Question

1. set the tilt back to 23.5°, then use the \latitude\ feature to change between the equator, tropic of cancer, tropic of capricorn, and the arctic circle.

a. how does the amount of sunlight each location receives change as you move away from the equator?
b. what do you notice about day length and sun angle at higher latitudes?

Explanation:

Part a

As latitude increases (moving away from the Equator towards the poles), the sun's rays strike the Earth's surface at a more oblique angle. This causes the same amount of solar energy to be spread over a larger area, so the intensity of sunlight (amount per unit area) decreases. Also, the length of daylight varies more with seasons at higher latitudes, but in terms of average or direct sunlight receipt, the key is the angle: the more oblique the angle, the less concentrated the sunlight, and generally, the total daily sunlight (in terms of energy) also tends to decrease as you move to higher latitudes (except for extreme seasonal variations like polar days/nights, but for the general trend from Equator out, the amount of sunlight per unit area and the total daily insolation (in non - extreme cases) decreases as latitude increases because of the angle and the path length of sunlight through the atmosphere (longer path at higher latitudes means more atmospheric absorption/scattering).

At higher latitudes:

1. Day length: The variation in day length throughout the year becomes more extreme. Near the Equator, day length is relatively constant (around 12 hours). As latitude increases, during summer, days become much longer (approaching 24 hours at the Arctic Circle during the summer solstice) and in winter, days become much shorter (approaching 0 hours at the Arctic Circle during the winter solstice).
2. Sun angle: The sun's angle above the horizon (solar altitude angle) decreases as latitude increases. At the Equator, the sun can be directly overhead (90° angle at solstices), while at higher latitudes, the maximum sun angle is always less than 90° and gets smaller as you go further from the Equator. For example, at 45° latitude, the maximum sun angle (at summer solstice) is about 68.5° (90 - 45+23.5), and at 60° latitude, it's about 53.5° (90 - 60 + 23.5), and at the Arctic Circle (66.5° latitude), the maximum sun angle at summer solstice is 23.5°+ (90 - 66.5)=47°? Wait, no, the formula for solar altitude angle at a given latitude \( L \), on a given day with declination \( \delta \) is \( h = 90^{\circ}-\vert L-\delta\vert \) (for \( L\geq\delta \) in the Northern Hemisphere summer). So at the Arctic Circle (\( L = 66.5^{\circ}N\)) on summer solstice (\( \delta=23.5^{\circ}N\)), \( h = 90-(66.5 - 23.5)=47^{\circ} \). But the key point is that as latitude increases, the sun angle is lower, meaning the sun is closer to the horizon, and its rays are more oblique.

Answer:

As you move away from the Equator (increase latitude), the amount of sunlight each location receives (per unit area) decreases. This is because the sun's rays strike the Earth at a more oblique angle, spreading the same solar energy over a larger area. Also, the path of sunlight through the atmosphere is longer, leading to more energy loss via absorption and scattering.

Part b