## Friday, January 28, 2011

### Space Shuttle Math

Today's the 25th anniversary of the explosion of the space shuttle Challenger.  Do you remember where you were?

I was in the 5th grade and was at a different school for my weekly Enrichment class (which I hated, btw).  The kids from that school got to go watch the launch but we didn't (boo).  They came back just after it happened, told us the news, and then we got to turn the tv on.  (I'm still bitter about that.)  I wanted to be an astronaut so that was a huge deal to me.  And now that I'm a teacher I see the other side of it.

The kids in my Algebra 1 class are mostly freshman (with a couple of exceptions), so I knew that this event was just something in a history book to them.  I started class today by showing them this video:

They were pretty respectful (especially for them) and listened quietly.  We talked a little bit about it - I told them my background and what a big deal it was at that time.

Then one of my girls was wondering how far up they were when the shuttle exploded.  (Hmm... math anyone?)  The video didn't say, but it did tell how fast they were going and one boy told me that it happened something like 45 seconds into the flight.  We did a little work and decided they were about 23 miles up(though it probably wasn't going straight up... ).  We then did some work with google (and wikipedia) and found out that it was more like 73 seconds.  That changed our answer a little bit. (!)

The video shows a clip of John Glenn speaking - it turns out that none of the kids know who he is.  (Keep in mind that I'm in Ohio and he was one of our senators for 25 years.)  I told them that he was the first man to orbit the earth "Wasn't that Neil Armstrong?" someone asked.  Then we started talking about orbiting the earth.  How long exactly does that take?

Before we went about finding out, we made a list of what information we'd need to know.
1.  How fast does a space shuttle travel in orbit?  (17,500 mph)
2.  How far does it go?  (The distance around the Earth.)
3.  But what's the distance around the Earth?  (The circumference.)
4.  What do we need to find the circumference?  (The radius.)

One helpful boy with a calculator did a little figuring and determined that it would take approximately 1.42 hours for a shuttle to orbit the Earth.  Wait.... is that right?  Less than 1 1/2 hours?  No way.

So something must be wrong.  We did a little refiguring.  The space shuttle doesn't travel on the Earth like we do, it's several miles up.  Google to the rescue again - how high is a space shuttle in orbit?  The first resource I found said 115 - 400 miles (quite a range) so we decided to use 250 miles.

More calculations.

Our new time?  1.51 hours.  Those extra 250 miles don't make that much of a difference when you're going 17,500 mph!

To check (because I wanted to show them that we were doing some legit math and having fun at the same time), back to google.  How long does it take for a space shuttle to orbit the earth?

Answer (from here):  The Shuttle orbits the Earth in LEO at about 17,500 mph. Which means it makes one full orbit about every 90 minutes.  The shuttle crew will see about 16 Sunrises in a day.

I'm going to consider this a successful class.  Who cares that we didn't get to talk about writing equations of lines?  :)

(PS - I found this interesting:  "Media coverage of the accident was extensive: one study reported that 85 percent of Americans surveyed had heard the news within an hour of the accident."  Nowadays that would be slow (with twitter and the internet and such) but 25 years ago I'm sure that that was fast!)