Casa di Mir Summer Mathematics: Adventure #4

Star Party

Have you ever looked at the stars and planets through a telescope? You can do just that at a local star party, sponsored by the San Jose Astronomical Association, and guess what? Stargazing is actually quite mathematical!

There are a number of opportunities this summer. For dark sky viewing, you can attend a Starry Nights Star Party at Rancho Canada Del Oro Open Space Preserve in Morgan Hill on July 15th. For something a little closer to home, you can attend an In-Town Star Party at Houge Park in San Jose on July 14th.  You can see the details for these events, including star party etiquette, at SJAA’s website.

Where’s the math?!?!

For the littlest tykes, this could be an opportunity to use the compass directions, north, east, south, west, in a real-world setting. If you do a little prep work on the constellations (see http://liebacklookup.com/printables/), then your child can look for them in the night sky. Or, forget the constellations, and simply ask your child, “What do you notice?  What do you wonder?”

For slightly older kids, this is an opportunity to think about angle measures or perhaps fractions of full turns (if they haven’t yet learned about angle measure). If you start with your body facing north, about how many degrees (about what fraction of a full turn) must you turn clockwise, to face a particular star or planet? If your body is facing that star or planet and your gaze is on the horizon, about how many degrees (about what fraction of a full turn) must your gaze turn upward from the horizon to look at it? 

For example, on June 20 from San Jose, we saw Jupiter for a good part of each evening. It reaches its highest point (its meridian) in the night sky at about 8 pm. Where is it in the night sky at that point?  Its direction is about ½ turn clockwise from north (180° clockwise from north, also known as south) and its altitude is about ⅛ turn upward from the horizon (45° from the horizon).  Take a look at the website https://www.timeanddate.com/astronomy/night/usa/san-jose to find out what other planets you can see in the night sky from San Jose tonight. 

The oldest kids can think about the apparent brightness of the stars. It turns out that astronomers have figured out a way to quantify the apparent brightness of celestial objects. Instead of pointing and exclaiming, “Wow! That star is really, really, super-duper bright – much brighter than that other one right next to it,” they have devised a systematic way to measure the brightness numerically. Taking the star Vega as the anchor for the apparent brightness scale (Vega is taken to have apparent brightness 0), some objects appear to be dimmer than Vega (Polaris = 2, Saturn at minimum brightness = 1.5) while other objects appear to be brighter than Vega (Sirius = –1.5, Jupiter at maximum brightness = –3, full moon = –12).  Look at that – another use of negative numbers!

Would you like to get a preview of the night sky? There is a free, open source software program called Stellarium available for download. It is essentially a planetarium for your computer that shows “a realistic sky in 3D, just like what you see with the naked eye, binoculars, or a telescope.” See www.stellarium.org to find out more about this amazing product.  

Happy stargazing!

About the author: Trisha Bergthold has been the middle school math teacher at Casa di Mir Montessori School since 2014. She holds a PhD in mathematics with emphases in curriculum and pedagogy. Prior to her work at Casa di Mir, she designed curriculum for kindergarten through college level. She also taught university-level mathematics courses for sixteen years.

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