Lab 8: seasons, solstices and equinoxes

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Lab 8: Seasons, Solstices and Equinoxes

Part I: The Reasons for the Seasons

Below are three facts about the seasons that we wish to explain. Below the facts are
four hypotheses about what might cause the seasons to occur. Your job is to think
about each one and figure out which of the four hypotheses are most right and which
ones are wrong. Be sure to keep these three facts in mind while going through the lab.

Key facts about the seasons:

I. In northern latitudes, it’s warm in June/July and cool in Dec/Jan, on average.

II. In southern latitudes, the seasons are reversed: it’s warm in Dec/Jan and cool in
June/July.

III. It’s warmer at latitudes close to the equator than at latitudes close to the poles
(on average).

Hypothesis #1: The Sun-Earth distance changing due to

Earth’s elliptical orbit causes the seasons.

If its orbit were a circle, the Earth would always be the same distance from the Sun.
But it’s not. The orbit is an ellipse. As compared to the average Earth/Sun distance, the
Earth is sometimes 1.7% closer and at other times 1.7% farther away from the Sun than
the average.

Is this difference significant? To answer this question, it helps to be able to refer to
a scale model of the Sun/Earth system. Recall the scale model of the solar system we
made in Lab 1. We made the size of the Sun and Earth and the distance between them
all smaller by the same factor: 1010. Let’s repeat these calculations for the Earth-Sun
system.

Sun diameter: 1.4 × 106 km → scale model Sun diameter = 14 cm

To get the above, remember that we divide by the scale factor to shrink the normal
size:

1.4 × 106 km
1010

= 1.4 × 10−4 km

Then we convert to units of cm:

1.4 × 10−4��km ×
103m

1��km
= 1.4 × 10−1��m ×

102cm

1��m
= 1.4 × 101cm = 14cm

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Now try to get the values for the Earth diameter and the Earth-Sun distance, you can
also look up the values from Lab 1, but make sure they are right:

Earth diameter: 1.3 × 104 km → scale model Earth diameter = cm

→ scale model Earth diameter = mm

Earth-Sun distance: 1.5 × 108 km → scale model distance = m

A 1.7% change in the Earth-Sun distance is thus:

scale model Earth-Sun distance = m ×0.017 = m =
cm

To make sure we all have the same model, you may remember, the Sun was represented
by a small watermelon, the Earth would be about the size of a candy sprinkle and the
distance between them would be the size of an apartment, small house or a big great room
inside a medium/large house (15 meters).

Now that we have the Earth-Sun model in our heads, imagine standing in one corner
of a big room holding the tiny Earth sprinkle and you see the watermelon Sun in the
other corner of the room. Also pretend that the watermelon is sitting in a bon fire, this
will represent the heat we feel from the Sun.

1. If you moved closer to the fire by the amount above (1.7%), do you think you would
get significantly warmer? Why or why not?

2. The Earth is closest to the Sun in early January and farthest from it in early July.
Can both facts I and II above be explained by the changing Earth-Sun distance? Give
your reasoning.

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Hypothesis #2: The change in the Sun-Earth distance due to

the tilt of the Earth causes the seasons.

In the summer months, the northern hemisphere of Earth tilts 23.5 degrees toward
the Sun, while in the winter months, it tilts away from the Sun. Another hypothesis we
could make is that the hemisphere that is tilted toward the sun is warmer because it’s
closer to the Sun than the hemisphere that is tilted away from the Sun. (See diagram
from Prather, Slater, Adams, and Brissenden below)

To test this hypothesis, consider the scale model you constructed. Try tilting the
North Pole of your model Earth toward or away from the model Sun on the other side of
the room (without changing the distance from the center of the Earth to the Sun).

1. Is there a significant difference in distance from our model Sun (15 meters away) to the
northern hemisphere of the sprinkle then from our model Sun to the southern hemisphere
of the sprinkle?

2. Is this a plausible explanation for the seasons? Explain.

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Hypothesis #3: The change in the length of the day due to the

tilt of the Earth’s axis causes the seasons.

Before going into how the length of the day changes due to the tilt, let’s focus on the
tilt itself. The image below shows how over the course of a year (orbit) the tilt stays the
same. Why is that? Recall that the Earth’s spin axis points at the North Celestial Pole,
a point on the Celestial Sphere that is very close to Polaris, also known as the North Star.
It keeps pointing steadily at the same position as the Earth goes around the Sun. (Recall
that precession occurs so slowly that even over your whole lifetime, the effect will be very
small and can be ignored for most purposes.)

Figure 1: source: https://www.timeanddate.com/astronomy/equinox-not-equal.html

Notice how when it is the Summer in the Northern hemisphere and Winter in the
Southern Hemisphere (June), the North Pole is tilted towards the Sun while the South
Pole is tilted away. Also notice that when it is the Winter in the Northern Hemisphere
and Summer in the Southern Hemisphere (December), the North Pole is tilted away from
the Sun and the South Pole is tilted towards the Sun. The two Earth’s in the middle of
the diagram are neither tilted towards or away from the Sun. This is when it is Spring
and Autumn in the Northern and Southern Hemispheres.

1. How does the Earth’s tilt change with respect to the Sun over the course of one
year?

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Now let’s see what effect the tilt has on the length of days. Watch the youtube video
linked below and answer the following questions. Remember, you can always pause and
rewind the video if you missed something! (Note: If you are in a place that can’t access
YouTube, you can still answer the questions below by using Figure 1 above.)

Video break down:

2. Pay attention to the Earth at 1:09 OR look at the March and September Earths in
Figure 1. With the Earth’s spin axis vertical, does it look like the whole Earth gets the
same amount of daylight no matter your latitude?

3. Now pay attention to the Earth at 1:48 OR look at the June Earth in Figure 1. With
the North Pole pointed towards the Sun, does it look like both the Northern Hemisphere
and the Southern Hemisphere get the same amount of day light? If not, which gets longer
days?

a. Does it look like the North Pole gets both day and night? If not, what does it get?

b. What is happening in Antarctica (South Pole)? Does it get day and night? If not,
what does it get?

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4. Finally, pay attention to the Earth at 3:16 OR take a look at the December Earth in
Figure 1. With the North Pole pointed away from the Sun, does it look like both the
Northern and Southern Hemispheres get the same amount of day light? If not, which gets
longer days?

a. Has anything changed about the amount of daylight at the North or South Poles?
If so, describe the changes.

5. Which do you think corresponds to summer in the northern hemisphere: the Earth’s
axis pointing toward the Sun or away from the Sun? Explain.

6. Based on your results above, can the change in the length of the day potentially help
to explain the seasons? Discuss.

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Hypothesis #4: The change in the intensity of the Sun’s rays

due to the tilt of the Earth’s axis causes the seasons.

The changing tilt of Earth relative to the Sun also affects the intensity of the Sun’s
rays on different parts of the Earth at different times of the year. First, let’s compare
the intensity of the Sun’s rays in the summer vs. winter in northern latitudes on Earth.

Figure 2: source: https://media.nationalgeographic.org/assets/photos/000/312/31279.jpg

Pay attention to Earth A on the left. Notice how the North Pole is tilted towards the
Sun, also notice how the most direct Sun rays (shown in brighter yellow) land above the
Earth’s equator in the Northern Hemisphere and how the Sun’s rays seem to just graze
the Southern Hemisphere.

Now pay attention to Earth B on the right. The North Pole is now pointing away
from the Sun. Notice now how the Sun’s most direct rays fall below the Earth’s equator
in the Southern Hemisphere and that they only graze the Northern Hemisphere.

1. What season do you think it is in the Northern Hemisphere for:

a) Earth A?

b) Earth B?

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The image below shows how these direct sun rays land on the Earth during the Summer
and how the indirect rays land on the Earth during the Winter. Notice how the same
amount of rays land on the Earth in both Summer and Winter, but during the Summer
the rays land in a smaller area then in the Winter.

Figure 3: source: https://physics.weber.edu/schroeder/ua/SunAndSeasons.html

You can test this for yourself by using a flashlight (or phone flash light). Point the
light directly at a table (perpendicular) to represent Summer, then point the light at an
angle (45◦) to represent Winter. You can also test this by using a small space heater. If
you point the heater directly at yourself you may notice how much hotter it feels than if
it were pointed next to you.

2. Do you think the patch of light on the table looks brighter or fainter in the winter or
summer?

3. Do you think the Earth gets more energy in the summer or in the winter? Explain
your reasoning.

4. Do you think that the effect of the Earth’s tilt on the intensity of the Sun’s rays can
help to explain the seasons? Justify your answer.

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Summary Questions:

1. Which of the four hypotheses listed at the beginning of the exercise were you able to
rule out as plausible causes of the seasons, and why? (Include all that were ruled out.)

2. Which of the four hypotheses did you find could help to account for the seasons? More
than one may be important; discuss the role played by each one.

For Fun: Here is a short Bill Nye video explaining the seasons: https://youtu.be/
KUU7IyfR34o

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Part II: The Sun, Solstices, Equinoxes, and Seasons
on Earth

Apparent motion of the Sun (Hint: refer to Lab 7 if you are having trouble
remembering)

1. In which direction does the Sun travel along the ecliptic (relative to the stars) over the
course of a year? Eastward or westward?

2. What is the cause of the annual motion of the Sun relative to the stars?

3. What is the direction of daily motion of the Sun? Eastward or westward?

4. What is the cause of the daily apparent motion of the Sun?

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The Solstices and Equinoxes

Since the Earth is tilted relative to the plane defined by the Earth’s orbit around the
Sun, the apparent path of the Sun is not along the Celestial Equator, but instead follows
a path in the sky known as the “ecliptic”. The ecliptic is tilted by 23.5 degrees relative
to the Celestial Equator.

Over the course of one year, the Sun completes one cycle around the ecliptic. On the
following four dates, the Sun is at the following special locations:

Mar. 21: the Vernal Equinox the first day of spring (the Sun crosses the Celestial
Equator, moving north)

June 21: the Summer Solstice the first day of summer (the Sun is as far north on the
Celestial Sphere as it gets)

Sept. 21: the Autumnal Equinox the first day of autumn (the Sun crosses the Celestial
Equator, moving south)

Dec. 21: the Winter Solstice the first day of winter (the Sun is as far south on the
Celestial Sphere as it gets)

In this exercise we will use Stellarium to explore three of the effects of the Earth’s tilt
by checking how the Sun’s behavior compares on these various dates. These behaviors
are related to the seasons. In particular, we will measure: (1) the length of the day; (2)
the compass positions where the Sun rises and sets; and (3) the altitude of the Sun at
noon.

1) Set the location. We are all going to use San Francisco as our location so that
we can all see the same constellations. At the bottom of the webpage you should see a
button that tells you where you’re observing from. It’ll say “near (location),” click that
button. Once the map pops up, drag the location pin to San Francisco and click “> use
this location” above the map. Also make sure that the toggle for “Use Autolocation” is
turned off.

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2) Turn on/off icon features. At the bottom, you’ll also see a bunch of symbols which
will turn on and off certain features of the night sky. Turn on the “Constellations” and
turn off the “Atmosphere” symbol as shown below. If this isn’t done, you won’t be
able to see the stars!

3) Turn on the Meridian. Click the three horizontal line icon in the top left of the screen
and look for “View Settings”. Open the settings and check the box that says “Meridian
Line”. Once done, you can close out of the settings menu. If you look around the sky,
you should notice that the Meridian is a line in the sky (much like the Prime Meridian on
Earth) that goes from due North on the horizon through your Zenith (90àaltitude) to due
South again on the horizon. It essentially divides the sky into an Eastern and Western
halves.

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5. Make sure to turn South for this exercise. Fill in the tables below. For each position,
use Stellarium to observe and record the following things about the path of the Sun during
the course of the day. Use the Altitude coordinate grid scale to determine the altitude at
noon. Use the time menu (bottom right) to change the time of day, the “hour” of sunrise
and sunset and thus the total number of daylight hours. Sunrise is when the Sun is on
the Eastern horizon, noon is when the Sun is on the meridian and sunset is when the Sun
is on the Western horizon.

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6. At what time(s) of the year is the length of the day equal to the length of the night?

7. How many more hours of daylight are there on the summer solstice than on the winter
solstice?

8. Would you expect the temperature to be warmer or cooler than the yearly average
when the hours of daylight are longest?

9. How much higher in the sky is the Sun at noon on the Summer Solstice than on the
Winter Solstice?

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