SCI1000C HW11 Solutions PDF

Preview

Summary

hw for sci. inquiry: astrology chapter 11...

Description

Name:___________________________ ! Scientific Inquiry: Astronomy Week 11 Written Homework – Due in class on Mon, 11/13 Part I. Our Expanding Universe Identify whether the following statements are true or false based on evidence that we have for the big bang. In one to two sentences, explain why the statements are true or false. (Refer to this week’s reading if these are difficult.)

1. The big bang was an explosion that sent all other galaxies in motion away from the Milky Way. Currently, the Milky Way stays stationary while all other galaxies recede from it. False. The big bang was not an explosion, it was the beginning of the expansion of space. As space expands, all galaxies grow more distant from each other. No single galaxy remains stationary, although from within that galaxy it does appear as if most other galaxies move away from it.

2. Light from distant galaxies is redshifted because the expansion of space causes the wavelength of the light to increase, not because those galaxies are in motion through the universe. True. There may be some additional redshift or blueshift due to the relative motion of the galaxy with respect to our own. However, most of the redshift we see is cosmological redshift, redshift caused by the expansion of space.

3. As the universe expands, the space between stars in a galaxy also expands, which makes galaxies grow larger over time. False. Gravity will hold galaxies together against the expansion of space. Similarly, gravity will hold our solar system (and Earth) together. The molecular bonds holding most matter together on Earth is also strong enough to overcome the expansion of the universe.

4. We observe that most galaxies are redshifted when viewed from the Milky Way. If we were to observe the universe from within another galaxy, we would also find that all galaxies are redshifted. True. Because the expansion of space increases the distance between all galaxies, from the point of view within any individual galaxy it will appear that all other galaxies recede. Because they recede, light coming from them will be redshifted.

1

Scientific Inquiry: Astronomy Week 11 Homework Part II. The Age of the Universe The graph below shows Edwin Hubble’s original measurements of the distance and speed of distant galaxies, which he performed in 1929. Each data point in the plot represents a galaxy.

Note: The units of distance are mega-parsecs (Mpc). 1 Mpc = 3.1 x 1019 km.

1. What is the relationship between a galaxy’s distance from us and the speed with which the galaxy is receding (moving away) from us? As distance from the Milky Way increases, the recession velocity (speed) of any given galaxy also increases. In simpler terms, galaxies that are farther away appear to recede faster.

2. It turns out that the closest galaxy (Andromeda) to the Milky way has a negative recession velocity, meaning it is moving toward us. What might be the reason for this? Andromeda is close enough to the Milky Way that gravity is drawing the two galaxies together. In about 4 billion years the Milky Way will merge with Andromeda.

! 2

Scientific Inquiry: Astronomy Week 11 Homework 3. In class, we were able to calculate the age of our balloon model of the universe by drawing a trendline to fit the data on a velocity vs. distance plot, then and finding the slope of the trendline. The slope is also referred to as the Hubble constant. On the graph of Hubble’s data, choose two points on the trendline, and find the rise and the run using those points. Convert the rise and run to standard metric units. See the graph for the two points that I chose. To find rise, subtract the recession velocity of each point: 1000 km/s – 500 km/s = 500 km/s. To find run, subtract the distance of each point: 2 Mpc – 1Mpc = 1 Mpc. Because Mpc are not standard metric units, we should convert: 1 Mpc = 3.1 x 1019 km.

4. Using the values of rise and run from the previous problem, calculate the Hubble constant (slope). 𝑆𝑙𝑜𝑝𝑒 = 𝐻( =

𝑅𝑖𝑠𝑒 5000𝑘𝑚/𝑠 = 𝟏. 𝟔𝟏0×0𝟏𝟎-𝟏𝟕 0𝟏/𝒔 = 89 𝑘𝑚 3.10×010 𝑅𝑢𝑛

5. Using the slope from the previous problem, find the age of the universe according to Hubble’s data. Convert this age to years, and express it in scientific notation.

𝐴𝑔𝑒 =

1 1 = 𝟔. 𝟐𝟏0×0𝟏𝟎𝟏𝟔 0𝒔 = 𝐻( 1.610×010C8D 01/𝑠

Now convert to years: 10𝑚𝑖𝑛 10ℎ𝑟 10𝑑𝑎𝑦 10𝑦𝑟 6.210×0108G0𝑠0×0 0 ×0 0×0 0×0 = 𝟏. 𝟗𝟕0×0𝟏𝟎𝟗 0𝒚𝒓 600𝑠 600𝑚𝑖𝑛 240ℎ𝑟 365.250𝑑𝑎𝑦𝑠

6. Does the age of the universe you calculated match the modern estimate of 13.8 billion years? If there are differences, what might be the reason? (Think about the limitations of Hubble’s measurements in the early 1920s.) No, it is smaller by an order of magnitude. The two measurements that were used to calculate this age were distance and speed. Hubble could have underestimated the distances to far away galaxies, or overestimated their speed. Distance is very difficult to measure in astronomy, so it is likely that this is what caused the error.

! 3

Scientific Inquiry: Astronomy Week 11 Homework Now consider the more recent data shown below. The graph shows data collected in 2001. Again, each point represents a galaxy. The error bars on each point show the uncertainty in each measurement. The solid line represents the trendline that best fits the measured data, and the dotted lines represent the uncertainty in the trendline.

7. What differences do you notice in the 2001 data compared to the measurements made by Hubble? Name at least two. The distances axis extends much further than in Hubble’s original plot. This is because modern telescopes are able to see fainter, more distant galaxies than those measured in the 1920s. The velocity axis extends to higher velocities to incorporate the speeds of these more distant galaxies. The new plot also includes error bars to represent the uncertainty in each measurement. Three trendlines are shown to represent the range of possible slopes that correspond to these data.

8. Using the solid trendline on the 2001 graph, choose two points and estimate the rise and the run. Convert the rise and the run to standard metric units. See the graph for the two points that I chose. To find rise, subtract the velocity of each point: 1500 km/s – 500 km/s = 1000 km/s. To find run, subtract the distance of each point: 20 Mpc – 7 Mpc = 13 Mpc. Because Mpc are not standard metric units, we should convert:

! 4

Scientific Inquiry: Astronomy Week 11 Homework 130𝑀𝑝𝑐0×0

3.10×01089 0𝑘𝑚 = 𝟒. 𝟎𝟑0×0𝟏𝟎𝟐𝟎 0𝒌𝒎 10𝑀𝑝𝑐

9. Using the rise and run from the previous problem, calculate the Hubble constant (slope). 𝑆𝑙𝑜𝑝𝑒 = 𝐻( =

𝑅𝑖𝑠𝑒 10000𝑘𝑚/𝑠 = 𝟐. 𝟒𝟖0×0𝟏𝟎-𝟏𝟖 0𝟏/𝒔 = W( 𝑘𝑚 4. 03 0×0 10 𝑅𝑢𝑛

10. Using the slope from the previous problem, find the age of the universe according to the 2001 data. Convert this age to years, and express it in scientific notation. Does it match the modern estimate of 13.8 billion years?

𝐴𝑔𝑒 =

1 1 = = 𝟒. 𝟎𝟑0×0𝟏𝟎𝟏𝟕 0𝒔 𝐻( 2.480×010C8Z 01/𝑠

Now convert to years: 10𝑑𝑎𝑦 10𝑦𝑟 10𝑚𝑖𝑛 10ℎ𝑟 0×0 0×0 = 0𝟏𝟐. 𝟖0×0𝟏𝟎𝟗 0𝒚𝒓 4.030×0108D 0𝑠0×0 0×0 600𝑠 600𝑚𝑖𝑛 240ℎ𝑟 365.250𝑑𝑎𝑦𝑠

This number is slightly smaller than 13.8 billion years, but that is to be expected, since we estimated it from the graph by hand. If you got an answer of tens of billions of years, then good job! You’ve estimated the age of the universe reasonably well from actual galactic data.

! 5...