# Astronomy 300: Homework Assignment #10

Due: Wednesday , May 16 th

Chapter 13 in Croswell

1. Where do most of the Iron atoms in your body come from? Specifically, in what environment/location are they produced?

2. A.) What is the third most common element in the universe?
B.) For every 1 million Hydrogen atoms, how many atoms of this element are present in the universe? How does this compare to the number of Iron atoms?

3. On p. 170 Croswell writes:

"The 1987 supernova in the Large Megallanic Cloud [a Type II core collapse supernova] gave the galaxy roughly 1.6 solar masses of oxygen but only 0.075 solar masses of Iron."

Is this enough to supply the iron content of the entire Earth? By what factor (roughly)? State your methods and sources for this calculation.

4. Make a table of the properties of Supernovae, using two columns "Supernovae Type 1a" and "Core Collape (eg. Type II)". Under each of these columns list differences such as: binary vs. single star, elements present before explosion, elements ejected into the ISM and lifetime of stars involved.

Chapter 16 in C&O

5. C&O Chapter 16. Problem 16.10

6. The millisecond pulsar PSR 1257+12 has a period of 0.006219 seconds = 6.2 ms. In 1992, A. Wolszczan announced discovery of planets orbiting this pulsar. The orbital periods and semi-major axes of these "planets" are:

• Planet A: P = 25.2 d ; a = 0.19 AU
• Planet B: P = 66.5 d ; a = 0.36 AU
• Planet C: P = 98.2 d ; a = 0.46 AU

A.) Use one of these planets to determine the mass of the pulsar.
Use all three planets to determine the mass of the pulsar. Report a value plus standard deviation.

7. The fastest known pulsar is PSR J1748-2446ad which rotates at 716 Hz. (rotation period: 1.4 ms). Assuming the radius of the neutron star is 15 km, at what speed does the surface of the neutron star rotate? Express your answer as a fraction of the speed of light. (Note: if you asked a related question in class, then indicate this on your solution...you get double credit for this problem!)

Black Holes

8. It is a common misunderstanding that Black Holes will swallow up everything anywhere surrounding them. Suppose someone is worried about the Sun becoming a black hole and swallowing Earth.

A.) How would you reassure this person that the Sun will not become a BH?

In fact even if the Sun became a black hole, Earth would continue in its orbit unaffected. Only if there were some source of friction would Earth spiral in to the BH.

B.) How much mass would the Sun need to have to be a black hole with Schwarzchild radius of 1 AU?

9. Compute the Schwarzschild radius of the black hole at the center of the Milky Way galaxy. Its mass is roughly 4 million solar masses.

10. This mass was determined by analyzing the orbits of stars near this black hole and using Kepler's Third Law. Using this link:

or presentatios from class to estimate how close (in arc seconds) the star labeled SO-2 gets to the central black hole (presumed to lie a the center of the superimposed star symbol). Given Earth's distance to the center of the Milky Way of 8 kpc, estimate the physical distance of closest approch of this star to the Galactic Center Black Hole. (Hint: make reference to our favorite triangle) Is SO-2 at risk of crossing the event horizon?