So while golfing, I noticed that the shadows of my golf balls looked like perfect ellipses. However, I thought about it, and this seems like a very sketch claim. If we consider the ground to be a perfectly flat plane, and the sun to be a point source infinitely far away, is the shadow created perfectly elliptical? Or is it slightly skewed away from the ball (personally this is my thought)? Or is this skew virtually 0.

## Comments

Sort by:

TopNewestThis is a perfect ellipse as ellipse is formed by stretching a circle. – Aditya Kumar · 1 year, 1 month ago

Log in to reply

Just don't get too distracted by the ball's shadow, @Trevor Arashiro ; you'll end up taking a huge divot. :P – Brian Charlesworth · 1 year, 1 month ago

Log in to reply

I imagined that if the light source was infinitely far away but was just as far from the plane as the tip of the ball, the shadow's tip would be infinitely far from the ball. However, if we looked at where the so called "ellipse" was widest, it would be a finite distance \(x\) away from the ball. If we take a slightly less extreme view of this, it would still be skewed right. – Trevor Arashiro · 1 year, 1 month ago

Log in to reply

– Brian Charlesworth · 1 year, 1 month ago

Since the sun is in essence an infinite light source we can consider the incoming rays to all be parallel. If they were parallel to the plane of the ground then the shadow of the ball would only be seen on a vertical surface place behind the ball. If the incoming rays are at an angle then the relative proportions of the ball, (which as an obstacle to the light is the same as a disc), will be projected onto the ground linearly to create a perfect ellipse. I could still be wrong, so keep looking at shadows to find an exception. I'm surprised that an extensive google search has come up empty; it seems like such a natural question to contemplate.Log in to reply

– Trevor Arashiro · 1 year, 1 month ago

Come to think of it, the one case that I was thinking of was the extraneous case. We're simply looking at the cross section of a plane passing through a cone at an angle which is of course an ellipse.Log in to reply

Nice observation! Good meat to ponder upon :P – Nihar Mahajan · 1 year, 1 month ago

Log in to reply