The Shape of the Shaodow
The basic geometric shape of the shadow cast by the moon from the sun towards the Earth is a cone. The Sun is not a point source of light. It is a ball of light 400 times larger than the Moon. The Moon is 400 times closer which is why the Sun and Moon appear to be the same size. Because the Sun is bigger the shadow cast by the moon forms a cone.
If you were to take a basketball and make it a light source in a dark room. Now put a small round ball in the room. The shadow from the small round ball is a cone. The closer the balls are together the smaller the cone.
When the shadow cone first hits the Earth the shadow appears as an elongated ellipse. As the shadow moves across the Earth’s surface is becomes closer to a circle until reversing back to a an elongated ellipse.
The Earth is a third ball in the room with the illuminated basketball and small ball. It is bigger than the small ball and placed in line with both balls but further from the basketball. If the Earth ball is moved so that one side of the shadow goes across the ball the shadow is thickest at the points where the Earth ball is closer to the shadow ball. The shadow thins towards the edges of the Earth ball because that is further away (the cone shadow is smaller). As a result the longest eclipse occurs at the point where the surface is closest to the shadow ball.
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