Ellipse Illusion Copyright ©2015 by Paul Niquette. All rights reserved. |

hat must be the most extraordinary
For stars
and planets, for moons and satellites of all kinds,
orbits
are the thing. Each is said to be an ellipse. Several handy methods are available
for drawing an ellipse on paper: pin-and-string,
trammel,
parallelogram.
However, curves followed by celestial bodies are drawn
on invisible planes coerced by
ellipses
sliced from fictitious cones at various angles.
Which would not be especially bothersome were it not
for the ot everybody suffers from the Ellipse Illusion, but I
sure do, and -- hey, I admit that it's all in my
mind. The sketch above is definitely
not
correct. It depicts an oval not
an ellipse. That's the shape my personal
intuition stubbornly projects for a sliced cone.Many solvers of Measuring the Moon have studied my proposed celebration of ironic fitness values from The Moon Illusion. Be advised, the Ellipse Illusion is merely an embarrassment. It doesThe explanation for the Ellipse Illusion is simple enough [deep breath here]: The local radius of curvature for a smooth shape is defined by the radius of the osculating circle at each point such that one end of the oval drawn upon the sectioning plane seems to
share the osculating circle of the cone at a point
near its apex where the radius is small while the
opposite end of the oval drawn upon the same
sectioning plane seems to share the
osculating circle of the cone at a point farther
away from its apex where the radius is larger.
licing a cylinder with a plane at any old angle will always produce an ellipse, which my personal intuition does not resist. Why don't astronomers use cylindrical sections instead of conic sections for celestial orbits? |