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PHY 150 - Astronomy
Homework Assignment #1
September 11, 2007
1. What is the difference between the sidereal year and the tropical year? Why are calendars based on the
tropical year?
The sidereal year is based on the time it takes the Earth to revolve around the Sun and return to the exact
same orientation with respect to the fixed stars. The tropical year is the time it takes the Earth to revolve
around the Sun and returns to the same orientation with respect to the Sun in front of the stars. The tropical
year has the seasons fall at the same time each year.
2. When Voyager 2 sent back picture of Neptune during its historic flyby of that planet in 1989, the
spacecraft’s radio signal traveled for 4 hours to reach Earth. How far away was the spacecraft? Give your
answer in kilometers, using powers-of-ten notation. You will find Table 7-1 on page 161 useful.
⎛ 1 day ⎞ ⎛ 1 year ⎞ ⎛ 9.46 x1012 km⎞
D = 4 lhr ⎜
⎟ = 4.32 x10 9 km
⎟⎜
⎟⎜
lyear
⎝ 24 hr ⎠ ⎝ 365 days⎠ ⎝
⎠
3. The star Epsilon Eridani is 3.22 pc from Earth. How long, in years, does it take for light emanating from
Epsilon Eridani to reach Earth?
⎛ 3.26 ly ⎞
We need the conversion factor 1 pc = 3.26 ly, then D = 3.22 pc ⎜
⎟ = 10.5y
⎝ 1 pc ⎠
4. At what distance would a person have to hold a nickel (which has a diameter of about 2.0 cm) in order for
the nickel to subtend an angle of
(A) 1o?
(B) 1' = arcmin?
(C) 1" = 1 arcsec? Give your answers in meters.
Hint: Use the small angle formula given in the book or on the formula sheet.
D
(A) We can use the small angle formula α = 5 7 .3 deg rees of arc . Then
d
d=
(
D 5 7 .3 o
α
) = (.0 2 m)(5 7 .3 o ) = 1.1 5 m , where 2 cm = .02m.
1o
(B) We can use the small angle formula α =
D
3 4 2 8 arc min . Then
d
D( 3 4 2 8 ') (.0 2 m)( 3 4 2 8 ')
=
= 6 8 .6 m
1'
α
D
(C) We can use the small angle formula α = 206265 arc sec . Then
d
D( 2 0 6 2 6 5 ") (.0 2 m)( 2 0 6 2 6 5 ")
d=
=
= 4114 m
1"
α
d=
5. At what latitudes on Earth do you have to be in order to see the Sun at the zenith? Will it be at the zenith
every day at that location? Explain. Is there more than one place where this is true?
For the sun to appear on the zenith an observer must live between the Tropic of Cancer and the Tropic of
Capricorn or between +23½ o and -23½ o of the Earth's equator (celestial equator). This is the result of the
23½ o tilt of the Earth's celestial equator with respect to the ecliptic (the path of the sun through the fixed
stars). This will occur twice a year as the sun passes through the zenith and then back, except at the two
tropic latitudes when it will occur once a year.
6. What is a penumbral eclipse of the Moon? Why do you suppose that it is easy to overlook such an eclipse?
A penumbral eclipse occurs when the Earth partially eclipses the Sun as seen from the Moon. That is, from
the Moon you would see the Earth partially shielding the Sun. The amount of sunlight reaching the Moon
depends on the degree of eclipse and could range anywhere from very little to complete. The Moon would
thus appear almost as bright as normal to very dim. A casual observer might very well miss a partial
dimming of the Moon or attribute the dimming to atmospheric conditions and not realize that the Moon was
actually in the penumbral shadow of the Earth.
7. The time-exposure in the figure shows the trails made by individual stars as the celestial sphere appears to
rotate around the Earth.
(A) If you were standing in Australia next to the camera that took this picture and looking in the same
direction that the camera was pointing, would you see the
stars moving clockwise or counterclockwise?
(B) For approximately what length of time was the camera
shutter left open to take this photograph?
(A) In the southern hemisphere the stars rotate clockwise
about the southern celestial pole, opposite to that about the
northern celestial pole.
(B) The star trails (those that are not obscured by other trails)
appear to rotate about a half a revolution. My best guess is
that this photograph represents an exposure of about 11 hours.
8. How many sidereal months are there in a year. How many
synodic months are there in a year? Explain the difference.
The sidereal month is 27.3 days long; therefore, there are 13.4
sidereal months in a year. The synodic month is 29.53 days
long; therefore, there are 12.4 synodic months in a year. Thus,
there is roughly one more sidereal month in a year than a
synodic month.
9. Starry Night project 1-69
On September 11, 2007, the Moon rises at 10:07 p.m. and sets at 7:10 a.m. the next morning. It is almost full
and visible all might..
Mercury rises at 9:45 a.m. after the Sun does, but is too close to the Sun to be seen at dusk. It sets at 7 p.m.
Venus rises at 11:50 a.m. It is briefly visible at dusk and sets at 8:18 p.m.
Mars rises at 6:18 a.m. and is barely visible before the Sun rises. It sets at 5:30 p.m.
Jupiter rises at 4:55 a.m. and then is obscured by the rising Sun. It sets at 4:30 p.m.
Saturn is next to the Moon and is visible all night long.
10. Starry Night project 2-64 .
(A) Over a period of a year the sun moves along the ecliptic from West to East along the ecliptic and through
the constellations of the zodiac returning to the same place it was the year before. It never changes direction.
(B) The Sun is currently in the middle of Leo. Astrologically the Sun should be in Libra. The reason for this
is that the sun was once in Libra from August 21 to September 21 about four thousand years ago. The zodiac
contains 12 constellation roughly equally spaced about the ecliptic. Since the rotational axis of the Earth
precesses once every 26,000 years the sun at a certain time of year moves through the zodiac at a rate of about
1 constellation every 2+ thousand years. Thus, it is reasonable to find the Sun after four thousand years
somewhere about two constellations beyond Libra or, in this case, in Leo.
(C) The Sun passes through Leo, Virgo, Libra, Scorpius, Sagittarius, Capricorn, Aquarius, Pisces, Aries, Taurus,
and Gemini.