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News from Mathnasium of Harwood Heights

Aug 16, 2017

Everyone is talking about the amazing eclipse on August 21st 2017. Kids are asking questions about the cosmic event that you may not know how to answer. Mathnasium of Harwood Heights is here to the rescue!

A total solar eclipse is when the moon appears to totally cover the sun. A partial eclipse means that part of the sun is still visible. That’s why you can’t look at the partial eclipse directly. The part of the sun that is uncovered will burn your eyes if you look directly at it.

If you are standing in the correct place on earth, at the correct time, the moon will block out the sunlight as it orbits Earth. Kids in will not experience a total eclipse.

How can a moon block the sun? Isn’t the sun much bigger than the moon?

Math Answer: The proximity (closeness) of the moon compared to the sun makes this possible. This is called “scale.”

Try this tonight, block out the moon with your thumb. Of course your thumb isn’t as big as the moon, but it appears that way because your thumb is closer to your face than the moon is. The same idea of scale applies to the eclipse. The moon is 400 times smaller than the sun but moon is 400 times closer to the earth than the sun is. That’s why the moon can block out the sun during a total eclipse.

Why is a total eclipse such a big deal?

Math Answer: The geometry of the sun, moon, earth, and viewer have to have just the right conditions. These conditions rarely occur.

Viewing a total eclipse depends on the proper alignment of the viewer, the earth, the moon, and the sun. “Alignment” means that objects are in a straight line. If they aren’t in a straight line, the moon will only partially block out the sun, or not at all. That’s why only a narrow portion of the earth (about 73 miles wide) will experience a total eclipse, and only for a few minutes. The moon and Earth will continue on their orbits and not be in alignment after a few minutes.

The moon travels in an elliptical, not circular, orbit around the sun. An ellipse is like an oval but the earth is not in the center of the oval. A total eclipse can only be seen when the moon is close to the earth, not when it is on the far side of the elliptical path.

How fast does the eclipse travel? Why doesn’t everyone see it at the same time?

Math Answer: The speed of the rotation of the earth and the moon orbiting around the earth create a fast moving eclipse.  But the shadow, or the “umbra” will actually slow down as it crosses from the west coast to the east coast.

Speed = distance/ time

If you are coming to Mathnasium of Harwood Heights from home and its 3 miles away and it takes you 4 minutes to drive here that is a speed of 45 miles per hour (MPH).

3 miles/4 minutes = 3 miles/ .066 hours (To convert minutes to hours 4/60 =.066) (3/.066=45) = 45 mph

Acceleration refers to speeding up and slowing down, so if parents are in hurry to get to Mathnasium they may step on the gas to accelerate the car. Then you might get to Mathnasium in 3.5 minutes instead of 4 minutes. Maybe they hit a little traffic on the way home and so they slow down, or decelerate.

Your average speed for the entire trip was still 45 MPH but it wasn’t at a constant speed. Sometimes you were going faster than other times.

6 miles/8 minutes = 6 miles/ .1333 hours = 45 mph

The moon orbits the earth at an average speed of 2,288 miles per hour. The moon doesn’t have a constant velocity. It accelerates as it gets closer to earth and decelerates, or slows down, as it moves away.

The shadow from the eclipse, known as the “umbra,” will travel at a speed of 2,240 MPH across Oregon. The totality of the eclipse there will last 2 minutes and 2 seconds. By the time the umbra reaches South Carolina the shadow will only be traveling at 1,479 mph, so they will get to experience totality for 2 minutes and 30 seconds.

We hope you enjoyed this mathematical explanation of the eclipse. At Mathnasium of Harwood Heights, we like to make math fun. We also make math make sense. Give us a call at 872-222-5042 to learn more about our program.  Please use these great sites for more information about math and the eclipse.

https://eclipse2017.nasa.gov/math-challenges

https://nrich.maths.org/6683

https://www.exploratorium.edu/eclipse/why-eclipses-happen

https://www.vox.com/science-and-health/2017/7/25/15925410/total-solar-eclipse-2017-explained

https://en.wikipedia.org/wiki/Elliptic_orbit

https://www.space.com/36388-total-solar-eclipse-2017-duration.html

https://www.globe.gov/web/eclipse/overview

Image Credit: NASA 2017 Total Solar Eclipse event page