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Off on a Tangent

A while ago, we made a LEGO robot with a light sensor on its nose. We programmed it to move towards a light. The program was pretty straightforward: if there was more light on the left, the robot turned a bit to the left; if there was more light on the right, the robot turned a bit to the right. In this way, the robot constantly adjusted its heading and moved towards the light.

At one point, someone took off the light sensor and accidentally put it back sideways, pointing to the robot's left rather than straight ahead. When we ran the original program, we were surprised to see the robot circling the light, rather than moving towards it.

Click Go. The turtle acts somewhat like the LEGO robot. TOWARDS SUN points the turtle towards the sun at the center of the screen. After turning right 90 degrees, the turtle's left side is pointed toward the center, as if it had a sensor on its side. (RT is short for RIGHT; FD is short for FORWARD.)

The turtle tries to keep its heading perpendicular to the line between it and the center -- and ends up moving in a circle. The turtle is constantly pointed along one of the circle's tangents (even if you drag the turtle or the sun).

There's a slight problem. The turtle tends to spiral outward. The reason: With each step along a tangent, the turtle moves a tiny bit further from the center. If you make the steps smaller, the resulting shape become more and more circular.

This circle provides a way of thinking about the earth's movement around the sun. The sun's gravity "tries" to pull the earth inward. But the earth is moving perpendicular to the sun's pull. The sun doesn't succeed at pulling the earth any closer, but it succeeds at turning the earth's heading, keeping it always perpendicular to the sun's pull.

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Last modified: November 17, 2003
by Rupert Russell