29:61 General Astronomy
Fall 2004
Lecture 7 ...September 15,2004
The Orbit of the Moon and Eclipses

Just the facts, Ma'am

$\bullet$ The altitude angle of a celestial object at transit is

$$Al = \bar{\lambda} + \delta$$ (1)

where $\delta$ is the declination of the object, and $\bar{\lambda}$ is the complement of the latitude.

$\bullet$ The average inclination of the Moon's orbit to the plane of the ecliptic, $\iota = 5^{\circ} 08^{'}$.

$\bullet$ The average angular diameter of the Sun as seen from Earth, $\theta = 32^{'}$.

$\bullet$ The maximum distance $l$ in back of an object in which an umbral eclipse of the Sun will be seen is

$$l = \frac{d}{2\tan [\theta/2]}$$ (2)

where $d$ is the diameter of the object, and $\theta$ is the angular diameter of the Sun at that point (32 arcminutes at the orbit of the Earth).