# Scaling the Solar System

Too often, people throw around numbers without even thinking about the tremendous differences in the scales of those numbers.  Here’s the result of an exploration I did this week with my  afternoon math club of 4th and 5th graders to get a perspective on just how big our solar system really is.  They call themselves $mc^2$.

My school has an three foot diameter iGlobe in the middle of its lower school entry hall.  The group decided to see if they could use the school’s iGlobe to create a scaled model of the solar system.  After some quick research, they learned that the earth was about 8000 miles in diameter and the sun was about 875,000 miles wide.  I challenged them to put that in perspective.

They first tried to think in terms of the iGlobe model they already had.  Some quick division convinced them that a relatively sized sun would be about 109 iGlobes wide.  When I asked them how they could get a handle on just how big that was, one suggested measuring off 109 iGlobes across the field outside.  That’s when another realized that 109 iGlobes = 109 yards = about one football field plus an end zone.  Eyes widened.  After all, the sun doesn’t look nearly that big in the sky!

Since we couldn’t move the iGlobe from its perch, I asked them to come up with a different way to relate these sizes.  That’s when one student realized that if we could call the iGlobe our unit, why not any other object?  He grabbed some Cuisenaire rods, called the Earth one of the square centimeter singles, and started explaining.

OK, that was a nice connection and it gave the students a chance to get some perspective on the size of the Earth.  But I still wasn’t convinced they really got just how enormous the scales were here.  That’s when I asked if they could use the same Sun-Earth model to place the Earth cube in its proper relative position to their Sun diameter.  They found the average distance from the Earth to the Sun (93 million miles), converted that to their new scale, and paced off the distance. NOTE:  It gets pretty small at the end, so I recommend a full-screen view, but it will still be pretty small.

At the end of the video, it’s very difficult to see the running student throw his hands in the air, much less the little tiny Earth cube he’s still holding.  But that’s the point.  Distances across our solar system are mind-bogglingly large.  Sending probes from our little Earth cube to any other object requires a tremendous feat of engineering.  Maybe this is a good first step in helping these students come to grips with the enormity of the scaling of the universe.