. And it turns out that just a little bit more radiation goes out the side of the spacecraft pointed away from the Sun than goes out the side of the spacecraft that goes toward the Sun. This is exactly the direction of the Pioneer Anomaly.  Turyshev reported that the model can generate an acceleration that amounts to about 30% of the Anomaly for that distance from the Sun.

Next Steps

Turyshev and his team presented their model and the preliminary results to a group of interested engineers, including several from outside of the Jet Propulsion Laboratory group (Craig Markwardt, Viktor Toth, and Louis Cheffer) at a meeting at JPL on April 4, 2008.  That group generated a list of recommendations for how to improve the model's fidelity to the actual spacecraft. Also, the model included some assumptions about how the materials on the spacecraft may have degraded over time with exposure to the interplanetary radiation environment.  Because little empirical data exists on how spacecraft surfaces degrade with decades of exposure to space, Turyshev plans to do sensitivity analyses: the computer simulation of the temperatures will be run again with a varying set of material properties, to determine how sensitive the model is to the variance in these parameters. Once the team is confident in the model at 25 AU, it will be run multiple times cases at other representative distances sampled by the spacecraft to see how the thermal behavior changes with time -- in particular, to study time-varying effects due to the spacecraft's distance from the Sun and the slowly decaying heat output of its plutonium electricity generators.