Astronomy Practice for Final Exam

 

This is not an all inclusive list – i.e. there may be other types of questions/problems on the final!

 

1.      Three special units in astronomy are the astronomical unit (A.U.), the light-year (ly), and the parsec (pc).  (a) Calculate the number of kilometers in a light-year based on the speed of light 299792458 m/s.  (b) Calculate the number of astronomical units in a parsec by using the skinny triangle formula.  (c) Given that one astronomical unit is 150 Gm, determine the number of light-years in a parsec by using the factor label method.

Problems 2 – 7:  use a planisphere and/or star chart to determine approximate answers:
 

2.      (a) In what constellation is Vega located?  (b) Of which asterism is it a part?  (c) What are its coordinates?

3.      (a) What is the maximum altitude ever attained by the star Vega for an observer in Knoxville?  (b) On what day of the year would it reach this altitude at midnight mean solar time?  (c) At what time on the day of the vernal equinox does it reach the same altitude?

4.      (a) What are the celestial coordinates of the winter solstice and in what constellation is this?  (b) Repeat for the year 8450 AD.  (hint:  25,800 years is the period of _?_ )

5.      A certain observer located somewhere on Earth can see the star Polaris right at the horizon on clear nights.  (a) What is the latitude of this observer?  (b) What is the brightest star that will pass within 5° of this observer’s zenith?  (c) On what day(s) of the year will the Sun climb highest in the sky for this observer?

6.      (a) On what day of the year does the Sun appear nearest to the star Antares in Scorpius?  (b) If a lunar eclipse is occurring on the same day, in what constellation is the Moon located?  (c) If a solar eclipse preceded this lunar eclipse, it likely occurred on what day of the year and in what constellation?

7.      Mars will reach its opposition on January 29, 2010.  (a) In what constellation will it be?  (b) Will it be moving toward or away from the star Regulus?  (c) As oppositions go, this one will be one of the “worst” for Mars because its apparent angular diameter of 14˛ will be less than at most other oppositions.  Explain why the apparent angular diameter can vary at different oppositions and what must be true in order to explain this relatively low value.

8.      Suppose an eclipse occurs in which the tip of the Moon’s conical umbra comes close to, but does not touch, the surface of the Earth.  (a) What type of eclipse occurs for observers closest to the tip of the umbra?  (b) What type of eclipse occurs for observers a hundred miles away?  (c) The Moon must be at what part of its orbit and/or the Earth must be at what part of its orbit in order for this type of eclipse to occur?  Explain.

9.      A certain star’s spectrum is most intense at a wavelength of 580 nm.  (a) Determine the frequency and type of this radiation.  (b) Determine the surface temperature of this star.

10.  A type B star can have a surface temperature of 20,000 K.  Determine the frequency and wavelength at which such a star emits the greatest amount of radiation.

11.  The Extreme Ultraviolet Explorer satellite measured radiation with wavelengths as short as 1 nm and as long as 50 nm.  Determine the minimum and maximum frequencies that this satellite could detect.

12.  Compare the telescopes of the Keck Observatory at Mauna Kea, Hawaii to the telescopes of the Very Large Telescope (VLT) project at the European Southern Observatory in Chile.  The Keck facility has two 10 meter diameter mirrors and the VLT has four 8.2 meter diameter mirrors.  (a) Which facility has the greater total light gathering capacity and by what factor?  (b) Comparing a single telescope from one facility to a single telescope from the other, which has the greater light gathering capacity and by what factor?

13.  Suppose you buy a refracting telescope.  The objective has a diameter of 80.0 mm and a focal length of 400 mm.  The telescope comes with two eyepieces with focal lengths of 25 mm and 10 mm.  (a) If the telescope is advertised as “diffraction limited optics” then it’s resolution should meet or beat the diffraction limit – what would that be for this telescope assuming an operating wavelength of 600 nm?  (b) Determine the range of magnifications possible with the given eyepieces.

14.  When viewed during Jupiter’s opposition, the outermost Galilean moon, Callisto, can appear up to 11 arc minutes separated from Jupiter.  Given that the closest approach of Earth to Jupiter is about 589 Gm, determine the approximate radius of Callisto’s orbit about Jupiter.

15.  Determine what planet has the greatest apparent angular diameter as seen from Earth.  There are three candidates for this distinction:  Venus, Mars, Jupiter.  Calculate the maximum apparent angular diameter for all three. 
Earth:         perihelion = 147.1 Gm aphelion = 152.1 Gm
Venus:        diameter = 12104 km               aphelion = 108.9 Gm 
Mars:         diameter = 6788 km                 perihelion = 206.6 Gm
Jupiter:       diameter = 142,984 km            perihelion = 740.7 Gm

16.  The Sun is about 8000 pc away from the center of the Milky Way Galaxy.  By careful analysis of redshifts and blueshifts of the surrounding stars astronomers have determined that the Sun (and the entire solar system with it) is moving in a circular orbit about the galaxy’s center with a speed of about 220 km/s.  (a) Determine the circumference of the Sun’s orbital path in kilometers.  (b) Determine the orbital period for the Sun (this is sometimes called the “Galactic Year”).  (c) Assuming the Sun is about 5 billion years old, how many orbits has it completed since its birth?

17.  Suppose a certain asteroid orbits the Sun at a mean distance of 3.5 A.U. with eccentricity 0.18.  (a) Determine the orbital period.  (b) Determine the closest approach to the Sun.

18.  Sedna is a Trans-Neptunian Object about half the size of the Moon that orbits the Sun with perihelion 76.16 A.U. and aphelion 975 A.U.  (a) What is its semi-major axis?  (b) What is its orbital period?  (c) What is the eccentricity of its orbit?  (d) At what point in its orbit does it have the lowest speed?

19.  The Sun has a luminosity of 3.9 × 1026 watts (it gives off this many joules of energy every second.)  (a) Use the equation E = mc2 to determine the mass that must be “destroyed” every second in order to release this energy.  (b) In how many years will the mass of the Sun decrease by 0.1% (given its current value of 1.99 × 1030 kg)?  Assume rate stays the same.

20.  In one part of the proton-proton chain a positron, m = 9.11 × 10−31 kg, is “created”.  This positron then will encounter an electron and the two particles undergo “mutual annihilation”.  (a) What energy is released by the mutual destruction of such a pair of antimatter particles?  (b) How many such pairs must be annihilated to create one joule of energy?

21.  (a) If a certain star is twice the radius and twice the temperature of the Sun, its luminosity is how many times the Sun?  (b) If a certain star is 16 times the luminosity and the same temperature as the Sun, its diameter is how many times the Sun?  (c) If a certain star is 16 times the luminosity and the same diameter as the Sun, its temperature is how many times the Sun? 

22.  The absolute magnitude of the Sun is 4.85.  (a) How many times more or less luminous is a star with absolute magnitude of 9.85?  (b) How many times more or less luminous is a star with absolute magnitude of −0.15?  (c) How many times more or less luminous is a star with absolute magnitude of −2? (d) A star that is 10000 times more luminous than the Sun has what absolute magnitude? 

23.  If a person could travel to a distance of 1 parsec from the Sun, what would be its apparent magnitude?

24.  A certain star has apparent and absolute magnitudes of:  m = 3, M = −1.  Find its distance.

25.  Use spectroscopic parallax to determine the distance to a G0V star that has apparent magnitude 6.


Answers

 

1.      a. 9.46 × 1012 km
b. 206,000 A.U.
c. 3.3 ly

2.      a. Lyra
b. the Summer Triangle
c. decl = 38°, R.A. = 18h 35m

3.      a. 88°
b. July 1
c. 6:30 a.m.

4.      a. decl = −23.5°, R.A. = 18h, Sagittarius
b. decl = −23.5°, R.A. = 18h, Virgo

5.      a. 0°
b. Procyon
c. at both the vernal and autumnal equinox
    (Mar. 21 and Sept. 21)

6.      a. Nov. 30
b. Taurus
c. Nov 16, Libra

7.      a. Cancer
b. away (retrograde motion)
c. If Mars is at aphelion and Earth is at perihelion then the distance between the two is
    maximized and the apparent diameter of Mars is minimized.

8.      a. annular solar eclipse
b. partial solar eclipse
c. Moon at apogee and Earth at perihelion so that Moon’s apparent angular diameter is less
    than the Sun’s apparent angular diameter.  Moon appears smaller if it is farther away. 
    Sun appears bigger if it is closer.

9.      a. 5.2 ´ 1014 Hz (visible light)
b. 5000 K

10.  2.07 ´ 1015 Hz, 145 nm (ultraviolet)

11.  6 ´ 1015 Hz to 3 ´ 1017 Hz

12.  a. VLT collects 1.34 times the light (on a total basis)
b. Keck collects 1.49 times the light (per telescope)

13.  a. 1.9˛
b. 16 to 40 times

14.  1.88 Gm

15.  Venus         65˛  (greatest)
Mars          26˛
Jupiter        50˛

16.  a. 1.55 ´ 1018 km
b. 220 million years
c. 22 orbits

17.  a. 6.55 years
b. 2.87 A.U.

18.  a. 526 A.U.
b. 12000 yrs
c. 0.855
d. aphelion

19.  a. 4.3 × 109 kg
b. about 15 billion years

20.  a. 1.64 × 10−13 J
b. 6.10 trillion

21.  a. 64
b. 4
c. 2

22.  a. 100 times less
b. 100 times more
c. 550 times more
d. −5.15

23.  −0.15

24.  63 pc

25.  25 pc