Astro Exam 3 Homework Review

The total mass of our galaxy is 200 billion solar masses (Msun). What percent of our galaxy's total mass does the central black hole contain?

.002 0.002 0.00002 .00002 because Your answer should be a very small percentage. Divide the mass of the black hole (4 million solar masses) by the total mass of the galaxy (200 billion solar masses). Since the units are the same (solar masses), you end up needing to divide just the numbers: 4 million divided by 200 billion. Hint: write both numbers in scientific notation.

The two diagrams above show the arrangement of several galaxies in the Universe, first in the early universe and then some time later. Imagine that you are in the E galaxy. RANK the A, B, C, and D galaxies in terms of their relative speeds away from you, from SLOWEST (1) to fastest (4).

1- galaxy B 2- galaxy C 3- galaxy D 4- galaxy A (see image)

Rank the following objects in order of increasing density, from 1 (least dense) to 5 (most dense).

1- main sequence stars 2- Earth 3- white dwarfs 4- neutron stars 5- black holes

Express Rs in units of lightyears (ly), and express in scientific notation.

1.26x10^-6 Hint: Multiply your value of Rs in km (it should be 12 million km) by the conversion factor expressed as a fraction, like so: 12 x 106km x (1 ly) / (9.5 x 1012km) = ...?The units of km should cancel, leaving you with an answer in ly.The first answer box is for the coefficient of the number in scientific notation. The second answer box is just for the exponent. Be sure to include a negative sign, since the exponent should be a negative number.

Assuming a constant rate of expansion, the age of the Universe equals

1/H0(0 is subscript)

It turns out that the Andromeda galaxy is actually moving TOWARD the Milky Way galaxy, and we will eventually collide. If Andromeda is moving toward us at a speed of 120 km/s, and it is currently 2.9 million light years away, how long will it be until we collide? (Assume constant speed.) Convert your answer to years. Answer choices have been rounded and are nowhere near each other, so you can SERIOUSLY round any numbers you use without need for a calculator. Some handy conversions: 1 ly = 9.5 x 1012 km, and 1 year = 3.1 x 107 s.

10 billion (10,000,000,000) years Hint: This is just a distance = speed x time problem. Rearrange the equation to get time by itself, and plug in the given quantities for distance and speed. Be mindful of units. You will have to do at least one or two unit conversions.

What is the Schwarzschild radius (Rs) of the black hole in km? Hint: Figure this out by making a ratio comparison of a smaller black hole with a known mass and corresponding Rs: For a one solar-mass (1 Msun) black hole, Rs = 3km. Recall that Rs and M are directly proportional, because Rs = 2GM/c2.

12 million km hint: If a 1 solar mass black hole has Rs = 3 km, a 4 million solar mass black hole (with a mass 4 million times bigger) will have a Rs that is 4 million times bigger...

If a galaxy is 20 Mpc away from us, about how fast is it receding from us? Use 70 km/s/Mpc for the Hubble constant (H0).

1400 km/s Setup: v = H0 x dPlug in 70 km/s/Mpc for H0, and 20 Mpc for d.

Convert the distances on the horizontal axis into units of megaparsecs (Mpc) instead of parsecs. In Mpc, what is the distance of the most distant galaxies shown on the graph above?

2 mpc Hint: Keep in mind that 106 is the same as "million", and "Mega" also means "million". Therefore all of the following are equivalent: "106 pc", "million parsecs", "megaparsecs", and "Mpc".

If a galaxy is receding from us at 1.4 x 105 km/s, how far away is it? Use 70 km/s/Mpc for the Hubble constant (H0).

2.0 x 10^3 Mpc Setup: Start with v = H0 x d, and rearrange it to solve for d: d = v / H0Plug in 70 km/s/Mpc for H0, and 1.4 x 105 km/s for v.d = (1.4 x 105 km/s) / (70 km/s/Mpc) = ....Now just be careful with your units!

Hypothetical: If the Hubble constant were 50 km/s/Mpc (instead of the value of 70 km/s/Mpc that we assumed in class), what would be the estimated age of the universe? Assume a constant expansion. Answer choices have been rounded, so pick the closest one.

20 billion years Hint for doing this problem without a calculator: Use the calculation that we did in class as a reference: If Ho=70 km/s/Mpc, then To=14 billion years. So, if Ho had a slightly SMALLER value, what would happen to the value of To?

How does the radius of the event horizon of a 9 solar mass black hole (BH) compare to that of a 3 solar mass BH? The 9 solar mass BH is...

3 times bigger. because The radius of the event horizon is also called the Schwarzschild Radius. The equation for that is Rs = 2GM / c2. This is often what is referred to as the "size" of a BH, unless the singularity itself is explicitly specified. Notice that Rs is directly proportional to mass of the BH.

What is the approximate slope of the solid line on the graph above, in units of km/s/Mpc? (Hint: You will do (or did) a calculation just like this in class when we discuss(ed) Hubble's Law.)(Historical note: this is the value that Edwin Hubble originally calculated for H0. It does not match the value of H0 we used in class, because Hubble used a limited sample of nearby galaxies that were not representative of faraway galaxies. The sample was improved later by including many more galaxies, and the slope was refined as many more galaxies were measured and added to the plot. The value that we used in class is the one widely accepted by astronomers today.)

5 x 10^2 km/s/Mpc

You can do this problem without a calculator if you round the numbers to get an approximate answer. Let's scale the size of our galaxy (radius = 50,000 ly) down to that of a basketball (radius = 10 cm). The closest galaxy to ours is Andromeda, at 2.9 million lightyears away. How far is this in our scaled-down model?

5.8 m

You can do this problem without a calculator if you round the numbers to get an approximate answer. Now let's scale the size of the Sun (radius = 7x105 km) down to that of a basketball (radius = 10 cm). The closest star to our Sun is Proxima Centauri, at 4.3 lightyears away in real life. How far is this in our scaled-down model? (Note: 1 ly = 9.5 x 1012 km, 1 km = 1000 m, and 1 m = 100 cm. You will likely need to do at least one unit conversion.)

5800 km

On a clear night, you can see about 1,000 stars with your naked eye. These stars are all part of the Milky Way Galaxy. The average bright star is a few dozen parsecs away from us, but some of them are a few hundred or even more than a thousand parsecs away. Below are three depictions of the Milky Way with circles overlaid to denote three possible boundaries inside of which all the naked eye stars might lie. Which boundary, A, B, or C, best represents the true distribution of naked eye stars?

A (see image)

This question is taken from question #3 in the "Hubble's Law" worksheet, on page 85-88 of your workbook. It is the student debate, which references both Q1 and Q2.Be sure you have answered the first three questions completely in your workbook (including the debate, and explaining your reasoning), and then identify which portion of each student's statement is correct, or incorrect. Some of the statements are paraphrased, so they won't match verbatim -- Look for the meaning of the statements to find the matches. Each option is used exactly once.

All the distances increased by the same amount- an incorrect statement student 1 said All the distances increased by the same factor- a *correction* we could make to an incorrect statement student 1 said The galaxy that was farthest away initially will have its distance increase by the greatest amount- a correct statement that only student 2 said All the distances doubled- a correct statement that BOTH students said

Based upon these answers, decide which objects are more "crowded" (i.e. closer together relative to their size) in space. These will thus be more likely to collide with one another. So which are more crowded and thus likely to collide with one another: stars within a galaxy, or entire galaxies with one another?

Entire galaxies, since neighboring galaxies are much closer together relative to their size.

This question is taken from #11 on the "Hubble's Law" worksheet on pg 85-88 of your workbook. Study the Figures 2, 3, and 4 on pg 86-87. If the Hubble plots in these Figures 2-4 represent three universes that are the same "size" (or average spacing of galaxies), which Hubble plot belongs to the youngest universe, and why?

Figure 3, because it has the steepest slope

The following figure comes from the worksheet "Making Sense of the Universe and Expansion" in your workbook. For more background on the figure, look on page 81 of your workbook.Each tiny dot in the picture below represents a galaxy. The Milky Way Galaxy is at the center of the circular region shown, and galaxy X is on the edge. This circle defines what is called our observable universe.

Galaxy X sees all other distant galaxies moving away from itself. The Milky Way Galaxy sees Galaxy X moving away from it. Galaxy X sees the Milky Way Galaxy on the edge of its observable universe. Galaxy X sees the Milky Way moving away from itself. (see image)

How does the escape velocity from Earth change if you climb to the top of Mt. Everest?

It decreases a tiny little bit. because Mt. Everest is a few km tall. (If you're curious, it's 8.8 km more precisely, though precision is NOT needed for this problem.) This is a minuscule fraction of the radius of the Earth. (If you're curious about the precise number, it's 8.8km / 6371km = 0.001, or 0.1%, but again precision is NOT needed to answer this question.) So if you climb to the top of Mt. Everest, your distance from the center of the Earth ("R") increases by a minuscule amount. But the mass of the Earth ("M") remains the same. How does this change affect the terms in the escape velocity equation? How does this affect the value of vesc?

When the Andromeda galaxy collides with the Milky Way galaxy, what will most likely happen to our Sun as a result?

It will not collide with any other stars.

Compare the size of the black hole's event horizon to the typical spacing between stars in a galaxy. Neighboring stars are typically dozens of lightyears apart. Are the stars in our galaxy in danger of being swallowed up by the black hole?

No, virtually all the stars in the galaxy are safe.

This question comes from the worksheet "Milky Way Scales" on pg 73-75 in your workbook. Assume that the picture below represents our Milky Way Galaxy and has the dimensions labeled below in light years (ly). Below is a list of five bright stars in our night sky. In the last column, type the letter of the dot (A-E) from the picture above that best represents the location of each star. You can use letters more than once.

Sirius 9 ly- A Vega 26 ly- A Spica 260 ly- A Rigel 810 ly- A Deneb 1,400 ly-A A is the closest point to the sun and although these are all different distances they are all extremely close to the sun in the grand scheme of things

Which of the following states "Hubble's Law" in words?

The farther away a galaxy is, the faster it is moving.

This question is #9 from the worksheet "Looking at Distant Objects" on pg 78 of your workbook: Imagine that you take images of two main sequence stars that have the same mass. From your observations, both stars appear to be the same age. Consider the following possible interpretations that could be made from your observations. Which ones are possible? Check all that apply.

The star that is farther from you is actually the older of the two stars Both stars are the same age and the same distance from you.

What is a similarity between the object at the center of our galaxy today and a quasar?

They are both supermassive black holes.

This question is taken from the last question in the "Expansion of the Universe" worksheet on page 89-90. It is the student debate.Review the debate, and then identify which portion of each student's statement is correct, or incorrect. Each option is used exactly once.

We must be at the center of the Universe- an incorrect statement student 1 said All (or most) galaxies are moving away from us- a correct statement student 1 said All (or most) galaxies move away from each other- a correct statement student 2 said Each galaxy must be at the center of the universe- a partially incorrect statement student 2 said

Galaxies all formed at the same time, long ago. If you observe two galaxies at different distances from you, the more distant one will...

appear younger hint: Note that if galaxies all formed at the same time, then it means they are the same age.

Why is the Andromeda galaxy moving toward us, anyway?

because it is gravitationally bound to our galaxy

To study what galaxies look like when they are young, we look at

galaxies that are very distant.

Consider that the radius of our galaxy is 50,000 light years (ly). How does the size of the black hole's event horizon (Rs) compare to the size of the galaxy

it less than a billionth the radius of the galaxy — an utterly negligible fraction of the size of the galaxy

Above is the original plot that Edwin Hubble made of galaxy recession velocity vs. distance for a couple dozen galaxies. The units of the numbers on the horizontal axis are parsecs or "pc" (remember 1 million pc = 1 Mpc). The units of the numbers on the vertical axis are actually INCORRECT. They should NOT be in kilometers. What units should they be?

km/s Hint: The vertical axis should represent velocity, so it needs to have units of velocity...

How do a white dwarf's observable properties change as it ages, if it is left alone? Choose the TWO correct answers.

luminosity decreases and temperature decreases

Based upon the number you calculated above, do you think the central black hole plays an important role in the overall dynamics of the galaxy -- i.e. the orbits of the stars?

no

This question is taken from question 4 in the "Making Sense of the Universe and Expansion" worksheet on page 81-82 of your workbook. It is the first student debate. Read the full argument of both students in your workbook, and then indicate which student(s) is (are) completely correct, if either.Which student(s) is/are correct, if either?

only student 2 is correct

A quasar is NOT _____

powered by nuclear fusion.

Scenario: Imagine that you are observing the light from a distant star that was located in a galaxy 100 million ly (light years) away from you. The image that you see from that light is of a 10-million-year-old star. You recognize the particular type of star, and know that such stars have a total lifetime of 50 million years, at which point they explode in a catastrophic supernova. Piece together a timeline for the sequence of events described in the problem, with time (t) = 0 million years representing the moment the star is actually born. Subsequent times are all referenced to t=0. Hint: One time is used twice; four are used once each, and four are used not at all. Note: The events are listed in random order in the left column, and not chronological order.

star appears to be born, to observer on Earth t=100 million years star appears to be 50 million years old, to observer on Earth t=150 million years star appears to go supernova, to observer on Earth t=150 million years star appears to be 10 million years old, to observer on Earth t=110 million years star is actually born t=0 million years supernova actually occurs t=50 million years