I need some clarification a statement by Hewitt[1]. He writes (grammer and punctuation are his):
"The moon's shadow tapers almost to a point at the earth's surface, evidence that the taper of the moon's shadow at this distance is one moon diameter. So during a lunar eclipse the earth's shadow, covering the same distance, must also taper one moon diameter."
Of course I understand why the Moon's shadow tapers (the Sun's finite size and distance). It's the second statement that I can't "see". I suspect it's because light rays from the Sun's upper limb are all parallel and those from the lower limb are parallel, but the upper rays are not parallel to the lower rays. Upper rays from the Sun are tangent to both Earth and the Moon and so are lower rays from the Sun. So the slope of an upper ray tangent to the Moon and the slope of an upper ray tangent to Earth should be the same, right? I'm missing something simple.
Cheers,
Joe Heafner - Instructional Astronomy and Physics
Home Page http://users.vnet.net/heafnerj/index.html
I don't have a Lexus, but I do have a Mac. Same thing.
This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.