Please do not use AI. Thanks.

1. a) Imagine that a white dwarf has a luminosity of1.0 10⁴???? but the same surface temperature as the Sun. What is the radius of this white dwarf. Express your result inkm.

1. If this white dwarf has a mass of0.7???? (a pretty typical value), what is the mean mass density of the white dwarf? Express this result in????/????????³.
2. How many ofyouwould need to be crammed into a single cubiccm to equal this density?

2. The Crab Nebula is the home of the famous pulsar described in Destination 12. Below is a table of the radius of the nebula (really, half its major axis since the nebula is not circular in appearance in the sky) and the date on which that radius was measured. This table starts in 1054 when the nebula was born during a bright supernova explosion observed that year. One of the first telescopic observations of the Crab was around 1755 by Charles Messier, with many subsequent measurements to the present day.

Date	Radius (pc)
1054	0.00
1755	1.09
1787	1.08
1810	1.14
1875	1.21
1928	1.32
1952	1.34
1995	1.42
2017	1.45

1. Using the data in the table,accurately plot the radius of the Crab Nebula (on they axis) versus the date (on thexaxis). Be sure to note the units (keep in mind that 'Date' doeshave specific units . . .).
2. Estimate the slope of a line that fits the data well. This result is the expansion velocity of the nebula. Be sure to note the units of the slope!
3. Convert the result from part (b) to units ofkm/s .
4. The escape velocity from the Sun is about 11.2km/s. How many times faster is the CrabNebula expanding compared to the Sun's escape velocity? This gives some sense of theimmense amount of energy required to blow up a massive star!

3. The atomic weights ofAl²⁸,Fe⁵⁶ andCd¹¹²(those are Aluminum, Iron and Cadmium) are 27.982, 55.935 and 111.903 atomic mass units (amu), respectively. Imagine fusing two of these Al nuclei to form one Fe nucleus. Then, imagine fusing two of these Fe nuclei to make one Cd nucleus.

1. What are the mass differences between the input nuclei and the output nucleus in the two cases described? Provide your answer inamu andg. Be consistent about signs!
2. Which of these two reactions is exothermic (produces energy) and which endothermic (consumes energy)?
3. Given what you observe from these comparisons, explain under what conditions Fe might be able to form in stars and under what conditions Cd might be able to form in stars.

4.The Virial Theorem was used to estimate the mass of the Galactic Halo in Destination 13.

But this approach works for any spheroid system, including globular clusters.

1. Imagine you have measured the velocity dispersion of a cluster to be 10.5km/s based on measurements of stars that are, on average, located 12 pc from the center of a globular cluster. Use the Virial Theorem to estimate the mass of the cluster. Give you result in units of???? (Solar Masses).
2. If the luminosity of this cluster is 500,000????, what is the mass-to-light (M/L) ratio of the cluster (in Solar units)?
3. Based on this result, do you conclude that this cluster has a lot, a little, or no dark matter. HINT: As described in Destination 13, a M/L greater than 10-20 (in Solar units) is indicative of dark matter; a value less than 2-4 can be explained with normal matter (stars), while the range from about 3-15 is ambiguous.

5. Look up information on a planetary nebula (PN)or a supernova remnant (SNR; defined here as the expanding material from a stellar explosion). Refer to Destinations 11 and 12 for the general features of these objects. If you initially choose an object that does not have all the information requested below, pick another PN or SNR!

1. How far away is the object you selected?
2. How 'old' is the PN or SNR as defined from the time its expansion began?
3. How fast is the gas expanding in the PN or SNR you selected?
4. Calculate the diameter of the nebula in units of Astronomical Units based on any combination of the information in partsa-c. Be clear how you calculated this.