... The Round Earth . ... Aristarchus around 270 BC derived the Moon's distance from the duration of a lunar eclipse (Hipparchus later found an independent method). ... Let R be the radius of that circle and T the time it takes the Moon to go around once, about one month. ... Viewed from Earth, a "new Moon" (occuring between the time a thin crescent is last seen before sunrise and the time one is seen shortly after sunset) happens when the Moon in its apparent motion around the sky overtakes the Sun. ...

For circular orbits around Earth, we found . ... The distance of a satellite from the center of Earth in meters is an inconveniently big number, even before we raise it to the 3rd power. ... SQRT (25 638 838) = 5063.5 From this . ... T= 5063.5 seconds SQRT(r') 3 = 5063 sec r'SQRT=(r') . This is the practical form of Kepler's 3rd law for Earth satellites. ... International communication satellites are in the equatorial plane of the Earth and have orbits with a 24-hour period. ...

Educator's Guide to Eclipses . ... In a solar eclipse you observe the Sun (using only safe methods, of course). ... In a lunar eclipse you observe the Moon. ... Because of the geometry described below, you can only view a solar eclipse when the Sun is up, and the Moon is nowhere to be seen. ... Eclipses occur when the Sun, Earth and Moon line up. ... In a solar eclipse the Moon passes directly in front of the Sun. ... In a lunar eclipse the Moon moves into Earth's shadow. ...