Please solve the following questions. This is not an assignment, it will not be graded, and you do not need to submit your solutions to anyone. The questions are simply intended to help you practice for the exam.

These questions will not appear in the exam itself. Students who don't genuinely attempt to solve the questions on their own, and only memorize the solutions, will have a very hard time in the actual exam!

These questions are not multiple-choice, to encourage you to think of the answers on your own, but the questions in the actual exam will be multiple-choice.

If you need any clarifications for these questions, you can ask for them on the course Teams channel.

Question 1 Show/hide solution

I found an object with a mass of 1/20 solar masses. What is this object, most likely?

Solution: A brown dwarf, since it is not massive enough to be a star but more massive than a planet.

Question 2 Show/hide solution

Star A is 16 times more luminous than star B. What will be the approximate difference in their masses?

Solution: Luminosity is approximately proportional to the fourth power of the mass, and 16 = 2⁴, so the mass of star A will be twice as large as the mass of star B.

Question 3 Show/hide solution

A star is in the top right of the H-R diagram. What can you say about it?

Solution: It is very luminous but also very cold. Its spectral class is M (sometimes the diagram is expanded to include spectral classes L, T, and Y to the right of M, but these classes only apply to brown dwarfs, which are on the bottom right). It is a red giant, most likely a class Ia supergiant or a hypergiant.

Question 4 Show/hide solution

What is the main sequence?

Solution: On an H-R diagram, which is a plot of luminosity vs. temperature, the main sequence is an approximately diagonal region of stars for which luminosity is proportional to temperature. This region contains most of the known stars (around 90%, including our Sun). Other types of stars, such as giants and white dwarfs, lie outside the main sequence and they do not exhibit the same relation between luminosity and temperature.

Question 5 Show/hide solution

How do we know, from the H-R diagram, that giant must be larger than main-sequence stars of the same luminosity?

Solution: The giants are colder, so they produce less light per square meter of surface area. Therefore, in order to generate the same total amount of light (luminosity) as main-sequence stars of the same luminosity, which are much hotter, the surface area of the giants must be much larger.

Question 6 Show/hide solution

A star has spectral class K5 V. What does that tell you about it?

Solution: It's an orange dwarf.

Question 7 Show/hide solution

A star has spectral class B3 V. What does that tell you about it?

Solution: It's a B-type main-sequence star.

Question 8 Show/hide solution

A star has spectral class F7 Ia. What does that tell you about it?

Solution: It's a yellow luminous supergiant.

Question 9 Show/hide solution

A star has spectral class B4 IV. What does that tell you about it?

Solution: It's a blue subgiant.

Question 10 Show/hide solution

If a star is named Beta Andromedae, what does that tell you about it?

Solution: Andromeda is a constellation, and beta is the second letter in the Greek alphabet, so Beta Andromedae is a star in the constellation Andromeda (in fact, it's the second-brightest star).

Question 11 Show/hide solution

What is the most precise way to measure the distance to the Moon?

Solution: By reflecting laser beams off retroreflectors on the surface and calculating the distance using the travel time of the beam and the speed of light.

Question 12 Show/hide solution

If a star is located 20 parsecs away, what is its parallax angle?

Solution: 0.05 arc seconds.

Question 13 Show/hide solution

The closest star to the Sun, Proxima Centauri, is located around 4.2 light-years away. How much is that in kilometers? In parsecs?

Solution: 1 light-year is approximately 9.5 trillion km, so 4.2 light-years is approximately 40 trillion km. 1 light-year is approximately 0.31 parsecs, so 4.2 light-years is approximately 1.3 parsecs.

Question 14 Show/hide solution

How many kilometers are in a light-hour (the distance light travels in an hour)?

Solution: There are 3600 seconds in 1 hour. Multiply that by 300,000 km/s and you get 1,080,000,000 or around 1 billion km.

Question 15 Show/hide solution

How many AU are in a light-hour?

Solution: If we divide the result from the previous question by 1 AU, which is around 150,000,000 km, we get 7.2 AU.

Question 16 Show/hide solution

What are cepheid and RR Lyrae variables, and what are they used for?

Solution: They are two types of variable stars; the main difference between the two types are the luminosity and period. They are used to measure distances. For cepheid variables, we use the fact that they have a luminosity that is related to their period. We can't measure the luminosity, since the brightness of the star varies with distance, but we can easily measure the period regardless of distance. Once we measure the period, we can use it to estimate the luminosity. Now that we know the luminosity, we can compare that with how bright the star appears to us in the sky, and use that to calculate the distance to the star, since we know the light gets fainter with distance according to the inverse square law. For RR Lyrae variables, we use the fact that they all have roughly the same luminosity no matter where they are. Again, once we know the luminosity, we can calculate the distance.

Question 17 Show/hide solution

I want to measure the distance to a star that is estimated to be around 25,000 light years away. Which method should I use?

Solution: Stellar parallax.

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