Date: February 7, 2010
Title: Retro Science: Determining the Eccentricity of the Moon’s Orbit
Podcaster: Mike Simonsen and Kevin Krisciunas
Organization: Slacker Astronomy
Description: Mike Simonsen from Slacker Astronomy interviews Kevin Krisciunas about his recent paper that describes how to measure the eccentricity of the moon’s orbit with a yardstick and some cardboard.
Bio: Slacker Astronomy is a light-hearted podcast that wanders the astronomical road-less-traveled. Visit us at http://www.slackerastronomy.org/.
Today’s sponsor: This episode of “365 Days of Astronomy” is sponsored by Kylie Sturgess of the Token Skeptic podcast, investigating superstitions and the science behind them at www.tokenskeptic.org.
Transcript:
Michael Koppelman: Hey everybody, hello again it’s Michael here from Slacker Astronomy. I’m here with Mike Simonsen. Hello Mike.
Mike Simonsen: Hello Slackers!
Michael: Welcome to the 365 Days of Astronomy Podcast and welcome to Slacker Astronomy – the other astronomy podcast.
You have a new interview for us and I’m so bad at saying names that I get chills when I see this guy’s name. But Kevin
Mike: Krisciunas.
Michael: Kevin Krisjunas?
Mike: Yeah, that’s close. [Laughter]
Michael: Tell us a little bit about Kevin.
Mike: Kevin is an astronomer, a lecturer at Texas A&M University. His current area of research is supernovae and studying them in the infrared in particular. The reason why I really wanted to talk to Kevin was because at heart, he’s basically one of us.
He’s an amateur astronomer at heart, or he started out that way. I don’t want to give away everything in the interview but basically he’s been able to live out a dream and work with some of the biggest telescopes and with some interesting instruments in his career.
Michael: Cool, let’s stop with the drama here and get right to the interview. Here’s Mike Simonsen with Kevin Krisciunas. [Laughter] Here we go.
Mike: Hi, we’re here today with Kevin Krisciunas, a lecturer at Texas A&M University, Department of Physics and Astronomy. You just released a paper where you determined the eccentricity of the moon’s orbit without a telescope.
Kevin Krisciunas: That’s right. When you teach Astronomy 101 you tell them about Kepler’s Laws of planetary motion. For most of the students this is the first time they’ve ever heard this. You emphasize that they have to know this for the test and so they memorize it. But it’s pretty abstract, especially Kepler’s third law relating to periods in the orbit size. It’s hard to remember that when you first hear it.
Kepler’s first law states that the orbit of a planet is an ellipse with the sun at one focus. Kepler worked really, really hard to show that it was mathematically an ellipse not an ovoid and not just a circle that is offset from the center. Every ellipse is an eccentric orbit but not every eccentric orbit is an ellipse.
I had it in my head that Hipparchus in the second century B.C. had actually measured the variation of angular size of the moon and of course he didn’t have a telescope so he would have used some counting device or a sighting hole moved up and down some equivalent of a yardstick to do this. It turns out Hipparchus didn’t do this and apparently hardly anybody else took any data relating to this. So, I have my students go try to measure the angular size of the moon.
One of the things they can do is measure the nearly full moon very low in the sky and high in the sky because one thing that many, many people “know” is that the moon is gigantic on the horizon and then it gets smaller. This is the thing called the moon illusion. None of my students have been able to measure that the moon is significantly larger in angular diameter when it is low towards the horizon and high in the sky.
I started to try to measure it myself about a year ago and finally it dawned on me that I should use my better eye, the one with less astigmatism. So the data with that eye since last April does show a regular and systematic increase and decrease of the moon’s angular size of just about the right amount.
The signal that I’m looking for is a range of about four arcminutes in angular size and the uncertainty of an individual observation with my better eye is about eight tenths of an arcminute. It’s sort of at the limits of my naked eye but it is doable.
Mike: Can you describe the instrument that you made to do this? Some of our audience might want to try this.
Kevin: Okay, here’s the easiest way to do just the moon experiment. Take a box of Aunt Jemima buttermilk pancake mix when it’s empty and take a razor blade knife and saw off the bottom inch of the box. Then take a yardstick that has one edge calibrated in centimeters and millimeters and cut 2 slots in the 2 long edges of the bottom of this box so that the box bottom slides snuggly up and down the yardstick.
Then take a thinner piece of cardboard, maybe an inch by two inches and punch a hole with a metal hole punch – it’s about a quarter of an inch. Then tape that to this thing that slides up and down the yardstick. That can be used to sight the moon.
But I will recommend that when you make these observations that you sit in a chair with both of your feet flat on the ground to make yourself steadier. It seems to be you get more accurate results if you measure the moon during twilight when the sky is still reasonably bright.
Mike: Hmm, so you actually hold the yard stick up to your eye and you sight the moon through the hole in this little sliding mechanism.
Kevin: Exactly, you put the one edge of the yardstick just at the top of your cheekbone underneath your eye and you sight through the hole. What I do is I put the cross piece considerably too close to my eye and then I move it out until it seems to match the moon. Then I move the cross piece to the far end and then I bring it in until it seems to match the moon. Then I average those two values.
Sometimes they differ by twenty millimeters and sometimes they only differ by two millimeters. It depends sort of on how high the moon is in the sky, what phase it is. I haven’t quite figured out exactly all the problems but it is doable without a telescope to come up with evidence that you can measure the right range of angular size of the moon.
There is one more wrinkle here and that is that your pupil is not infinitely small. In fact it is comparable in size to a hole made with a hole punch. So depending on the lighting level, twilight or daylight or nighttime, your pupil is going to be larger or smaller.
So one way you can calibrate your observation is to take a 91 millimeter disk. Cut out a circle 91 millimeters and place it at eye level exactly ten meters away from you and measure that. Why 91 millimeters viewed at ten meters? Because that has an angular size exactly equal to the mean angular size of the moon.
If you work out the simple geometry you’ll find that you probably have to place your sighting hole further from your eye than simple geometry would stipulate because of this effect of the non-zero size of your pupil.
Mike: Hmm, so it’s a little more complicated than it sounds at first.
Kevin: Yes, it’s a little more complicated than it sounds.
Mike: But it’s still surprising that no one, not even Tycho actually did this.
Kevin: Yeah because Tycho worked very hard on the orbit of the moon. But he was primarily concerned with matching the celestial longitude because apparently when the three-body problem of the sun, moon and the Earth has the moon further to the east and west at first and third quarter than you would guess on the basis of a simple orbit.
It turns out that the moon does not orbit the Earth according to Kepler’s first law of orbital motion and the Earth does not orbit the sun either. The Earth, moon barycentre orbits the sun on an ellipse. But the moon springs closer to the Earth than the mean value than it gets further away at apogee.
There was a big long article twelve years ago in the Reviews of Modern Physics by a guy named Gutzwiller I think is his name. There is more about the moon’s orbit in there than the average person might want to know but he is clearly an expert.
For example, the modern model of the orbit of the moon require between 600 and 900 and some terms in order to calculate the best value for the distance between the Earth’s center and the moon’s center.
Mike: [Laughter] It must be easier to just shoot a laser at the moon and bounce it off those little reflectors.
Kevin: Absolutely.
Mike: Well thank you very much Kevin. You’ve been great. I know that our Slacker audience is going to love listening to you. Anything else you’d like to say before we sign off?
Kevin: So long and thanks for all the fish? How about things are looking up? [Laughter] I know, Bugs Bunny said it best: “Don’t say it hasn’t been a slice of Heaven.”
Mike: Thank you [laughter] it definitely has been a slice of Heaven. Thanks a lot Kevin.
Kevin: Okay, bye for now.
This transcript is not an exact match to the audio file. It has been edited for clarity. Transcription and editing by Cindy Leonard.
End of podcast:
365 Days of Astronomy
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