Lab 8: Sun Shadows
- Inferring sun location from a shadow
- Interpretation of sun shadow plots
1) If two observers, one located in Lexington, and another at the equator, were to make
sun shadow plots (with identically-lengthed gnomons) on the same day, would their
results look the same, or different? Is it ever possible for the two shadow plots to look
the same? Use a sketch on the diagram below to help you explain why or why not.
Several sun rays coming
in (solid) parallel from the faraway sun are shown hitting the top of poles at
various places on earth - the end of the shadow is much longer at northern
latitudes than at southern latitudes. Tilting the rays at an angle (dotted
lines), which is equivalent to tilting the earth, doesn’t change the situation.
Sun shadow plots will therefore look different at every latitude line on a
given date.
2) If two observers, both located in Lexington, but one using a gnomon with twice the
height of the other, were to make sun shadow plots on the same day, would their results
look the same, or different? Would the angle they measured toward the sun be the
same, or different? Use sketches on the two gnomons below to demonstrate this.
The height of the gnomon doesn’t matter - the same sun ray will make the
same angle with the gnomon in either case. The scale of the sun shadow
plots will differ, but as long as they account for the height of the gnomon,
their analysis will be the same.
Lab 36: The Sun and Seasons
- Causes of the seasons
- The axial tilt of the earth
- Length of the day and seasons
3) Following are 8 simple diagrams, showing the tilt of the earth in the direction facing
the sun at different points in its revolution around the sun, in sequence of time. (The
greatest angle of tilt shown in these diagrams is 23.5°.)
a) Lightly shade the dark half of each diagram, and label the diagram showing the
northern hemisphere winter solstice “W”, the summer solstice “S”, the spring (or vernal)
equinox “V” and the fall equinox “F”.
The dark half is divided by the vertical black line in each diagram; the right
half is always the shaded half. The letters are marked in red on the
diagram.
b) On each diagram, draw an “X” on a point on the earth for which the sun is directly
overhead in the exact middle of the day. Draw a solid latitude line around the earth
representing the locations where the sun is directly overhead as the earth rotates.
These are marked by the blue X and the blue solid lines.
c) Draw a dot showing Lexington at exact midday in each diagram, and label it “L”.
According to your diagrams, is the sun ever directly overhead in Lexington? If so,
when? If not, why not?
The yellow dot marks Lexington - it is about 38° north of the equator. The
sun’s rays never are direct on Lexington - the highest latitude the sun’s
rays are direct, and the sun is directly overhead, is 23.5° north of the
equator.
d) On each diagram, if possible, draw dotted lines representing the latitude lines near
the north or south poles where the sun does not rise or set at all.
These are marked by blue dotted lines on the diagrams. Note that at the fall
and vernal equinoxes, these lines disappear altogether.
e) At the north and south poles, how long is a period of daylight or night?
The sequence of diagrams shows that the pole are always covered in either
light or darkness, and change over at the equinoxes, twice a year. So, the
poles each get six month of sunlight, followed by six months of darkness.
f) Does the actual “tilt” of the earth’s axis really change throughout the year, as these
two-dimensional diagrams might lead someone to believe? Explain.
No, it’s not the earth’s tilt that actually changes - it is its location with
respect to the sun that changes. The earth is always tilted at 23.5° - think of
these as 3-D diagrams. At the equinoxes, it looks like the earth has no tilt in
the drawings - but it does - it is tilting either into or out of the page, toward
the viewer (you!) - it is just not tilted toward or away from the sun during
this time.
8) We noted in this activity that the 23.5° tilt of the earth with respect to its solar orbit is
responsible for the seasons on earth. Similarly to Problem 4), we will slightly alter the
behavior of our model, in order to better understand the effects of the motion of the sun
and earth.
a) If the earth had no tilt at all (its axis was perpendicular to its orbit about the sun), what
effect would this have on the seasons? Where would the latitude line be for which the
sun is directly overhead at midday, at all times during the year? Draw a diagram that
shows this.
If the earth had no tilt, the sun would be directly overhead at midday at the
equator at all times during the year. There would be no seasons in this
scenario, because the angle of the sun’s rays on any given part of the earth
would never change.
b) If the earth had a HUGE, 90°
tilt, so that it lay on its “side” with
respect to the sun, what effect
would this have on the seasons?
Draw 2 diagrams, showing how the sun’s rays would light the earth at the summer and
winter solstices. How long would a day and night be at each solstice in Lexington, in this
extreme scenario?
If the earth had a 90°(!) tilt, the sun would be directly overhead of the north
pole on the summer solstice, and directly overhead of the south pole on
the winter solstice. In summer, Lexington (marked by the dotted latitude
labeled “L”) would get 24 hours of sunlight, and in winter, Lexington would
get 24 hours in darkness - like the poles, this would only change at the
equinoxes, so that “daylight” would last 6 months, followed by a 6 month
“night”.
c) Using a sketched diagram, determine what the axial tilt of the earth, in degrees,
would have to be for the sun to be directly overhead at midday on the summer solstice
in Lexington.
At the summer solstice, the earth’s northern hemisphere is tilted furthest
toward the sun. Lexington is at a latitude of 38°, so the earth would need a
38° tilt for the sun to be directly overhead on this day, as the right angles in
the diagram show.