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LAST WEEK OF AUGUST, 2007--This Tuesday, a lunar eclipse will begin! To find out when/if it will be visible in your geographic region, consult the NASA eclipse page:
http://sunearth.gsfc.nasa.gov/eclipse/LEmono/TLE2007Aug28/TLE2007Aug28.html.

Here is what will happen. The moon will actually pass completely into the area where the Sun's light is blocked by the Earth. We can approximate the process with triangles.

The moon will be passing completely into the umbra. Therefore, if we can measure "how long" the moon remains in the shadow, we can approximate the diameter of the shadow at the distance of the moon. How do we do that? We can use the relationships created by the moon's apparent motion: consider the time it takes the moon to pass from lightness to darkness. The "time" it takes the moon to pass across the boundary of the umbra will indicate the rate at which the moon moves through a distance equal to its apparent diameter. THEN, time how long the moon remains completely in the shadow.

From this you can approximate the diameter, CC' of the umbra, where bc is the earth-moon distance. see below. (Remember, these are geometrical approximations for a physical process).

We will therefore have three similar triangles, the bases being the approximate diameter of the Sun (AA'), Earth (BB'), and CC' calculated above, with their proportionate altitudes ad, bd, and cd.

If you measured the angle between the last half-moon and the sun, then you will be able to approximate the relative distances ab, and bc, as well as the relative diameters of the sun and moon (If you didn't then just use the value of 89 degrees, and find them now). With a little concentration, figuring out an approximation for the relative diameter of earth--without even being able to see it!!!--should be possible!

In Part II of Kepler's New Astronomy, in order to determine Mars' orbit, Kepler first needs to know: what is the inclination of Mars' orbit to the Earth-Sun plane of the ecliptic? But before this can be determined, it is necessary to find the nodes, or, the two points of intersection of the Mars' orbit with the ecliptic, which must necessarily exist based on the rest of his assumptions.

Tonight, during the eclipse (4:51 a.m. EDT, 1:51 a.m. PDT), not only will the moon be in opposition to the Sun in longitude, but in latitude as well. Thus, the place where we see the Moon must also be the point of the Moon's orbit that coincides with the plane of the ecliptic--the Moon's node!