Trigonometric Inverses: About Angles & Solar Eclipses

Trigonometric Inverses: About Angles & Solar Eclipses (cont.)
A rather lengthy total solar eclipse occurred on July 11, 1991. On that particular day, the Moon was at the closest possible distance from the Earth (a.k.a., perigee) whereas the Sun was virtually near its most maximum distance from the Earth (a.k.a. aphelion). According to the July issue of *Astronomy* magazine, the Moon was 222,202 `mi` from Earth and the Sun was nearly 94.5 × 10⁶ `mi` away. Using this information, the following is intended to demonstrate that on this day the relative positions of the Moon & Sun from the Earth allow for a "total" solar eclipse... Begin by noting that the average radius of the moon is 1080 `mi` and that the Sun's average radius is 432,300 `mi`... Show that: θ_M > θ_S Note: Distances between astronomical bodies are from center to center.

A rather lengthy total solar eclipse occurred on July 11, 1991. On that particular day, the Moon was at the closest possible distance from the Earth (a.k.a., perigee) whereas the Sun was virtually near its most maximum distance from the Earth (a.k.a. aphelion). According to the July issue of Astronomy magazine, the Moon was 222,202 mi from Earth and the Sun was nearly 94.5 × 10⁶ mi away. Using this information, the following is intended to demonstrate that on this day the relative positions of the Moon & Sun from the Earth allow for a "total" solar eclipse...

Begin by noting that the average radius of the moon is 1080 mi and that the Sun's average radius is 432,300 mi... Show that: θ_M > θ_S
Note: Distances between astronomical bodies are from center to center.