Introductory Astronomy Final Exam Study Guide, University of Connecticut

Exam Details

1025Q Introductory Astronomy
Final Exam Study Guide
Spring 2024, University of Connecticut

Exam time and location:
Monday 04/30/24
8:00 - 10:00 AM
in GW001

The exam will consist of 30 questions drawn from the topics below. The questions will
be a mix of multiple choice and free response. They will also contain a mix of
conceptual and calculation questions. An equation sheet will be provided - and has
been posted on Husky CT.

You will need to bring your calculator. Example calculation questions are provided
below.

primary reference material: lecture slides, clicker questions, and quizzes.
other reference material: OpenStax Textbook and ExpertTA homework.The exam can cover the following topics ..

General Math Skills

• Perform calculations using scientific notation.
• Convert between units.

Celestial Sphere and Seasons

Celestial Sphere Terms

terms to know: altitude, azimuth, zenith, celestial pole, meridian

• Identify a location in the sky using the horizontal coordinate system.
• Explain why and in what direction the night sky rotates.
• Explain why we have seasons on Earth.

Phases of the Moon and Eclipses

Moon Phases and Eclipses Terms

terms to know: waning, waxing, gibbous, crescent, new moon, full moon, umbra,
penumbra

• Identify the phase and rise and set times of the Moon given a diagram of
  the relative positions of the Earth, Moon, and Sun.
• Identify the time of day for an observer given their position on Earth and
  the relative position of the Earth and Sun.
• Identify the relative alignment of the Earth, Moon, and Sun during a Solar
  and Lunar eclipse, respectively.

Astronomy History

Historical Astronomy Terms

terms to know: epicycle, Ptolemy, Copernicus, Galileo

• Explain the difference between Ptolemy and Copernicus' respective
  models of the Universe (really, our Solar System).
• Name the observations that led astronomers to prefer the Sun-centered
  model instead of the old Earth-centered model.

Kepler's and Newton's Laws

Laws of Motion Terms

terms to know: perigee, apogee, semi-major and semi-minor axes, force,
acceleration, velocity, speed

• Understand and conceptually apply each of Kepler's 3 laws, including how
  they relate to the distance, speed, and time of an orbit.
• Understand and conceptually apply each of Newton's 3 laws.
• Quantitatively apply Kepler's 3rd law for objects in our Solar System.

Light, Spectroscopy, and Telescopes

Light and Telescope Terms

terms to know: frequency, wavelength, refractor telescope, reflector telescope,
refraction, diffraction, Doppler shift

• Explain how the wavelength, frequency, and energy of light vary across
  the E&M spectrum and how the different named portions of the spectrum
  relate in wavelength, frequency, and energy (e.g., "which has a longer
  wavelength: radio or infrared?").
• Identify which portions of the E&M spectrum are suitable for ground-based
  observatories and which portions must be observed from space. Explain
  why.
• Describe the reasons for emission and absorption lines in a spectrum.
• Apply the Stefan-Boltzman Law for a blackbody.
• F = "T"
  (luminosity per surface area, i.e., "flux", of a blackbody)
• L = (4TR )OT4
  (total luminosity of a star of radius R and temperature T)
• Calculate the peak wavelength of a blackbody spectrum given its
  temperature (i.e., Wien's Displacement Law).
• Qualitatively explain the difference between refracting and reflecting
  telescopes.
• Qualitatively explain how the size of a telescope's aperture (lens or mirror)
  is related to its spatial resolution.
• Qualitatively explain how the relative velocity of an emitting source affects
  the wavelength of the light received by an observer: i.e., Doppler shift.

The Sun and the Solar System

Solar System Terms

terms to know: Nebular theory, Terrestrial planets, Jovian planets, Kuiper belt,
Oort cloud

• Identify the major components of the Solar System.
• Explain the origin theory of the Solar System.
• Explain why the properties of the objects in our Solar System vary as a
  function of their distance from the Sun.
• Explain why terrestrial and jovian planets differ in size, composition, and
  number of moons.
• Explain the source of the Sun's energy.

Exoplanets

Exoplanet Detection Terms

terms to know: transit, radial velocity, astrometry, direct imaging

• Explain the four primary methods that we use to detect exoplanets.
• Explain the observations that we use to measure the sizes of exoplanets.
• Calculate the size of an object given its transit depth.
• Explain the observations that we use to measure the masses of
  exoplanets.

Life in the Universe

Astrobiology Terms

terms to know: Habitable zone, Fermi Paradox, Drake Equation

• Explain the conditions that are necessary for life.
• Describe the components of the Drake Equation.
• Describe the Fermi Paradox and discuss potential resolutions.

Stars

Stellar Characteristics Terms

terms to know: parallax, HR diagram, luminosity, brightness

• Describe the HR diagram and identify the spectral class system.
• Explain how the size of a star (at fixed temperature) affects its location on
  the HR diagram.
• Describe the different classes of stars on the HR diagram (white dwarf,
  main sequence, giants).
• Given the brightness of a star and its distance, calculate its luminosity.
• Calculate the distance to a star given its parallax.
• Calculate the luminosity of a star using the Stefan-Boltzmann equation.

Stellar Evolution and Death

Stellar Evolution Terms

terms to know: HR diagram, supernova, white dwarf, neutron star, black hole

• Infer the relative ages of star clusters using the HR diagram.
• Explain the difference between type Ia and type II supernovae.
• Explain the evolutionary sequence of high-mass and low-mass stars.
• Identify the remnant objects following the deaths of stars of different
  masses.

Galaxies

Galaxy Classification Terms

terms to know: local group, dark matter, spiral galaxy, elliptical galaxy, irregular
galaxy, Milky Way

• Explain the observational evidence for dark matter.
• Explain the different classifications of galaxies.

The Universe

Cosmology Terms

terms to know: dark energy, Big Bang, redshift, Hubble's Law

• Describe the rungs of the cosmic distance ladder.
• Describe Hubble's law.
• Explain the observational evidence for the expansion of the universe.
• Explain the observational evidence for dark energy.

Practice Calculation Questions

the solutions are provided on the pages that follow

1. Convert 2000 km/s to km/hr. Express your answer in scientific notation.
2. Write the answer to the following using scientific notation:
   11
   4 ×10
   2 ×10
   7 ×10°
   5
   5
   =
   7 ×10
   -3
   =
   (3.5 x 10°) x (2 x 10-3) =
   5
   (4 × 10) x (35.5 × 10°) =
3. What is the surface area of a star with a radius of 1000 km. Report your answer
   in km^2 and express it in scientific notation.

Voyager Spacecraft Calculations

4. The Voyager spacecraft has traveled roughly 25 billion km over a time period of
17,000 days.

1. Convert the time period into hours (express your answer in scientific
   notation).
2. What has been the average speed of Voyager over this period (in km/hr)?

Wien's Displacement Law Application

5. A star with a surface temperature of 5800 K peaks at what wavelength [hint: use
Wien's displacement law]. Report your answer in nm.

Parallax Angle Calculations

6. A star has a parallax angle of 2 arcsec.

1. How distant is the star from Earth. Report your answer in parsecs (pc).
2. Convert your answer from (a.) into AU.

Kepler's Law Application

7. The Earth is at a distance of 1 AU from the Sun and takes 1 year to orbit. How
long in years does it take for Mars at 1.52 AU to complete 1 orbit (hint: one of
Kepler's laws).

Exoplanet Transit Calculation

8. An exoplanet passes in front of a star, temporarily blocking the star's light and
causing a transit. The radius of the star is 25 times larger than that of the planet.
What fraction of the star's light will the planet block?

Stellar Luminosity Comparison

9. Star A and Star B have the same size. Star A has a surface temperature of
2,000 K and Star B has a surface temperature of 8,000 K. How do their
luminosities compare?

Practice Calculation Solutions

Solution to Question 1

1. Convert 2000 km/s to km/hr. Express your answer in scientific notation.
speed = 2000
km
S
= 2000
km
S
× 1
= 2000
km
3600 s
hr
×
S
(
)
= 7.2 × 10
6
km
hr

Solution to Question 2

2. Write the answer to the following using scientific notation:
4 ×10
2 ×10
11
5
= 2 × 10°
7 ×10
5
-3
=1 ×10
8
7 ×10
(3.5 x 10°) x (2 x 10-3) = 7 x 10
2
(4 x 10) x (35.5 x 10) = 1.42 x 10
3

Solution to Question 3

33. What is the surface area of a star with a radius of 1000 km. Report your answer
in km^2 and express it in scientific notation.
2
2
A = 4TTR" = 4TT(1000 km)
= 1. 256 x 10 km
2

Solution to Question 4

4. The Voyager spacecraft has traveled roughly 25 billion km over a time period of
17,000 days.

1. Convert the time period into hours (express your answer in scientific
   notation).
   t = 17,000 days
   = 17,000 days
   × 1
   = 17,000 days
   X
   (
   1 day
   24 hours
   )
   = 4.08 x 10 hours
   5
2. What has been the average speed of Voyager over this period (in km/hr)?
   speed =
   distance
   time
   =
   25 ×103 km
   4.08 ×10° hr
   = 61, 274 km/hr

Solution to Question 5

5. A star with a surface temperature of 5800 K peaks at what wavelength [hint: use
Wien's displacement law]. Report your answer in nm.
λ
max
=
2.9 ×10 (nm · K)
T (K)
2.9 ×10°(nm · K)
=
5800 K
= 500 nm

Solution to Question 6

6. A star has a parallax angle of 2 arcsec.

1. How distant is the star from Earth. Report your answer in parsecs (pc).
   d = 1
   p
   1
   =
   2 arcsec
   = 0. 5 pc
2. Convert your answer from #8 into AU.
   d = 0. 5 pc
   = 0.5 pc × 1
   = 0.5 pc
   X
   206, 265 AU
   1 pc
   )
   = 103, 123 AU

Solution to Question 7

7. The Earth is at a distance of 1 AU from the Sun and takes 1 year to orbit. How
long in years does it take for Mars at 1.52 AU to complete 1 orbit (hint: one of
Kepler's laws).
P = a
2
3
(this is applicable for our Solar system if P is
expressed in years and a is expressed in AU)
P
)
2
=
(a
)
mars
3
mars
P
= (a
mars
3/2
mars
P
= (1.52 AU)
3/2
mars
P
mars
= 1.87 yr

Solution to Question 8

8. An exoplanet passes in front of a star, temporarily blocking the star's light and
causing a transit. The radius of the star is 25 times larger than that of the planet.
What fraction of the star's light will the planet block?
AF =
(
R
R
p
S
)
2
= (
25
)
2
= 0.0016

Solution to Question 9

19. Star A and Star B have the same size. Star A has a surface temperature of
2,000 K and Star B has a surface temperature of 8,000 K. How do their
luminosities compare?
= 4TR OT
2
.4
L
4TRO(TR)
4
B
=
4
L
L
A
4TUR o(T)
2
A
The size of the stars are the same, and so everything except the
temperature terms cancel:
L
L
B
A
=
T
B
T
A
(
)
4
=
(
= 256
2000 K
8000 K 4
= 4
4
Star B is 256x more luminous than Star A.