Spacecraft’s behavior no longer an “unsolved problem in physics”

New physics takes a back seat to heat in understanding the Pioneer anomaly.

The Pioneer 10 spacecraft launched from Cape Canaveral, Florida on March 2, 1972. Its planned mission was to be the first man-made craft to traverse the asteroid belt and image Jupiter up close. Pioneer 10's power plant design was required to last for a minimum of two years in space, but the craft was still traveling and transmitting on January 23, 2003—30 years, 10 months, and 22 days later—when the signal became too weak to pick up on Earth. It was 80 AU (12 billion kilometers) away, at the edge of the solar system.

After Pioneer 10 and its younger sibling, Pioneer 11, passed the 20 AU mark, radio-metric Doppler data showed that there was a deviation in the acceleration of the spacecraft from the numbers predicted by scientists and astronautical engineers. This was first noticed in 1980, but did not receive significant attention until the mid 1990s. It was found that if a tiny, constant, sunward acceleration of (8.74±1.33)x10-10 m/s2 was applied to the predicted orbital model, the discrepancy between the model and the data would go away. However, the source of this acceleration has remained an open question that has had many possible explanations, from the mundane to what was termed "newphysics."

Recent analysis suggests that some form of "new physics"—such as the breakdown of the inverse square law of gravity as described by Newton—will have to wait, as the more pedestrian answer of thermal recoil solves the problem. Thermal recoil force is the (ever so slight) force that results from thermal photons being emitted from a surface—it's Newton's "for every action there is an equal and opposite reaction" in a straightforward form. If heat emissions are distributed unevenly on the spacecraft, then more thermal photons emanating from a given area will impart more of a force in the opposite direction—enough to account for the acceleration anomaly.

To figure out if this is possible here, a team of researchers from Caltech's Jet Propulsion Laboratory and the Applied Science Laboratory built a highly detailed finite-element (FE) thermal model of the Pioneer 10 spacecraft. Many modern FE packages can import CAD drawings of the surface or solid you wish to model; however, a spacecraft designed in the 1960s predates the use of CAD (it was done by hand with old school isometric drawings and instrumentation diagrams). The final thermal FE model consisted of about 3,300 surface elements, 3,700 nodes, and 8,700 linear conductors plus the thermal and radiative properties for each—putting all that together shows off the fun an intern or first year graduate student can look forward to.

The Pioneer 10 spacecraft was powered by four radioisotope thermoelectric generators (RTG), each one holding about 100 grams of 238Pu. As they generated heat, it would not be distributed evenly around the spacecraft, and the FE analysis was used to determine the actual distribution of temperature. To determine the magnitude of the recoil force, the spacecraft model was placed at the center of a large black sphere with a radius of 40 times the diameter of the high gain antenna on the craft.

The amount of radiative emission absorbed by the sphere's surface then corresponded to the amount of momentum carried in that direction. The authors were able to model the RTG thermal power output to within one percent of the known value, and temperatures that were always within ±2K.

Combining this data with the equation that relates the thermal power emitted in a given direction with the resulting acceleration, the team came up with a two parameter model that describes the acceleration due to thermal recoil force. The two terms in the equation relate the acceleration derived from the RTGs, and the acceleration that results from the thermal energy of the electronic equipment on board the spacecraft. The two free variables are the net efficiencies of each process, i.e. how much energy is really turned into acceleration. They come up with ηRTG = 0.0104 and ηElec = 0.406, with an RMS error of only 0.78 W, a value well below the inherent error in the telemetry.

To complement the novel thermal model presented in the paper, the researchers also incorporated their thermal recoil force model into a Doppler analysis of the actual craft's travels through the solar system. This allowed them to carry out a completely independent sanity check of their work to see if the values they obtained for the efficiency parameters from the thermal model would agree with another method. Here, they find an ηRTG = 0.0144 and ηElec = 0.480—very close to the numbers obtained by the thermal analysis, but producing about a 20 percent higher force. To determine if this was a statistically significant difference, the authors examined the ηRTG and ηElec parameter space, and plotted out the region within it that included a 1σ deviation. They found that at a 1σ level, these two estimates of the parameters overlapped each other, indicating that they were statistically similar.

The net result: accounting for this heat emission seems to bring the predicted trajectory much more in line with the craft's actual trajectory.

The authors finish their paper by listing areas of research that could further improve these numbers; better estimates of certain thermal properties of various coatings on the craft, out gassing of various components over the years, and even a repeat of the analysis with the Pioneer 11 spacecraft. They conclude with the following simple statement: "the anomalous acceleration of these spacecraft is consistent with known physics." Just another nail in the coffin for those hoping alternate theories of gravity like MOND may yet hold true.

I love it when you guys publish articles that are a little (or a lot) beyond my grasp of physics / chemistry / math / tacos / whatever, but make it accessible enough that I learn something anyway. Well done!

Just like a few weeks ago, when CERN announced it has very likely found the Higgs boson, I'm a tad bit disappointed that we didn't unearth some kind of Copernician revolution in physics. On the other hand, the explanation that heat radiation was enough to account for the slight deviation is also quite interesting.

Many modern FE packages can import CAD drawings of the surface or solid you wish to model; however, a spacecraft designed in the 1960s predates the use of CAD (it was done by hand with old school isometric drawings and instrumentation diagrams).

"30 years, 10 months, and 22 days later" and still transmitting then when the power source was designed for two years.

Impressive

Yeah! Now that's battery life! (Er...uh...not a battery, I guess. But Wow anyway.) I'm truly happy to have contributed tax money to this one. (Oh, and, in case anyone asks, I'm old enough to have done so.)

"30 years, 10 months, and 22 days later" and still transmitting then when the power source was designed for two years.

Impressive

Yeah! Now that's battery life! (Er...uh...not a battery, I guess. But Wow anyway.) I'm truly happy to have contributed tax money to this one. (Oh, and, in case anyone asks, I'm old enough to have done so.)

Makes me wonder if the RTG's are glued in or if they're "easily removable". Recycling FTW!

Is 'sunward acceleration' effectively the opposite to the direction of travel in this case? So then Pioneer10 has not travelled as far as one might calculate without talking into account thermal recoil?

Anyone know offhand around what that double-integrates to as diference in position over those ~30.8 years?

"30 years, 10 months, and 22 days later" and still transmitting then when the power source was designed for two years.

Impressive

The power source was required to work for a minimum of two years. Given 238Po's half life of 87.something years, it can keep going for a while.

But yeah, that tidbit amazed me and I had to work it into the article because THAT is some good engineering.

Is there anything else humans have designed with moving parts that runs for ~31 years with ZERO maintenance? It may be one of the greatest engineering feats of mankind, right along side the Hoover Dam and Boston's Big Dig... Design a craft that will operate in the harshest environments and can't be maintained mechanically. 31 years later it is still running. Too bad it is going out of range and when are we going to build a space ship to go looking for it after it crashes into a planet and becomes sentient?

I'm not surprised that the heat emanating forward of the craft is causing a slowdown similar to photons, considering heat will generate infrared radiation similar to visual light. I wonder whether there would be any way to reflect that radiation to the rear of the craft to use it as acceleration instead.

This is really awesome physics, but they've only accounted for 80% of the effect. I think they are correct when they say that the anomalous acceleration is "consistent" with known physics, but I wouldn't count this mystery entirely solved - that 20% allows for some wiggle room.

How typical is this kind of analysis (mapping heat distribution with FE software) for more earth-bound engineering problems?

Heat transfer is a solved problem. Using thermal FE analysis are an everyday thing in many engineering fields and engineer's tool boxes.

Yeah FE analysis is becoming more and more common in many applications. I'm finishing up my undergrad in mechanical engineering and we have classes specifically geared towards it. You always have to be careful though. One of the easiest things to do is to feed in a wrong assumption and many trust it without thinking so it's always good to do a few data points the old fashioned way to have a reality check.

"30 years, 10 months, and 22 days later" and still transmitting then when the power source was designed for two years.

Impressive

Yeah! Now that's battery life! (Er...uh...not a battery, I guess. But Wow anyway.) I'm truly happy to have contributed tax money to this one. (Oh, and, in case anyone asks, I'm old enough to have done so.)

Makes me wonder if the RTG's are glued in or if they're "easily removable". Recycling FTW!

Yeah, I hope that craft was EPEAT certified... if not, what will the aliens who find it think of us? I'm so ashamed.

Great article; it's interesting to see this anomaly *pretty much* accounted for.

Is the craft's mass trasmitted regularly? Chips, dents, chemical reactions on its surface, what have you would seem to change the mass of the craft over 30 years. We're talking about tiny numbers magnified by long periods of time at incredible speeds. Could a change in the craft's mass account for the 20%? This type of stuff is way out of my comfort zone so ignore my comment if it makes no sense.

Of course the assumption being that the dish side of the space craft remains pointed more or less at the Earth/Sun, since the Pioneer 10/11 and Voyager 1/2 are asymmetric front to back.

Cool result (maybe that should be Hot!). It also means that when we deliberately start designing spacecraft to travel to nearby star systems, we'll need to account for this effect. It's going to be pretty hard to actually measure such miniscule "thermal thrust" on-platform. A closed control loop will certainly offset velocity losses/gains but maybe a redesign of the thermal profiles could either minimize or balance the effect.

Next effect they'll need to account for is thrust loss/gain from interstellar micro-asteroid (space dust) impacts!

Is there anything else humans have designed with moving parts that runs for ~31 years with ZERO maintenance? It may be one of the greatest engineering feats of mankind, right along side the Hoover Dam and Boston's Big Dig... Design a craft that will operate in the harshest environments and can't be maintained mechanically. 31 years later it is still running. Too bad it is going out of range and when are we going to build a space ship to go looking for it after it crashes into a planet and becomes sentient?

I'm not gonna dismiss the engineering feat, but I wouldn't call space the harshest environment for machines: mostly empty, no pesky oxygen to turn it to rust, not many external forces (such as pressure or wind) to stress test it...Even the rather cool temperature might be to your advantage, because it seems (but I may be mistaking) that generating heat is easier than dissipating excess heat.

I know for certain missions they have to account for the thrust of the light from the sun hitting the spacecraft, but that effect is much larger than the thermal emission of photons, until you get a long way from the sun. In most designs the thermal radiation is dumped away from the sun to the colder sink of deep space, so typically this mechanism is going to have a breaking effect.

so, the very, very tiny force exherted by the loss of energy by heat in a certain direction from the craft, over 30+ years time, was enough to cause a very minor but perceptible course correction? ...and the calulated using models near to exactly how much? That's awesome.

What about the Voyager craft? Are they 'suffering' from this same effect? Or were their RTGs better at dissipating heat, or storing it elsewhere? Seeing as the Voyagers have a single boom for their three RTGs, maybe they are 'pushing' the craft in a lateral motion, so their instruments spin on the axis of the HGA?

What about the Voyager craft? Are they 'suffering' from this same effect? Or were their RTGs better at dissipating heat, or storing it elsewhere? Seeing as the Voyagers have a single boom for their three RTGs, maybe they are 'pushing' the craft in a lateral motion, so their instruments spin on the axis of the HGA?

Voyagers use thrusters to stay pointed at earth whereas pioneer was spin stabilized. Basically the effect is impossible to measure on voyager because of the uncertainty of the impact of the thrusters is way higher.

Kressilac wrote:Is the craft's mass trasmitted regularly? Chips, dents, chemical reactions on its surface, what have you would seem to change the mass of the craft over 30 years.

Only way I know to calculate the mass is to cause the spacecraft to move either with a carefully calibrated thruster or a magnetic reaction wheel/gyroscope. Fire a thruster with a known amount of fuel or make an attitude change, calculate relative movement by measuring change of apparent position or attitude by observing stars. That could give you a mass figure but its usually not something calculated on the satellite itself. Its going to be a big hairy calculus program sitting in somebody's Core i7 laptop or a gnarly old mainframe somewhere. My guess is that somebody has been keeping track of the mass since they figured out decades ago that Pioneer and Voyager weren't where they were supposed to be. They just couldn't figure out why.

I've been reading stories about this for a long time and its a puzzle that shows how intrinsically inter-twined all the various forces in the universe are. Even solar wind at one point was added into the mix. Dark matter was also invoked in one article I read. At least the physicists weren't blaming it on little green men!

BTW the biggest change in mass is the hydrazine thruster fuel. If Pioneer or Voyager gets hit with a significant sized rock, like a one oz pebble, things get weird fast.

Is there anything else humans have designed with moving parts that runs for ~31 years with ZERO maintenance? It may be one of the greatest engineering feats of mankind, right along side the Hoover Dam and Boston's Big Dig... Design a craft that will operate in the harshest environments and can't be maintained mechanically. 31 years later it is still running. Too bad it is going out of range and when are we going to build a space ship to go looking for it after it crashes into a planet and becomes sentient?

I'm not gonna dismiss the engineering feat, but I wouldn't call space the harshest environment for machines: mostly empty, no pesky oxygen to turn it to rust, not many external forces (such as pressure or wind) to stress test it...Even the rather cool temperature might be to your advantage, because it seems (but I may be mistaking) that generating heat is easier than dissipating excess heat.

Yea, but isn't it very difficult to dissipate heat in space? Since you can't rely on thermal transfer because there is effectively nothing to transfer the heat to.

Voyagers use thrusters to stay pointed at earth whereas pioneer was spin stabilized. Basically the effect is impossible to measure on voyager because of the uncertainty of the impact of the thrusters is way higher.

Right, but Pioneer has thrusters too. I imagine it's fuel is all spent at this point, and possibly not configured/pointed for acceleration, but for reorientation for taking measurements.....Looking on Wikipedia;

Quote:

Pair one maintained a constant spin-rate of 4.8-rpm, pair two controlled the forward thrust, and pair three controlled the attitude.

Kressilac wrote:Is the craft's mass trasmitted regularly? Chips, dents, chemical reactions on its surface, what have you would seem to change the mass of the craft over 30 years.

Only way I know to calculate the mass is to cause the spacecraft to move either with a carefully calibrated thruster or a magnetic reaction wheel/gyroscope. Fire a thruster with a known amount of fuel or make an attitude change, calculate relative movement by measuring change of apparent position or attitude by observing stars. That could give you a mass figure but its usually not something calculated on the satellite itself. Its going to be a big hairy calculus program sitting in somebody's Core i7 laptop or a gnarly old mainframe somewhere. My guess is that somebody has been keeping track of the mass since they figured out decades ago that Pioneer and Voyager weren't where they were supposed to be. They just couldn't figure out why.

I've been reading stories about this for a long time and its a puzzle that shows how intrinsically inter-twined all the various forces in the universe are. Even solar wind at one point was added into the mix. Dark matter was also invoked in one article I read. At least the physicists weren't blaming it on little green men!

BTW the biggest change in mass is the hydrazine thruster fuel. If Pioneer or Voyager gets hit with a significant sized rock, like a one oz pebble, things get weird fast.

Wouldn't it be easier to simply calculate the amount of space-time displaced by the satellite when approaching the nearest gravitational well? I mean, that's how Archimedes would do it.

Or, if you want to be pedantic, wait until it enters the closest black hole and calculate the change in diameter of the event horizon. Then translate the informational-represented surface area to mass...and voila! Easy-peasy. That's how Susskind would do it.

Is there anything else humans have designed with moving parts that runs for ~31 years with ZERO maintenance? It may be one of the greatest engineering feats of mankind, right along side the Hoover Dam and Boston's Big Dig... Design a craft that will operate in the harshest environments and can't be maintained mechanically. 31 years later it is still running. Too bad it is going out of range and when are we going to build a space ship to go looking for it after it crashes into a planet and becomes sentient?

I'm not gonna dismiss the engineering feat, but I wouldn't call space the harshest environment for machines: mostly empty, no pesky oxygen to turn it to rust, not many external forces (such as pressure or wind) to stress test it...Even the rather cool temperature might be to your advantage, because it seems (but I may be mistaking) that generating heat is easier than dissipating excess heat.

Yea, but isn't it very difficult to dissipate heat in space? Since you can't rely on thermal transfer because there is effectively nothing to transfer the heat to.

True. The most effective way to reduce heat in space is to vent internal gas or fluid. Obviously that's not an option here.

Pioneer 10's power plant design was required to last for a minimum of two years in space, but the craft was still traveling and transmitting on January 23, 2003—30 years, 10 months, and 22 days later—when the signal became too weak to pick up on Earth. It was 80 AU (12 billion kilometers) away, at the edge of the solar system.

This sort of makes me sad... I wish we had sent (increasingly smaller, cheaper & more capable) probes along a similar path every ten years or so, so we could have a chain of repeaters boosting the Pioneer signal back to us.

Matt Ford / Matt is a contributing writer at Ars Technica, focusing on physics, astronomy, chemistry, mathematics, and engineering. When he's not writing, he works on realtime models of large-scale engineering systems.