# ps10 - Astronomy 10 Fall 2008 Homework 10 40 points total...

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Astronomy 10, Fall 2008 Homework 10 - 40 points total Due in the boxes in the basement of Campbell Hall by 5pm Tuesday, November 25 . Be sure to include your name, SID, Section Number, and GSI name on your homework, and staple it together. 1. Mystery of Spiral Nebulae (7 points) When fuzzy, blobs were found with spiral structure, astronomers at Frst called them “spiral nebulae”. The big question was whether these objects were in our Galaxy, or “island universes” all to themselves. It wasn’t until the early 1920’s, when Edwin Hubble observed some Cepheid variables in the great spiral nebula in Andromeda, that the question was Fnally answered. The key was that Cepheid variable stars obey a period-luminosity relation: L = 300 L P 1 . 15 d , where L is the star’s luminosity and P d is the pulsation period in units of days. (a) If a Cepheid variable is observed in Andromeda with a period of 20 days, what is its luminosity? (2 points) (b) If the apparent brightness of that same star is 5 × 10 13 erg s 1 cm 2 , how far away must the great Andromeda nebula be? (2 points) (c) The great Andromeda nebula is measured to be 200 arcminutes wide on the sky. Using the distance just found, what is its physical diameter? (2 points) (d) We know that the Milky Way Galaxy is about 30 kpc (9 . 3 × 10 22 cm) across. Given the distance and size you found above, explain whether or not the Andromeda “spiral nebula” is part of our Galaxy? (1 point) 2. Relative Closeness (6 points) In any collection of objects, how closely packed they are may be gauged by their average separation divided by the physical size of each object. If that ratio is large, they are very far apart. If it is small, then they are close together. If the ratio is one, then they are basically packed right up against each other. Note that with appropriate unit conversions, this ratio should be dimensionless. (a) Stars typically have sizes similar to that of the Sun, whose diameter is D = 1 . 4 × 10 11 cm. Given that the distance between a star and its nearest neighbor is typically d 1 pc, what is the ratio of the separation between stars and their sizes? (1 point) (b) Galaxies are typically 30 kpc across, and two galaxies are typically separated by about 1 Mpc. What is the ratio of separation to size for galaxies? Are they more or less crowded together than stars? (2 points) (c) A person is typically about 60 cm (about 2 feet) “wide” at the shoulders. How far away would two people need to be in order to be as separated as stars typically are? How far away would they need to be to be more akin to galactic separations? (3 points)

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ps10 - Astronomy 10 Fall 2008 Homework 10 40 points total...

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