When I responded to Charles yesterday I stated that the penumbra is symmetrical and the centers were coincident. Today I responded to John that the center of the solar disk is closer to the umbra. How can I contradict myself and still claim to be correct.
It depends on the relationship between the gnomon and the plane the shadow is cast onto. In the first case I assumed a vertical gnomon (a tall building). The plane of the projection was at right angle to the light ray. Everything is symmetrical. The first answer is correct. In the second case the shadow from the top of the gnomon is cast onto a horizontal plane which is not at right angles to the light ray. The projection onto the this plane is not symetrical. The center of the solar disk is closer to the umbra along the horizontal plane than the center of the penumbra. The second answer is correct. So are Charles and John. I always was good at situational ethics! Isn't e-mail wonderful. You can send a message without even thinking about it. Roger Bailey At 06:45 AM 5/4/99 -0700, Phil Pappas wrote: >Hello all: > >I was just thinking that on a horizontal sundial that the true shadow point >would ONLY be at the center of the penumbra at high (apparent) noon. In the >late afternoon or early morning, the sun would be to the side of the style, >causing the shadow to strike the dial face at an angle. Wouldn't this shift >the true shadow point towards the center of the sundial, away from the >center of the penumbra? (wish I could make you a little drawing of this as >a picture is worth a thousand words). > >John Carmichael > >> > >
