Fermi Problems--Saturn’s Cassini rings, rocks and size

On April 8, 2009, some people were looking at photographs just returned from the Cassini spacecraft in orbit around Saturn and they noticed something extraordinary and heretofore never seen: rocks in the rings! What follows is my shameless plagiarization of Emily Lakdawalla’s analysis, paraphrased in Fermi problem format, found on “The Planetary Society Blog” for April 13, 2009 (“Moon shadow, moon shadow” at planetary.org/blog/article/00001909/). 

The photo from The Cassini Equinox Mission shows a long, dark, pointed shadow cast by the moon Mimas.  Look along the left edge of this shadow at the edge of the bright ring where it abuts the black ring.  Look closely!  See the ragged little features like snow plowed up along a street?  Those are the rocks.

The Fermi problem of interest is: “How big are these rocks?”

NASA gives a distance of 1,141,262 kilometers from the rings when Cassini took the photo.  They also tell us the camera resolution is 60 micro radians.  The product of these two numbers is roughly 7 km/pixel. 

It is well known from astronomical tables that in a couple of months Saturn’s rings will align with the sun, so our second piece of Fermi data is that the shadows cast by the rocks on the bright ring are very long because the rings are only 1.9 degrees away from pointing directly at the sun. 

Counting the number of pixels in the longest shadow (this is something that can be done, but we’ll just assume the given value is right) we get 15 pixels which works out to 15 pixels times 7 km/pixel or 105 km.

Now the Fermi calculation. If the sun is 1.9 degrees up in the ring’s sky and the shadow is 105 km long, then the trigonometric tangent of 1.9 degrees times 105 kilometers is 3 km.  The height of the rock is 3 kilometers…that’s a pretty significant rock!

NASA photo reference and caption:

(http://saturn.jpl.nasa.gov/photos/raw/rawimagedetails/index.cfm?imageID=188106)