Question: The Milky Way galaxy has about 5e9 solar masses of gas in total. If 2 solar mass of that gas is turned into stars each year, how many more years could the Milky Way keep up with such a star formation rate?
Answer: 5e9 divide by 2 is 2.5e9. So, the MW can keep up its star formation rate of 2 solar mass per year for 2.5e9 years.
Question: The Sun is circling around the Milky Way galaxy at a radius of about 8 kpc from the center with an orbital speed of 220 km/s. If stars and gas at a radius of 16 kpc are also orbiting the Galaxy at the same orbital speed, how much larger is the total mass inside the 16 kpc radius compared with the total mass inside the solar circle?
Answer: Orbital velocity law discussion in Unit 73 gives an example calculation for determining the mass inside the solar circle. You can also find a similar example worked out in my online lecture outline. The most relevant piece of information is that M = r x v2. In other words, the mass is proportional to the radius if the rotation speed v is constant. So, in this question, radius of 16 kpc is twice as large as the radius at the solar circle, 8 kpc. Therefore, the mass at r=16 kpc is two times larger as well.
Question: Suppose a galaxy is 10 Mpc away from us. How many years ago did the light we're receiving today leave that galaxy?
Answer: 10 Mpc is 10e6 parsec. 1 parsec is 3.26 light years. So, 10 Mpc = 10e6 pc = 10e6 x 3.26 = 3.26e7 light years. A light year is the distance light travels in 1 year. Therefore, 3.26e7 light years is the distance light travels in 3.26e7 years (or 32.6 million years).
Question: A spectral line that has a rest wavelength of 623 nm is observed from a galaxy at a wavelength of 624 nm. What velocity does the galaxy have (in units of km/sec)? Note that if the galaxy has a blueshift (moving toward us), its velocity should be written as a negative number.
Answer: The relationship between redshift and change in wavelength is discussed extensively in Unit 25 with some examples. Redshift z is given by [lambda(observed) - lambda(rest)]/lambda(rest). Here lambda(observed) = 624 nm, and lambda(rest) = 623 nm. Then z = (624 - 623)/623 = 1.6e-3. This question asks about the velocity, which is v = c x z = 299793 km/s x 1.6e-3 = 481 km/s.
Question: Suppose you observe a galaxy with a velocity of recession of 7,000 km/sec. If Hubble's Constant is 70 km/sec per Mpc, what is the distance to the galaxy in Mpc?
Answer: The Hubble's Law says "v = H x d". Dividing both sides by the Hubble constant H gives, v/H = d. So, distance d is recession velocity v divided by the Hubble's constant H. Or, d = 7000/70 = 100 in Mpc.
Question: If the universe is expanding at a constant rate, you can calculate the age from Hubble's constant. What would the age of the universe be if Hubble's constant were 70 km/sec per Mpc?
Answer: In class, you were shown that the age of the universe can be estimated as 1/H. For H = 65, it was shown that age is 1.5e10 years. For H = 70, the age should be smaller by an amount of 65/70 = 0.929. Or the age of the universe should be 0.929 x 1.5e10 = 13.9e10 years.
Question: Looking through historical records of the quasar 3C10, which is at a distance of 174 Mpc, you discover that it underwent a brightening beginning in 1981 and lasting for 10 years before fading back to its original brightness. At its maximum brightness, it was 3 times brighter than it is normally. What is the largest possible size of the region that underwent the outburst? Express your answer in light years.
Answer: We talked about this problem as one of the inclass quizes. The only relevant information here is that this source varied over 10 years of time. Think of this source as a collection of light bulbs laid out over an area of diameter D. If you try to turn on all of the light bulbs at once, the fastest you can accomplish this is over the time of D/c where c is the speed of light. In other words, the fastest you can send the command to "turn on the lights!" from one end of the field to another is limited by the speed of light. Turning this around, if you saw a field of lights turn on over a period of 10 years, the largest diameter of the area has to be the light travel distance over 10 years, or a distance of 10 light years.