College Physics
1st Edition
ISBN: 9781938168000
Author: Paul Peter Urone, Roger Hinrichs
Publisher: OpenStax College
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Textbook Question
Chapter 34, Problem 18CQ
Discuss the possibility that star velocities at the edges of galaxies being greater than expected is due to unknown properties of gravity rather than to the existence of dark matter. Would this mean, for example, that gravity is greater or smaller than expected at large distances? Are there other tests that could he made of gravity at large distances, such as observing the motions of neighboring galaxies?
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Discuss the possibility that star velocities at the edges of galaxies being greater than expected is due to unknown propertiesof gravity rather than to the existence of dark matter. Would this mean, for example, that gravity is greater or smaller thanexpected at large distances? Are there other tests that could be made of gravity at large distances, such as observing themotions of neighboring galaxies?
It can be shown that if an object orbiting a star of mass M in a circular orbit of radius R has speed v, then
Rv?
M
Suppose a star orbits the center of the galaxy it is contained in with an orbit that is nearly circular with radius
18
R = 2.5 x 10 and velocity v =
230 km/s. Use the result above to estimate the mass of the portion of the galaxy
inside the star's orbit (place all of this mass at the center of the orbit).
Mass =
Another commonly calculated velocity in galactic dynamics is the escape velocity vesc, that is
the minimum velocity a star must have in order to escape the gravitational field of the galaxy.
(a) Starting from the work required to move a body over a distance dr against f show that
the escape velocity from a point mass galaxy is vse = 2GM/r where r is your initial distance.
(b) Since we know galaxies aren't actually point-masses, also show that vesc from r for a
galaxy with a p(r) x r-² density profile is vse = 2v²(1+ ln(R/r)). Here you must assume
that R is a cutoff radius at which the mass density is zero.
(c) The largest velocity measured for any star in the solar neighbourhood, at r=8 kpc,
is 440 km/s. Assuming that this star is still bound to the galaxy, find the lower limit (in
kiloparsecs), to the cutoff radius R and a lower limit (in solar units) to the mass of the
galaxy. Note the solar rotation velocity is 220 km/s.
Chapter 34 Solutions
College Physics
Ch. 34 - Explain why it only appears that we are at the...Ch. 34 - If there is no observable edge to the universe,...Ch. 34 - If the universe is infinite, does it have a...Ch. 34 - Another known cause of red shift in light is the...Ch. 34 - If some unknown cause of red shiftsuch as light...Ch. 34 - Olbers’s paradox poses an interesting question: If...Ch. 34 - If the cosmic microwave background radiation...Ch. 34 - The decay of one type of Kmeson is cited as...Ch. 34 - Distances to local galaxies are determined by...Ch. 34 - Distances to very remote galaxies are estimated...
Ch. 34 - If the smallest meaningful time interval is...Ch. 34 - Quantum gravity, if developed, would be an...Ch. 34 - Does observed gravitational lensing correspond to...Ch. 34 - Suppose you measure the red shifts of all the...Ch. 34 - What are gravitational waves, and have they yet...Ch. 34 - Is the event horizon of a black hole the actual...Ch. 34 - Suppose black holes radiate their mass away and...Ch. 34 - Discuss the possibility that star velocities at...Ch. 34 - How does relativistic time dilation prohibit...Ch. 34 - If neutrino oscillations do occur, will they...Ch. 34 - Lacking direct evidence of WIMPs as dark matter,...Ch. 34 - Must a complex system be adaptive to be of...Ch. 34 - State a necessary condition for a System to be...Ch. 34 - What is critical temperature Tc? Do all materials...Ch. 34 - Explain how good thermal contact with liquid...Ch. 34 - Not only is liquid nitrogen a cheaper coolant than...Ch. 34 - For experimental evidence particularly of...Ch. 34 - Discuss whether you think there are limits to what...Ch. 34 - Find the approximate mass of the luminous matter...Ch. 34 - Find the approximate mass of the dark and luminous...Ch. 34 - (a) Estimate the mass of the luminous matter in...Ch. 34 - If a galaxy is 500 Mly away from us, how fast do...Ch. 34 - On average, how far away are galaxies mat are...Ch. 34 - Our solar system orbits the center of the Milky...Ch. 34 - (a) What is the approximate speed relative to us...Ch. 34 - (a) Calculate The approximate age of the universe...Ch. 34 - Assuming a circular orbit for the Sun about the...Ch. 34 - (a) What is the approximate force of gravity on a...Ch. 34 - Andromeda galaxy is the closest large galaxy and...Ch. 34 - (a) A particle and its antiparticle are at rest...Ch. 34 - The average particle energy needed to observe...Ch. 34 - The peak intensity of the CMBR occurs at a...Ch. 34 - (a) What Hubble constant corresponds to an...Ch. 34 - Show that the velocity of a star orbiting its...Ch. 34 - The core of a star collapses during a supernova,...Ch. 34 - Using data from the previous problem, find the...Ch. 34 - Distances to the nearest stars (up to 500 by away)...Ch. 34 - (a) Use the Heisenberg uncertainty principle to...Ch. 34 - Construct Your Own Problem Consider a star moving...Ch. 34 - What is the Schwarzschild radius of a blank hole...Ch. 34 - Black holes with masses smaller than muse formed...Ch. 34 - Supermassive black holes are thought to exist at...Ch. 34 - Construct Your Own Problem Consider a supermassive...Ch. 34 - The characteristic length of entities in...Ch. 34 - If the dark matter in the Milky Way were composed...Ch. 34 - The critical mass density needed to just halt the...Ch. 34 - Assume the average density of the universe is 0.1...Ch. 34 - To get an idea of how empty deep spam is on the...Ch. 34 - A section of superconducting wire carries a...
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- Why can we not determine distances to galaxies by the same method used to measure the parallaxes of stars?arrow_forwardWhat is the most useful standard bulb method for determining distances to galaxies?arrow_forwardWhy cant an open universe have a center? How can a closed universe not have a center?arrow_forward
- Suppose you were Hubble and Humason, working on the distances and Doppler shifts of the galaxies. What sorts of things would you have to do to convince yourself (and others) that the relationship you were seeing between the two quantities was a real feature of the behavior of the universe? (For example, would data from two galaxies be enough to demonstrate Hubble’s law? Would data from just the nearest galaxies-in what astronomers call “the Local Group”-suffice?)arrow_forwardAnother commonly calculated velocity in galactic dynamics is the escape velocity vesc, that is the minimum velocity a star must have in order to escape the gravitational field of the galaxy. (a) Starting from the work required to move a body over a distance dr against f show that the escape velocity from a point mass galaxy is vsc = 2GM/r where r is your initial distance. (b) Since we know galaxies aren't actually point-masses, also show that vesc from r for a galaxy with a p(r) xr¯² density profile is vese that R is a cutoff radius at which the mass density is zero. = 2v(1+ ln(R/r)). Here you must assume (c) The largest velocity measured for any star in the solar neighbourhood, at r=8 kpc, is 440 km/s. Assuming that this star is still bound to the galaxy, find the lower limit (in kiloparsecs), to the cutoff radius R and a lower limit (in solar units) to the mass of the galaxy. Note the solar rotation velocity is 220 km/s.arrow_forwardConsider a positively curved universe containing only matter (the "Big Crunch" model discussed in Section 5.4.1). At some time to lerunch/2, during the contraction phase of this universe, an astronomer named Elb- buh Niwde discovers that nearby galaxies have blueshifts (-1 1. Given Ho and So, how long a time will elapse between Dr. Niwde's observations at t = to and the final Big Crunch at t = 5.7 terunch? What is the highest amplitude blueshift that Dr. Niwde is able to observe? What is the lookback time to an object with this blueshift?arrow_forward
- Distances to local galaxies are determined by measuring the brightness of stars, called Cepheid variables, that can beobserved individually and that have absolute brightnesses at a standard distance that are well known. Explain how the measuredbrightness would vary with distance as compared with the absolute brightness.arrow_forwardA 0.75 m radio signal is detected from a galaxy as 2.0 m. Estimate the relative velocity.arrow_forwardDistances to very remote galaxies are estimated based on their apparent type, which indicate the number of stars in thegalaxy, and their measured brightness. Explain how the measured brightness would vary with distance. Would there be anycorrection necessary to compensate for the red shift of the galaxy (all distant galaxies have significant red shifts)? Discusspossible causes of uncertainties in these measurementsarrow_forward
- If we knew that a distant galaxy were 8.56 x 1021 meters away from earth, what velocity could we expect to measure for the galaxy in km/s?arrow_forwardExplain why it only appears that we are at the center of expansion of the universe and why an observer in another galaxywould see the same relative motion of all but the closest galaxies away from herarrow_forwarda) If you were to measure the distances and recessional velocities to nearby galaxies, you would find that they don’t fall exactly on the Hubble law, with their scatter around this law being larger for the nearest galaxies. What is the reason for this scatter? Assume that you made the measurements perfectly (i.e. that you really did measure the exact distances and velocities). b) At what distances do you expect the scatter from this effect to be about 10% of the velocity inferred from Hubble's law? What about 1%?arrow_forward
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