Re: How can 10 year olds measure the distance to the moon?

Ten year olds can measure the distance to the moon by teamwork!!!

The basic idea is to use triangulation.  Have students group together in 2
or 3 person teams.  I would suggest having them work on a practice object
like a street light.  This method works for objects along the ground also, if 
you want to include that exercise as a easier pre-warmup.

Equipment needed:
Protractor.
tape measure or string.
meter or yard stick.
paper and pencil.
graph paper.
ruler.
A street light or other high object.

Student A stands somewhere around 40 feet from the street light and looks at 
the street light over his shoulder like an archer and points the meter stick
at the light with a straight arm.  The teammate, Student B measures the angle
between student A's body and the arm.  This probable best accomplished a few feet
away.  Record this angle.  Mark the spot where student A is standing.

Now move on to another spot a considerable distance away from the first spot, like 100 feet.
It would probably work best to go to the other side of the street light, but 
you might allow the students to pick their second point with just some advice
from the teacher.  Do the same procedure as above.

The students need to measure the distance between the two points on the ground.
Have the students do a to scale drawing of their measurement setup on graph paper. 
It should be something like:

                   (o)
                 *  |  *  
               *    |    * 
             *      |         *  
           *        |             *
Point 1. ----------------------------Point 2.

1 square = 10 feet (for example)

Have them subtract 90 degrees from their angles measured.  And record those numbers.
This is for your check that they did the work.

The uniqueness of the ANGLE-SIDE-ANGLE triangle makes the problem solvable.
By solving the simple trigonometric equation they can solve this problem.  Now
I know 10 year olds don't do trig, but I think you could make it doable by making
it a graphical problem.  The perpendicular distance will give the height of 
the street light. 

You might point out this is how navigation can be done without
a compass.  


Of course, there will be errors.  These can be learning opportunities.  One
big error besides measurement errors, would be slant errors, if the object
being height measured is not directly over the line of the ground distance.
Discuss this with them.

Now they can move onto doing the same thing with the moon.  It will be harder, and 
more prone to errors, but getting the right order of magnitude would be a great
success.  And this method does not require measuring angle subtended of the moon, but rather
angle of inclination which will be greater than 10 degrees.

I would expect measurements to be within 20% for really good students.
The mean distance to the moon is 3.8 * 10^8 meters = 1.25 * 10^9 feet.

Try it.  You'll like it.  And it should work.

Sincerely,
Tom Cull
Backyard Physicist