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Galaxies in the Hubble Deep Field Or Determining the Ultimate Fate of the Universe

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Galaxies in the Hubble Deep Field Or Determining the Ultimate Fate of the Universe name Galaxies in the Hubble Deep Field or Determining the Ultimate Fate of the Universe This is a Picture of the Hubble Deep Field (HDF). It was taken with the Hubble Space Telescope for 15 consecutive days. It is the deepest image taken of the sky (apart from the Hubble Deep Field South). You virtually see galaxies at the edge of the universe (and everything else in between). From this picture we will “guestimate” (aka, guess & estimate) the total number of galaxies in the universe and how much matter there is in the universe. This may tell us what type of universe we live in and whether it will expand forever, or re-collapse with a “Big Crunch,” then start up again with another “Big Bang.” All images in this labs are taken from http://oposite.stsci.edu/pubinfo/jpeg/HDFWF3.jpg Hubble Deep Field Lab 14 1 Part I – The Size of the HDF First we need to know some details about the picture itself — where it was taken and how big it is. The image of the HDF has an L-shape. This is because it is a picture taken simultaneously with four cameras — three “Wide Field” (WF) cameras, and one “Planetary” camera (PC). The combined image (the three Wide Field and the one Planetary Camera, WFPC) is 2.4” x 2.4”. This is a very small area, much smaller than the moon. Let’s visualize this, but first we will need to change “degrees into arc- seconds” (there are 60 arc-minutes in one degree, and 60 arc-seconds in one arc-minute). The area of the moon is: 0.5o x 0.5o Determine the area of the moon in arc-minutes: ____________________ Determine the area of the moon in arc-seconds: ____________________ Now compare this to the HDF. The area of the HDF is: 2.4” x 2.4” How much larger is the Moon’s diameter? ____________________ How many HDF’s can you fit into the moons area? ____________________ (Hint: Recall that a circle whose diameter is twice as big has an area that is four times as much; similarly a circle that is 3 times the diameter has an area that is 9 times as big) Let’s imagine the size of that. Take a sharpened pencil, and hold it at arms length. Then look at the tip of the pencil — the size of that tip of the pencil is roughly as big as the HDF. Do you see all the galaxies in the HDF? They are all within this very small area in the sky. Let’s do a though experiment. If there are that many galaxies in that small area, how many galaxies would there be in the total universe? Look at the picture of the Hubble Deep Field and GUESS the number of galaxies in the universe. Your Guess is: ____________________ How well did you guess? Let’s determine that number a little more accurately. First we need to know how many HDF’s we would need to cover the total sky. Then we need to count the galaxies in the HDF and multiply that by the number of HDF’s in the sky. There are 360o in a circle; so the area of the sky in degrees is: ____________________ Convert this to arc-minutes: ____________________ Convert this to arc-seconds: ____________________ How many HDF’s you would need to map out the entire sky? numberof HDF's = That’s a huge number indeed!! Next you will multiply that by the number of galaxies in the HDF. 2 Lab 14 Hubble Deep Field Part II – The Total Number of Galaxies in the Universe Your next mission is to determine the total number of galaxies in the HDF. Well, they are many galaxies, and if you like, go ahead and count them all! But there is an easier way — remember this is supposed to be a “quick” lab, so let’s figure out how you could “guestimate” the total number of galaxies. Use the picture on the last page; it is a 1.0” x 1.0” fraction of the picture of the front page. (If the quality of that photocopy is bad, download the original image from the web at http://oposite.stsci.edu/pubinfo/hrtemp/96-01a.jpg. The image also looks much nicer in color!) Discuss some options with your partner; then DESCRIBE your method below. Check your method with the instructor before you continue, otherwise you will go off in a tangent and spend hours on this lab. In the space below determine the number of galaxies in the universe. Show your calculation. The total number of galaxies in the universe is Wowwww, what a number!!! Hubble Deep Field Lab 14 3 Part III – The Mass and Density of the Universe a) The Mass of the Universe Estimate the average mass of one galaxy (in solar units) — you might like to assume that the Milky Way is an average (or slightly larger than average) galaxy. Write down your estimate. Mass of the Galaxy = Now multiply this with the total number of galaxies in the universe. Mass of all galaxies = Next transform this number to grams (i.e., transform “the mass in solar units” to grams) Mass of entire universe = Now we know how much mass there is in the universe. This number is meaningless unless we can say something about the fate of the universe. For example, is there enough matter in the universe for it to collapse? Let’s rephrase that: Is the gravitational force between all the galaxies large enough for collapse? Well, the gravitational force depends on the mass AND the distance between the masses. b) Size of the Universe We do not know the size of our current universe, but we can estimate it. We know that light travels at 3x108 m/sec (v = d/t). If we assume that the light from the most distant galaxies was emitted roughly ten billion light years ago, we can calculate the distance. How many meters are there in one light year? And in ten billion light years? 1 light year = 10 bill light years = Then calculate the distance in centimeters to the most distant galaxies. Distance = 4 Lab 14 Hubble Deep Field c) The Density of the Universe Look up the formula for a volume of a sphere in terms of its radius. Then calculate the Volume of the entire universe in units of centimeter-cubed. Volume = Finally determine density of the universe in grams per centimeter3. The density is the Mass per Volume. Density = Take your textbook and look up the critical density of the universe, i.e., the density needed for the universe to collapse again. Critical Density = Compare this value with your own density. Is it larger or smaller? Think about the implications of your result. Is your universe going to collapse or expand forever? Explain. Hubble Deep Field Lab 14 5 Part IV — How reliable is your answer? Well, we did some real calculations in this exercise, but we also made several assumptions and included a range of “educated guesses.” So let’s list the assumptions, and make further educated guesses on the “accuracy of our educated guesses.” a) List all (at least 5, if not more) assumptions. b) Comment on the uncertainty of each guestimate you made in this lab. c) Can you say with certainty whether the universe will expand forever or collapse again? Explain. 6 Lab 14 Hubble Deep Field Lab Report Objective of the Lab. Describe in a few sentences what you have done. In particular explain in words how you have determined the density of the universe. Hubble Deep Field Lab 14 7 Critically evaluate your results; in particular discuss the accuracy of your results. Then comment on whether or not this is a good method to determine the fate of the universe. 8 Lab 14 Hubble Deep Field . All images are taken from http://oposite.stsci.edu/ Hubble Deep Field Lab 14 9 10 Lab 14 Hubble Deep Field .
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