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Before there was Angry Birds Space, there was Pioneer 10

April 24, 2012

A couple of weeks ago, Rhett Allain wrote a beautiful post about why he continues his quest to figure out the physics of Angry Birds Space, which is a must read: Why do I love Angry Birds Analysis.

I think Rhett’s analogy is spot on, and I want to dig into a bit more detail about the Pioneer 10 anomaly and the comparison with Angry Birds Space—since these two situations are far more similar than you might think.

But lets start with little diversion from Richard Feynman, about another game, Chess, and how it is an apt analogy for science.

I love Feynman’s analogy. Science is a game. More precisely, it’s about learning the rules to the game, just by watching the game, and now, thanks to computers, setting up model games of our own.

Now what’s the connection Angry Birds Space? You launch a bird from a planet using a giant slingshot, and the bird moves along a trajectory. How does the game know the trajectory of the Birds? It calculates it knowing that the current velocity of the bird will tell us the future position of the bird a small time step in the future.

future position=current position + velocity * delta t

If delta t is small enough, the computer can make a very accurate calculation of the next position. But how does the program calculate the velocity? It uses a similar idea, along with Newton’s second law, \vec{a}=\frac{\vec{F}_{net}}{m}.

future velocity = current velocity + Fnet/m*deltat

So in order to predict the future position of an object, given its current position, all we need are its current velocity and the forces acting on that object. If we can always calculate the forces acting on the object as it moves through space, we can predict the position. This works easily for Angry Birds, since the game designers decide exactly what the forces of the slingshot, planets and atmosphere will be, and code these forces into the program directly. This is the beauty of programming—the game designers are literally playing god in creating the Angry Bird universe and defining the laws that govern the motion of objects.

As players, we can’t read the laws that govern Angry Birds Space directly, we must deduce them through experiment—this is the science Feynman describes. This makes for a fun game for scientists like Rhett who like a good mystery. The program doesn’t tell us the forces, but if you carefully measure the trajectory of the Birds, you can begin to make some conclusions about the forces in Angry Birds Space. And then, if you’re super cool, you can use your conclusions about these forces to build your own model universe to calculate the trajectories of the birds and see how they match up to the ‘reality’ of the game.

Here’s an example of just what a wizard like Rhett can produce:

And as Rhett says, this is a fun exercise, much like indoor climbing, and if you really get stuck, you know that there’s someone you can turn to (the game designers) to help you out.

But the real fun happens when you start climbing on a real rock, and to understand what a real climb looks like in physics, we need to understand a bit more about Pioneer 10 and 11. These are robotic space probes launched in the early 1970s to explore the outer planets of Jupiter and Saturn, and ultimately escape the Solar System. The trajectory of the space probe is very similar to that of an Angry Bird, the launch by rocket is accelerates the spacecraft up to a particular velocity, and from there onward, with the exception of small course corrections made by thrusters, the trajectory of the space probe is determined by the gravitational forces from nearby masses, like planets.

That we can launch a space probe on a trajectory that has it pass just by a planet-moon system 800 million km away, speaks to the incredible understanding we have of “rules” of gravity and motion. But, as Feynman discusses in the video above, scientists are also always on the lookout for small signs that they may not have a full understanding of the rules of the game. In this case, it’s the observation that when measuring the velocity of Pioneer 10 using a doppler shift of its radio signal, scientists can’t account for \left(8.7 \pm 1.33)\right)\times10^(-10) \textrm{m/s}^2 of acceleration. Again, that such a seemingly small acceleration can be measured, considering the measurement is made from an accelerating platform (the earth) is a real testament to the power of science and the precision of our ability to measure quantities like the acceleration of the earth, which affect this measurement—out ability to observe the game.

Scientists have spent the past decade trying to account for this anomaly. In a move very similar to Rhett’s attempts to figure out the frictional drag on the angry birds, scientists have attempted to model some unknown drag force acting on the probe, or perhaps that the gravitational force is slightly stronger at those distances. Each of these possible explanations has been disproven with further experiments, such as measuring that Pluto does not experience a similar effect.

One of the most promising explanations of the anomalous acceleration was the possibility thermal radiation from the spacecraft’s main equipment compartment was reflecting off the back of the antenna and causing a very small acceleration toward the sun, tending to slow the spacecraft, as shown below.

But in order to test this idea, scientists needed to develop a computational model of the heat transfer of the spacecraft. And this makes a nice connection with the world of video games. It’s a pretty common problem in modern video games to need to model the how objects are illuminated in a virtual world. Current games now explicitly model this using a technique called Phong Shading, which divides objects into tiny polygons, and the calculates the reflection of light off of each of these small polygons. Both Phong Shading and the computational method for calculating position above illustrate the general approach to computational modeling. Take something complicated (the path of the spacecraft over a long period of time, or thermal reflection off of the back of the curved antenna), then break it apart into many small bits (tiny time steps, or tiny polygons on the antenna). Each bit can be described by simple physics (constant forces, or simple reflection), and a computer can then sum all of these bits to determine the overall result(the complete path of the spacecraft, or the total force on the space craft due to thermal reflection).

For our real Angry Birds Space problem, Pioneer 10, we not only need a computer to help us model the path of the spacecraft, we need a computer to help us model the possible forces that are acting on the object, and when we do this, we find our models, based on physics we understand fully, predict the path of the spacecraft completely within our current measurement, or as Francisco et. al. put it in their paper:

With the results presented here it becomes increasingly apparent that, unless new data arises, the puzzle of the anomalous acceleration of the Pioneer probes can finally be put to rest.

This is why Rhett’s work with computational modeling and Angry Birds Space is so interesting—it bring challenging and current problems like Pioneer 10 to physics students at the introductory level, and teaches students the same tools of computational modeling that are used even in the most complex problems. With the Pioneer anomaly solved, Angry Birds Space seems to offer plenty of mystery to keep physicists busy.

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