Question

hitting. use the simulation to complete the table.

date	ra	dec	latitude of most direct	latitude of least direct ray
march 21
may 5	2.9 h	+16.5°	16.5° n	73.5° s
june 21
august 5
september 21
november 5
december 21

question 12: using the data in the table above, formulate general rules relating the declination of the sun to the latitude where the most direct and least direct rays of the sun are hitting.

question 13: the region between the tropic of cancer and the tropic of capricorn is commonly known as the tropics. using the sunlight data table from question 11, define the significance of this region.

Explanation:

Question 12

1. Most Direct Rays Rule: The latitude of the most direct sun rays (subsolar point) is equal to the sun’s declination (DEC). For example, on May 5, DEC is \( +16.5^\circ \) and the most direct latitude is \( 16.5^\circ \text{ N} \), matching the declination’s sign (north for positive DEC).
2. Least Direct Rays Rule: The latitude of the least direct sun rays is \( 90^\circ \) from the subsolar point (since the sun’s rays are most spread out at the pole opposite the subsolar latitude). Mathematically, if the subsolar latitude is \( L \), the least direct latitude is \( 90^\circ - |L| \) with the opposite hemisphere sign. For May 5, \( 90^\circ - 16.5^\circ = 73.5^\circ \), and the least direct latitude is \( 73.5^\circ \text{ S} \), consistent with this.

The tropics (between Tropic of Cancer \( 23.5^\circ \text{ N} \) and Tropic of Capricorn \( 23.5^\circ \text{ S} \)) are the only region where the sun’s declination (and thus the subsolar point) falls within its latitude range. This means the sun is directly overhead (most direct rays) at least once a year in the tropics, while regions outside the tropics never experience direct overhead sun (the subsolar point never reaches their latitude).

Answer:

• Most Direct Rays: The latitude of the sun’s most direct rays equals the sun’s declination (DEC). If DEC is positive (\( + \)), the latitude is north (\( \text{N} \)); if negative (\( - \)), it is south (\( \text{S} \)).
• Least Direct Rays: The latitude of the sun’s least direct rays is \( 90^\circ \) minus the absolute value of the subsolar latitude (most direct latitude), with the opposite hemisphere sign (e.g., if most direct is north, least direct is south, and vice versa).

Question 13