UNDERSTANDING THE UNIVERSE(LL)-W/CODE
3rd Edition
ISBN: 9780393869903
Author: PALEN
Publisher: NORTON
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Chapter 15, Problem 39QAP
To determine
The radius at which mass of dark matter is equal to the mass of luminous matter enclosed; where this point lies in the orbit of Sun.
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In the reading, you were told that there were roughly 10,000 galaxies in the image of the Hubble Ultra Deep Field alone. The image is roughly 10 square arcminutes and there are roughly 1.5*10^8 square arcminutes composing the entire sky. With that in mind and assuming that the Hubble Ultra Deep Field represents an average part of the sky, roughly how many galaxies may exist in the observable universe? (Please include commas for every factor of 1,000; for example 2,343,567,890)
given:
a (distance to center of galaxy in AU) = 1,717,914,439 AU
P (suns orbital period in years) = 203,782,828.3 years
M (mass of milky way galaxy in solar masses) = 1.22 x 10^11 Msun
Question:
Assume the Milky Way Galaxy is made up entirely of stars like the Sun, i.e. on average each star has the mass of 1 MSun. Under this assumption, approximately how many stars are there in our galaxy? Express this answer in billions of stars (1 billion = 109).
Based on comparison with the Moon, it can be calculated that Andromeda would have to have a diameter of 35,000 km if it were at the same distance from us as the Moon. But it turns out that the distance from Earth to the Andromeda galaxy has been measured to be 6 × 1013 times farther than to the Moon. That's 60 trillion times farther.
What is the true diameter of Andromeda, based on these numbers?
Chapter 15 Solutions
UNDERSTANDING THE UNIVERSE(LL)-W/CODE
Ch. 15.1 - Prob. 15.1CYUCh. 15.2 - Prob. 15.2CYUCh. 15.3 - Prob. 15.3CYUCh. 15.4 - Prob. 15.4CYUCh. 15 - Prob. 1QAPCh. 15 - Prob. 2QAPCh. 15 - Prob. 3QAPCh. 15 - Prob. 4QAPCh. 15 - Prob. 5QAPCh. 15 - Prob. 6QAP
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- The best parallaxes obtained with Hipparcos have an accuracy of 0.001 arcsec. If you want to measure the distance to a star with an accuracy of 10%, its parallax must be 10 times larger than the typical error. How far away can you obtain a distance that is accurate to 10% with Hipparcos data? The disk of our Galaxy is 100,000 light-years in diameter. What fraction of the diameter of the Galaxy’s disk is the distance for which we can measure accurate parallaxes?arrow_forwardThe Tully-Fischer method relies on being able to relate the mass of a galaxy to its rotation velocity. Stars in the outer-most regions of the Milky Way galaxy, located at a distance of 50 kpc from the galactic centre, are observed to orbit at a speed vrot = 250 km s−1. Using Kepler’s 3rd Law, determine the mass in the Milky Way that lies interior to 50 kpc. Express your answer in units of the Solar mass.arrow_forwardOur galaxy is approximately 100,000 light years in diameter and 2,000 light years thick through the plane of the galaxy. If we were to compare the ratio of the diameter galaxy and its thickness to the ratio of the diameter of a CD and its thickness (CD has a diameter of 12 cm and thickness of 0.6 mm), what would be the factor differentiating those ratios? Put differently, if the galaxy were scaled down to the diameter of a CD, how many times thicker or thinner would the galaxy be than the CD? (For example if it would be twice as thick, you would answer 2 and if it were twice as thin you would answer 0.5 (aka 1/2))arrow_forward
- Figure 2 shows the "rotation curve" of NGC 2742. It plots the “radial velocity (V)" (how fast material is moving either toward or away from us) that is measured for objects at different distances (R = radius") from the center of the galaxy. The center of the galaxy is at 0 kpc (kiloparsecs) with a speed of 9 km/sec away from us. (These velocities have been corrected for the observed tilt of the galaxy and represent true orbital velocities of the stars and gas.) 200 100 U4779 -100 As you can see, one side of the galaxy is moving with a negative velocity (spinning toward us), while the other side has a positive velocity (spinning away from us). Using Newton's gravity equation, we will be able to determine the gravitational mass of the entire galaxy and how the mass varies versus distance from the galaxy's center. -200 -8 8 -4 Radius (kpc) Read the following text carefully and follow the instructions: Select five radii spaced evenly from 0-10 kpc across the galaxy. Your selections should…arrow_forwardThe Universe is approximately 13.8 Billion years old. What is the volume of the visible universe in m3?arrow_forwardI answer is not 100, I also tried 21. I need help! Thank you!arrow_forward
- Suppose that the outer stars of a galaxy have an orbital velocity of 150 km/s. If the radius of the galaxy is 4.0 kpc (1??? = 3.1 × 1016 ??), what is the orbital period of the outer stars in years?arrow_forwardWhat is the total mass of the Milky Way Galaxy?arrow_forwardSuppose that stars were born at random times over the last 1010 years. The rate of star formation is simply the number of stars divided by 1010 years. The fraction of stars with detected extrasolar planets is at least 18%. The rate of star formation can be multiplied by this fraction to find the rate planet formation. How often (in years) does a planetary system form in our galaxy? Assume the Milky Way contains 8 × 1011 stars.arrow_forward
- Assume the observable Universe is charge neutral, and that it contains n nuclei (hydrogen plus helium nuclei, ignoring other elements). Take the helium mass fraction as 1/4. How many electrons are there in the observable Universe? Enter your answer in scientific notation with one decimal place. Value: n = 4*1080arrow_forwardThe density profile of a galaxy's extended dark matter halo is given in the provided image. r0 and ρ0 are both constant. r is the distance from the center of the halo. Find the mass of dark matter inside a sphere with radius R around the center.arrow_forwardLet us assume that our galaxy consists of 2.5 × 1011 stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution ? Take the diameter of the Milky Way to be 105 light year.arrow_forward
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