Download Astronomy 1400: Homework 2

Astronomy 1400: Homework 2
Due in class, Monday, September 15
Name:
Instructions: To receive partial/full credit you must show your work or explain your answer thoroughly. Please circle your final answer to each problem
if it is a number. If you do not show your work, you will receive a zero!
1. (5 points) What is the maximum height above the southern horizon (in degrees) that a
star on the celestial equator reaches here in Lubbock? Use the diagram below as a guide
(it may help you to label angles on the diagram). (Hint: a half circle is 180 degrees;
the celestial equator is just the equator projected onto the celestial sphere, which is 90◦
from the pole.)
We know that the semicircle running from north to south is 180◦ , the north celestial pole
is 33.6◦ from the horizon, and the distance from the north celestial pole to the celestial
equator is 90◦ . So. . . 180◦ − 33.6◦ − 90◦ = 56.4◦ .
2. (5 points) What is the maximum height the Sun reaches in the sky in Lubbock on the
winter solstice?
Remember, the height of the Sun above the horizon is, in general, 90−latitude±23.5◦ .
For Lubbock: 90◦ − 33.6◦ − 23.5◦ = 32.9◦ .
Notice that this is 23.5◦ below the celestial equator from the previous problem. The
ecliptic would be another circle that is titled 23.5◦ (the Earth’s tilt) relative to the
celestial equator; the ecliptic passes through the celestial equator at two points and has
a maximum separation from the celestial equator of 23.5◦ at two points. If you Google
”celestial sphere”, you can find a number of images that show this.
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3. (10 points) In Lubbock, is it possible to see a full Moon during the middle of the day
(∼9AM – 5PM)? Explain.
No, it is not possible to see a full moon in the middle of the day because it is behind the
Earth. The closest you can come to seeing a full Moon during the day is at sunrise/sunset,
when it will be on the horizon.
4. (20 points) If the Earth had a highly elliptical orbit (2× closer to the Sun at one time
of year than another) but no axis tilt (0◦ ), would it still experience seasons? Would the
height, size, brightness, etc. of the Sun change during the year and at different latitudes?
How height, size, brightness, etc. of the Sun affect the temperatures on different parts
of the Earth? Explain your answer thoroughly.
a) Yes, the Earth would experience seasons, but would experience them differently. b)
Different times of the year would be warmer (when closest to the Sun) or colder (when
farthest from the Sun), but c) all parts of the planet would experience them at the
same time (summer and winter would not be reversed in the southern and northern
hemispheres). d) The Sun’s height in the sky would only depend on the observer’s
latitude, so the reason for the seasons would be different. e) The summer would be
when the Sun is largest and brightest (not highest) in the sky and f) the length of day
would never change or be different for anyone anywhere on the Earth except at the poles
where the Sun would always be on the horizon.
Extra credit (5 bonus points): Also, because of Kepler’s second law, the summer would
be shorter and the winter would be longer.
5. (10 points) A friend tells you that he/she saw the Jupiter near the Polaris in the sky.
Does this make sense? Why or why not?
No, it does not make sense because the ecliptic, the line in the sky representing the
plane of the solar system, which all of the planets line very close to, never gets close to
the north celestial pole or Polaris. The planets will only be in the zodiac constellations
throughout the year.
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6. (10 points) As you are surfing the web you find the following statement: ”Because of
precession, the Earth will experience seasons differently (more or less extreme) because
the Earth will change its tilt.” Is this statement correct? Why or why not?
This is directly discussed on page 37 of the book: ”Notice that precession does not
change the amount of the axis tilt (which stays close to 23.5◦ ) and therefore does not
affect the pattern of the seasons.” Precession only changes the direction that the Earth’s
axis points.
7. (10 points) Suppose the distance to the Moon were twice its actual value. Would it still
be possible to have a total solar eclipse? Why or why not?
If the Moon were twice as far from Earth, its angular size would be too small to create a
total solar eclipse. It would still be possible to have annular eclipses, although the Moon
would cover only a small portion of the solar disk.
8. (10 points) Suppose the Earth were smaller. Would solar eclipses be any different? If
so, how? What about lunar eclipses?
If Earth were smaller in size, solar eclipses would still occur in about the same way, since
they are determined by the Moons shadow on Earth. Lunar eclipses would still occur,
but less frequently, not last as long, and partial ones would be more frequent because
the shadow is smaller. These effects are affected by how much smaller the Earth would
be.
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Multiple Choice: Choose the best answer.
9. (5 points) Beijing and Philadelphia have about the same latitude but very different
longitudes. Tonight’s sky in these two places will. . .
A. . . .look about the same
B. . . .have completely different sets of constellations
C. . . .have partly different sets of constellations
10. (5 points) In ancient times your astrological sign corresponded to the constellation of
the Zodiac that Sun was in when you were born. However, for most people today this
is no longer true. Why?
A. the Earth rotates about its axis faster
B. the tilt of the Earth’s axis has increased from zero to 23.5◦ today
C. the direction that the Earth’s axis points has been precessing
D. the stars in the Zodiac have been moving around
11. (5 points) A planet very similar to Earth is discovered around a distant star similar to
the Sun. The planet has a perfectly circular orbit and an axial tilt of 45◦ . Which of the
following is the best inference you could make about its climate?
A. the planet does not have seasons
B. the planet has similar seasonal variations to the Earth
C. the planet has less extreme seasonal variations (i.e. summer-winter differences)
than Earth
D. the planet has more extreme seasonal variations than Earth
12. (5 points) A first quarter moon will. . .
A. . . .rise at sunrise and set a sunset
B. . . .rise at sunset and set at sunrise
C. . . .rise at noon and set at midnight
D. . . .rise at midnight and set at noon
** 3 points extra credit for drawing a nice diagram of the relative positions of the Sun,
Earth, and first quarter moon as viewed from the someone above the north pole.
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