ScienceFairs

One fine day I made my way into a middle school where I was to judge or evaluate school science fair projects. The usual procedure is: One shows up, fills out a form, gets a name tag, drinks some coffee, eats some pastry or strawberries, gets a clipboard with student names and project titles and evaluation sheets, and then one heads off to start looking at projects.

At one point during the day I wound up talking to a young woman about her astronomy project. She had (through the help of her parents) come into a database of stars--their locations and distances from earth--and she had also been handed a piece of analysis software which allowed her to plot the number of stars in different directions as a function of a single angle. She could also specify that the stars to be counted in making a plot must be within a fixed distance from the earth, a search distance limit.

Imagine living at the center of a disk of stars of radius R, a galactic disc in fact. Let's suppose that the stars are uniformly distributed throughout this disk. In the plane of the disk, varying the angle of observation from 0 to 360 degrees, a plot of the number of stars as a function of angle would be flat; there would be roughly the same number of stars in all directions in the disc. This would be the case for any search distance limit, but we can suppose it to be equal to R. This is the case where the search-angle disc corresponds with the disc of the galaxy and from the center things look the same in all directions, so the plot of number of stars as a function of angle is flat.

Now if one were to make the plane of the search angle perpendicular to the plane of the galactic disc (again with search distance limit R) then the plot of stars as a function of direction would have two big spikes in it 180 degrees apart from one another for when the direction angle corresponded with the plane of the galactic disc. If we look out perpendicular to the disk we see only a few nearby stars. If we look out into the plane of the galactic disk we see many stars.

Now suppose that this disc has a certain thickness t (much less than R). Instead of carrying out the second search described above using a search distance limit R, use a distance limit t. That means that any stars farther than t away are not used in making the plot. Since the disk is considered to be uniformly filled with stars, the plot will again be roughly flat. Make the search limit 2 x t and the plot will start to show those two bumps again.

Suppose you were to do make this plot many times, starting out with search limit R and successively reducing this value for each new plot. The first few plots will have the sharp double bump because the search limit will encompass the disc-geometry of the galaxy. But when the search limit reaches t the plot will become flat. Which means that the iterative technique of reducing the search limit until the plot is flat is a means of determining t, the thickness of the galaxy.

This is what she had done.

And she came up with the idea on her own.

And she got the right answer.