... Sun index . ... After that the site tells how the spherical shape of the Earth was recognized and measured, leading to the formula for the distance of the horizon, the concept of parallax and the ways the ancient Greeks estimated the distance of the Moon. ... The section ends with a fairly detailed discussion of Kepler's laws and planetary orbits, which serves as a bridge to the next section, on Newtonian Mechanics. ... The Moon: the Distant View . ... 4b. Optional: Libration of the Moon . ...

Given the functions (sin a , cos a , sin b and cos b ), we seek formulas that express sin( a+b ) and cos( a+b ). ... As shown in the drawing, to derive the formula we combine two right-angled triangles . ABC which has an angle a . ... AB = AC cos a = R cos b cos a The triangle ADF is right-angled and has the angle ( a+b ). ... Each of them is one of the two sharp ("acute") angles in its own right-angled triangle. ... In the right-angled triangle CED DE = DC cos a = R sin b cos a . ...

... Phases of the Moon is at the top of the list of things that students seriously misunderstand. ... This phase is called "new moon" (like "no moon"). ... Note: although the Moon is closer to the Sun during new and crescent phases, it is still 400 times closer to Earth; i.e., the Sun is VERY far away in reality.) ... When the Moon reaches the position directly opposite the Sun, as viewed from Earth, the half viewed from Earth is fully illuminated (unless the student's head is causing a lunar eclipse). ...