Date: September 21st, 2012
Title: Math Power!
Podcaster: Bob Hirshon and Barbie
Organization: American Association for the Advancement of Science (AAAS)
Description: Ever ask your beleaguered mathematics teacher “What am I going to DO with this stuff in real life?” Mathematician Scott Turner, at the Johns Hopkin Applied Physics Laboratory, has no end of answers. To him, the better question is “What CAN’T you do with math?” AAAS Science Update host Bob Hirshon spoke with Scott about how he uses mathematics to tackle tough problems presented by interplanetary space exploration.
Bio: Bob Hirshon is Program Director for Technology and Learning at the American Association for the Advancement of Science (AAAS) and host of the daily radio show and podcast Science Update. Now in its 25th year, Science Update is heard on over 300 commercial stations nationwide. Hirshon also heads up Kinetic City, including the Peabody Award winning children’s radio drama, McGraw-Hill book series and Codie Award winning website and education program. He oversees the Science NetLinks project for K-12 science teachers, part of the Verizon Foundation Thinkfinity partnership. Hirshon is a Computerworld/ Smithsonian Hero for a New Millennium laureate.
Today’s Sponsor: This episode of 365 Days of Astronomy is sponsored by The Education and Outreach team for the MESSENGER mission to planet Mercury. Follow the mission as the spacecraft helps to unlock the secrets of the inner solar system at www.messenger-education.org
Barbie: My name is Barbie! What’s yours?
Hirshon: I’m Bob Hirshon, from the American Association for the Advancement of Science! And today, we’ll be talking about space exploration and mathematics.
Barbie: Math class is tough!
Hirshon: You know, Barbie, we may not agree on many things, but in this case, I think you’re right: math class CAN be very challenging. I know it was for me. But you know, you’re College Barbie. And from that fact, and just the tone of your voice, I can tell that you are the sort of toy that welcomes a challenge. And if your pull-to-talk string was just a little longer, I bet what you’d really say is “Math class is tough—but so worth it!”
Because the more you get into math, the cooler it gets, and the more useful and interesting it is. Scott Turner is a mathematician who works at the Johns Hopkins University Applied Physics Laboratory in Laurel, MD. That means he actually gets paid to work on solving challenging puzzles every day.
For example, he works on the dual camera system that’s flying aboard the MESSENGER Mission to Planet Mercury. Called “MDIS,” or Mercury Dual Imaging System, it has a wide angle and a narrow angle camera mounted on a rotating platform. Its job is to make a detailed map of Mercury’s surface, and also zoom in on interesting features that scientists want to study. But to do these jobs, it has to point right to where the scientists tell it to, and the images it produces have to be as close to perfect as possible. Otherwise, the map will be inaccurate, and the shape, color, and location of the features could be wrong. So one of Turner’s jobs is to calibrate the camera—find out how it varies from perfection, and come up with ways to correct the errors.
Turner: And the cameras, when we do our calibration, we’ll point them at star fields and take pictures of the star fields. And we know from observations here on earth very precisely where the stars are in the sky. So you can think of it kind of like the navigators used to use to figure out what their latitude is on the earth. They would solve math problems with physical devices that were built by people I imagine much, that do things like I do today, but back then, that would tell them if this star constellation is at this certain part of the horizon then therefore you are at this latitude on the planet.
Hirshon: In the case of MESSENGER, they already know exactly where the spacecraft is. But they need to find out how much the pictures its cameras are taking are off the mark.
Turner: We take this star chart that we have and we say here’s this picture and we look at how the stars match in the picture to the star charts that we have. And the mathematics behind that, there are lots of degrees of freedom that have to be solved.
Hirshon: By degrees of freedom, he means all the variables that might be causing a problem. For example, there’s the rotating camera platform.
Turner: Well, when you tell the platform to go to this position, the camera thinks it knows where it is, and it goes to a position that is quite close to that, but it’s not close enough to be able to say, well, I told you to go to 10 degrees therefore you’re at 10 degrees. I told you to go to 10 degrees, maybe it’s 9.8 or 9.9. And so there’s a device that’s in the pivoting system, the gimbal, the motor system that measures the rotation of that platform very precisely. But we have to calibrate that. And one of the things that we’re responsible for doing is making measurements that allow us to calibrate that. So what we do is we take pictures of star fields, we’ll put the spacecraft at a certain orientation, and then we’ll command the pivot to different locations and then we’ll take pictures of different parts of the sky, knowing that the spacecraft is fixed, its orientation is not changing when we’re doing this. And then we can measure very precisely where the pivot platform is from one image to the next, and that allows us to sort of calibrate in a relative sense the performance of this measuring device.
Hirshon: Then they can make adjustments to improve that one thing. But that’s just the beginning.
Turner: Okay, and I can take pictures of star fields and the way I think about that is you have a sphere around you that has all these points of light that are punched out on it, and I know really well what the coordinate system on that sphere is, and so if you point me in any direction, and I take a picture of that, I can work out where I’m pointed from there. And, but so you do that and you get your results back, and you see something and you say, there’s something not quite right about this. When I look at stars that are near the right edge of the camera field of view, they’re always off by a little bit toward the left. Why is that? So you go do a little bit of research and you read about it and you try to figure it out, and you come to find out, well, that’s optical distortion and the camera’s not perfect. And every camera has it, it’s just a question of how well—even if you have a very well designed camera, there’s gonna be some distortion that can show up. And so, okay, can we get rid of that?
Hirshon: And the way they get rid of it is through modeling—
Barbie: Do you want to be a fashion model?
Hirshon: Oh, Barbie, not that kind of modeling. This is very different—though roughly analogous. In fashion modeling, designers drape their clothes onto people to indicate how they will look on their customers. But they pick models with proportions that are very different than those of their customers, so the modeling that they do is not very predictive. The modeling that Turner does is based on real data showing inconsistencies in the MDIS cameras’ images, and has to be so accurate that the scientists can look at his model and confidently use it to predict what will happen in the future, and make adjustments to correct for it. In a way, fashion modeling is kind of fooling people into making bad predictions, while Turner’s modeling is helping scientists make good ones. His modeling gets tested and if he’s successful, he can actually see that he was right.
Turner: It’s very rewarding when you’re working out a solution because you’re sitting there and you see, okay, here’s where I think the alignment of the camera is, here’s where I think the distortion of the optics are, this is where I think the pivot platform is mounted, you kind of load all that up and you’ve got software that can say, that we’ve written, that can say okay, here’s a star picture, we know where we think the stars are from all of our modeling work, draw them on top of the star field. And when you do that it and it just lines right up then you know, it’s a pretty satisfying feeling.
Hirshon: Another challenge that Turner enjoys is coming up with mathematical solutions when things go wrong. For example, the Lunar Reconnaissance Orbiter, or LRO, has a radar antenna that shoots radio signals at the Moon, captures their echoes when they bounce back, and uses that data to create images of the moon’s surface. One goal is to look deep into craters near the Moon’s poles to see if there’s any water ice in them. The work was going well, but then LRO’s radar antenna transmitter broke, and stopped sending out radio signals.
Turner: And that would have been the end of the radar instrument, if not for the fact that one of the scientists we were working with suggested that we use the Arecibo Observatory’s radio telescope, which is the largest radio telescope in the world to transmit a signal at the surface of the moon, bounce off the moon to the spacecraft, into the receiver. And then we can make measurements of the surface much like we were before, except now that we’ve got this gigantic telescope on earth providing the source energy.
Hirshon: But now the source of the radio signals would be Puerto Rico, instead of lunar orbit. And figuring that out took math.
Turner: So what my role on that on the project is is that I wrote the software that points Arecibo at the target on the moon; it orients, decides how to orient the spacecraft, and works out how to operate the radar in the conditions that we need to be. So though it’s a different sort of challenge– it’s not a modeling problem, it’s more of a direct – you know, I know where the spacecraft is gonna be, I know how the Earth is rotating, I know where Arecibo is, I know where on the moon we want to look, and it’s coordinating all these things together, and bringing it all together and solving this fairly complicated problem.
And the way that works is that by looking at the—there’s an angle, and if you think of the Arecibo as a point in space, there’s some surf—point in the surface of the moon that we want to look at, and there’s the spacecraft. And if you think about the—it sort of forms a triangle in space, right? So the angle between Arecibo, the surface of the moon and the spacecraft we call the bistatic beta angle. In standard illumination methodologies that would be called the phase angle. And the idea is that if we can make that angle be small, like 2, 3, 4, 5 maybe 10 degrees, something like that, and make our measurements, the signature that we would see in the data for ice would be dis—we’d be able to discriminate it from rough rocky surface material on the surface.
Hirshon: He says that as complex as that sounds, most of the mathematics he uses comes not from graduate school, or even undergraduate college.
Turner: And it’s a lot of geometry, I guess it’s the stuff you learn in like tenth or eleventh grade in high school, sort of pre-calculus or analytic geometry and those kinds of things. It’s that kind of stuff that I’m constantly wrestling with. And you know there’s different things that you do there, and all the angles and all those crazy geometry theorems that you learned in school about, you know, here’s a triangle and I know this angle, how do I get this side, I do that kind of stuff all day long (laughs) on that project, so you know you’re sitting in class when you’re in high school thinking to yourself, “when am I ever gonna use this?” And, well, here I am today to tell you that if you go into the field I’m in, you’ll have an opportunity to use it. It’s a little surprising, but that stuff is things that I wrestle with on a daily basis.
Hirshon: And it’s not just useful for aiming the world’s largest radio telescope at the moon and bouncing radio waves off it—he says the sort of work he does is also critical in engineering and design, in medical and health studies, in economics—even in planning transportation routes. All areas with tons of rewarding job opportunities.
So, Barbie, what do you say?
Barbie: Help me get ready for my date!
Hirshon: Oh, you’ve got a date, huh? Well, not to sound like your dad or anything, but I hope it’s a study date. You know, you really want to make the most of your time at college…
Barbie: College parties are super fun!
Hirshon: [Sigh] Well, that’s all we have for you this time.
Barbie: I’m Barbie!
Hirshon: And I’m Bob Hirshon, for the 365 Days of Astronomy.
End of podcast:
365 Days of Astronomy
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