Question

part 4: the southern hemisphere

1. refer to your \observers latitude\ in part 1. move the stick figure to that same latitude on the southern half of the earth.
2. fill out the table below using the same process as part 1.

date	suns altitude
june 21st
september 22nd
december 21st

1. compare the data to part 1. what differences and similarities do you notice?
2. how are the seasons in the southern hemisphere related to those in the northern hemisphere?

Explanation:

Step1: Determine the method

The problem requires practical - based data collection (filling the table) and comparison. Since the "observer's latitude" from part 1 is not given, we assume a general approach. The altitude of the sun at a given latitude on different dates can be calculated using astronomical formulas related to the Earth's tilt and orbit around the sun. However, without specific latitude, we can only provide general principles.
The sun's altitude ($h$) at solar noon can be calculated using the formula $h = 90^{\circ}-\vert\varphi-\delta\vert$, where $\varphi$ is the observer's latitude and $\delta$ is the solar declination. The solar declination changes throughout the year:

• On March 20th (vernal equinox), $\delta = 0^{\circ}$.
• On June 21st (summer solstice in the Northern Hemisphere), $\delta\approx23.5^{\circ}$.
• On September 22nd (autumnal equinox), $\delta = 0^{\circ}$.
• On December 21st (winter solstice in the Northern Hemisphere), $\delta\approx - 23.5^{\circ}$.

Step2: Fill the table for a general latitude $\varphi$ in the Southern Hemisphere

For March 20th: $h = 90^{\circ}-\vert\varphi - 0^{\circ}\vert=90^{\circ}-\vert\varphi\vert$.
For June 21st: $h = 90^{\circ}-\vert\varphi-23.5^{\circ}\vert$.
For September 22nd: $h = 90^{\circ}-\vert\varphi - 0^{\circ}\vert=90^{\circ}-\vert\varphi\vert$.
For December 21st: $h = 90^{\circ}-\vert\varphi+23.5^{\circ}\vert$.

Step3: Compare with data from part 1 (Northern Hemisphere)

• Similarities: The equinoxes (March 20th and September 22nd) will have the same sun - altitude formula results for the same absolute value of latitude in both hemispheres because $\delta = 0^{\circ}$.
• Differences: For the solstices, in the Northern Hemisphere, on June 21st $\delta = 23.5^{\circ}$ and on December 21st $\delta=-23.5^{\circ}$, while in the Southern Hemisphere, these values are reversed. So the sun's altitude at solstices will be different for the same latitude in different hemispheres.

Step4: Explain the relationship between seasons

The seasons in the southern hemisphere are opposite to those in the northern hemisphere. When it is summer in the Northern Hemisphere (around June 21st), it is winter in the Southern Hemisphere, and vice - versa. This is due to the Earth's tilt of approximately $23.5^{\circ}$ as it orbits the sun. When the Northern Hemisphere is tilted towards the sun, the Southern Hemisphere is tilted away, and vice - versa.

Answer:

Date	Sun's Altitude (general latitude $\varphi$ in Southern Hemisphere)
June 21st	$90^{\circ}-\vert\varphi - 23.5^{\circ}\vert$
September 22nd	$90^{\circ}-\vert\varphi\vert$
December 21st	$90^{\circ}-\vert\varphi+23.5^{\circ}\vert$

1. Similarities: Sun - altitude is the same at equinoxes for same absolute latitude in both hemispheres. Differences: Sun - altitude at solstices is different for same latitude in different hemispheres.
2. The seasons in the southern hemisphere are opposite to those in the northern hemisphere.