You are enjoying the santa barbara solstice parade at noon on june 21. the sun is beating down on you. how far is it from zenith? (there's a slight complication because of daylight savings time, but just ignore it). a. it's exactly overhead at that time of day b. it's about 4 degrees from the zenith. c. 11 degrees d. it's 34 degrees from zenith, because that's our latitude e. it's 34 degrees above the southern horizon, which is 90 - 34-56 degrees from straight overhead.

C. 11 degrees.

Explanation:

For understanding why, we first need to remember that solstices are the extreme points of the Sun's orbit. For the northern hemisphere, the Sun reaches its maximum distance in the Summer Solstice (June 21), and its minimum distance at Winter Solstice (December 21).

At this points, as seen from earth, the Sun reaches its maximum and minimum  declination, +23,5° in June 21 and -23,5° in December 21.

In the figure below, we can see how latitude, our position angle measured from the equator (0°) to the north pole (90°), is affecting the way we see the Sun on June 21.

For general rule, we can say that during June 21:

, where Z is the zenith angle, L is the laitude from where we are observing and 23,5° is the Sun's declination that day.

Doing the calculations, we obtain for Santa Barbara (latitude 34,5°) that the zenith angle for the Sun on June 21 will be 11°.

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