Saturday, January 23, 2016

Becoming Banneker: Making Movements in Space Meaningful on Earth

As I wait for the blizzard to end here in Stewartstown, I thought I would do another blog post about the latest unit I just completed.  So let's start with the performance expectations for this unit.   Using the topic based arrangement- "Space Systems: Stars and the Solar System".

Students who demonstrate understanding can:

5-PS2-1. Support an argument that the gravitational force exerted by Earth on objects is directed down. [Clarification Statement: “Down” is a local description of the direction that points toward the center of the spherical Earth.] [Assessment Boundary: Assessment does not include mathematical representation of gravitational force.]

5-ESS1-1. Support an argument that differences in the apparent brightness of the sun compared to other stars is due to their relative distances from the Earth. [Assessment Boundary: Assessment is limited to relative distances, not sizes, of stars. Assessment does not include other factors that affect apparent brightness (such as stellar masses, age, stage).]

5-ESS1-2. Represent data in graphical displays to reveal patterns of daily changes in length and direction of shadows, day and night, and the seasonal appearance of some stars in the night sky. [Clarification Statement: Examples of patterns could include the position and motion of Earth with respect to the sun and selected stars that are visible only in particular months.] [Assessment Boundary: Assessment does not include causes of seasons.]

As you may recall, the two questions I filter all curriculum through are:

  • Why am I doing this?
  • What will it help me to do?
If this is the starting point, what are the practical application for students  in Baltimore County?  As it turns out, there has been (and still is) a very practical application- calculating location.  For hundreds of years, people have used the stars and Sun as a guide.  It also turns out that Baltimore County had a local expert on the subject.  

In 1731, Benjamin Banneker was born and through his own study became an expert surveyor. Eventually, his skills were recognized by Andrew Ellicot and Mr. Banneker became part of the an important survey team.  The team that would eventually layout Washington, D.C.   

Mr. Banneker was able to use Polaris to measure latitude and the movements of Jupiter's moons to measure longitude.  The precision he was able to achieve with his tools and techniques could be measured to within a meter.   For comparison, the first GPS I used for recreational purposes was +/- 3-5 meters.   

So, here is how it works.   Latitude is easy.  Measure the angle of Polaris off the horizon using a sextant or clinometer and you have the latitude.  Finding Polaris gets me into comparing star magnitudes and which stars are visible at certain times of the year.  Two great resources to help show students the stars during the day.  Stellarium and Celestia  offer the opportunity for student to control time (#DoctorWho).  

Longitude is and has historically been the chief problem.  With latitude, you have a starting point called the equator.  Longitude has no natural starting point.  The prime meridian is an artificial starting place.   However, if you know when something happens in Greenwich and can see it happen where you are, then you can find longitude by finding the difference in time.  

Mr. Banneker would use an ephemeris of Jupiters' moons.  The ephemeris allows the user to know when one of Jupiter's moons is coming out of eclipse.  Observing Jupiter requires at least a six inch telescope.  It also requires a night sky.  These are problems given the confines of school hours and budgets.  

For my students, we will use Solar Noon.  Solar noon occurs at 12:00 only twice during the year. Beyond that, it ranges widely 16 minutes +/ - from 12:00 depending on the time of the year.  This relates to the "Equation of Time".   So how do you find Solar Noon?  At Solar Noon, the Sun produces the shortest shadow of the day.  See the complicated device (below) for measuring that shadow.  This picks up the performance expectation on the length and angle of shadows.  

This leaves the PE on gravity.  This one took me a while to figure out.  I shows up in two ways in the unit.  First, I did go a little beyond the standards by asking the question "Why is everything spinning in space?"  I could not resist a model which demonstrates this phenomena so elegantly.  

The second way is through measuring time.  Benjamin Banneker reverse engineered a clock from a pocket watch he borrowed.  His hand-carved wooden clock used a simple weight pulling down on a spool controlled by an escapement to regulate time.  The development of accurate clocks is what finally made it possible to measure longitude.  

About six minutes into the video above, you will see the host build a clock out of raw wood pieces.  I found a version of the same thing on Thingiverse.  It was interesting to get it working.

In the performance assessment, students are responsible for calculating their location to the nearest full degree or about 111 km of their actual location.  More importantly they have to explain how they calculated the location.  

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