This fun little video came across my computer screen not long ago:

It comes from the European Southern Observatory and contains 20 years of observations of the galactic center of the Milky Way.  Over this period, about 20 stars have been observed to travel in small orbits, moving quite quickly at some points in their orbits.

Near the center of the screen, one star makes a complete orbit over the duration of the clip and it is very clear when the star is farthest and closest from the focus of its elliptical orbit. Even though the focus is a black hole and not another star, let’s call the furthest distance apastron, and the closest, periastron.

The star moves quite quickly during periastron and just like comets in our own Solar System, which spend most of their time far from the Sun where they travel more slowly, this star spends most of its timer far from the black hole.

Notice that nothing is visible at the focus of this orbital ellipse.  Yet, there must be a great deal of mass there, to pull a star around in an orbit with a period of only 20 years.

Students can use these data to calculate the mass of the black hole at the center of the Milky Way Galaxy.  We show them how in Learning Astronomy by Doing Astronomy; Activity Number 29.  This video makes a great supplement to that activity!

By Stacy Palen

Summary: The Kepler mission, after at least one resurrection, has finally come to an end. During its 9.5 year “lifespan,” Kepler discovered more than 2,500 planets around other stars and changed our minds about how common planets actually are.

Article: https://www.sciencenews.org/article/planet-hunting-kepler-space-telescope-dead?fbclid=IwAR0iYMK2_9-tbCgb91JxpFVpLR9MCOgRpC7BxodF69P45Hhtq2_trWv4_4I

Questions for Students:

1. Study the graph of Exoplanet Discoveries. The yellow dots show all the planets discovered by Kepler. Compare the sizes of these planets with those discovered before and after Kepler.

Answer: Kepler discovered smaller planets than those discovered before or after.

2. Study the graph of Exoplanet Discoveries. This graph shows that very few planets have been discovered with orbital periods smaller than one day. Why might this be?

Answer: This is as close as a planet can get, even to a small star, and still be in a stable orbit.

3. Study the graph of Exoplanet Discoveries. This graph shows that few planets have been discovered with orbital periods larger than about 300 days. Why might this be?

Answer: This could be a selection effect. Kepler uses the transit method to detect planets, but planets with large orbits are much less likely to cross in front of the star; our line of sight must lie exactly in the plane of the orbit to see the planet transit. The idea that this is a selection effect is supported by the observation that planets with long periods have been detected by other methods (the blue and gray dots), but not by Kepler.

4. Prior to the Kepler spacecraft, the percentage of stars with planets was unknown. Now that Kepler has completed its mission, do astronomers think this number is large, with many stars having planets or small with few stars having planets?

Answer: This percentage appears to be close to 100%. “…astronomers have used Kepler’s exoplanet haul to predict that every one of the hundreds of billions of stars in the Milky Way should have at least one planet on average."

5. Comment on the impact of the Kepler mission on the Drake Equation.

Answer: The second term in the Drake Equation is the fraction of stars with planets. This term is now quite likely to be nearly one, whereas before the Kepler mission, its value was only speculative.

By Stacy Palen.

I have a TON of math-phobic students in my classes. I teach at an open-enrollment university, where the majority of students test into Developmental Math. Many of these students have such poor math skills that they are enrolled in Math 0950, which begins with counting and the number line and culminates with percentages.

We have no structure here to make sure that these students pass their quantitative literacy classes before they take astronomy.

I feel quite strongly that everyone can do basic math. More importantly, everyone should. If their numeracy does not improve, these students will be taken advantage of by banks and credit card companies and salespeople and loan officers with every major (or not so major) purchase, all the rest of their lives.

I can make an argument that is compelling to myself that the financial crash of 2008 was caused in large part by people who did not understand how to calculate mortgage payments. So the lack of numeracy in the population has larger implications than just whether they score well on an astronomy exam.

Because I don’t want to send the students out the door like lambs to the slaughter, but I simultaneously don’t want them to hate me, I’m always on the lookout for tips and tricks about learning things that are hard.

Ages ago, I learned about the “growth mindset.” That’s the idea that success comes from working hard at things, rather than innate talent.

Focusing on growth mindset turns out to be particularly useful for underrepresented groups, who for better or worse don’t see the talent route as available to them. People in underrepresented groups often internalize this. They think: if people “like them” were “naturally good” at x, more people like them would do x.

When you want to encourage students, it’s hard to think of a quick motto that encapsulates all this. And it’s not always obvious how to make use of the idea that maybe students just need more practice to feel proficient.

This is why I recently took note of this article in the New York Times, about learning patience.

The author of the article makes the point that “patience, the ability to keep calm in the face of disappointment, distress or suffering, is worth cultivating.”

I could instantly see how a more patient person would do better with mathematics than a less patient person, especially if they had learned to fear math. There’s a lot in the article about how to interrupt the function of the amygdala, which is the part of the brain that stimulates that frantic, impatient reaction to everyday frustrations like slow-moving cashiers or slow-loading web pages. Or calculator malfunction. Or algebra. It’s worth a read.

But the thing that caught my eye was this motto: “Train, don’t try.”

Mathematics is not a matter of sheer willpower: just trying harder will not make you numerate! Instead, students need to systematically practice problems of gradually increasing difficulty -- repeating as necessary -- until their ability grows and develops, just like a muscle would.

This is why I insist that they do math in my class, and it’s why I start them doing it during lab time when I (and their peers) can give them pointers on their technique and their methods.

So I’m going to try the experiment of explicitly pointing out the connection between developing patience and developing math skill. And I will encourage my students to “Train, don’t try.”

I bet I will have to try it more than once to get it right.