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236 Cards in this Set
- Front
- Back
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Why does the rotational axis of Earth precess?
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The sun and moon pull on Earth's equatorial bulge.
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A star's Greek letter designation tells you which of the following?
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its relative brightness within its constellation
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A star with an ancient Arabic name is which of the following?
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a relatively bright star
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The number 7.14 106 is equivalent to which of the following?
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7,140,000
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If the tilt of Earth's axis were to change from 23.5 degrees to 0 degrees, what celestial circles would coincide for all observers?
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the Celestial Equator and the Ecliptic
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Which of the following descriptions is a definition of an astronomical unit (AU)?
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the average distance between Earth and the sun
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What is the most likely Greek letter name of the second brightest star in the constellation Lyra?
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beta Lyrae
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Why is the amount of solar heating less on a clear day in January at northern latitudes than on a clear day in July?
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Both the sun is above the horizon for less than 12 hours in January in the north and at low sun angles, the received sunlight is spread over a larger surface area.
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The five naked-eye planets and three telescopic planets that wander among the stars in the sky are always near which of the following?
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ecliptic
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What types of distances are typically listed in astronomical units (AU)?
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distances in the solar system
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The diameter of Earth is 7928 miles. What is its diameter in feet?
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41,900,000 ft
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The apparent visual magnitudes of four stars are listed below. Of these four stars, which one appears dimmest in the sky?
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(+2.8), -0.5, -1.2, -0.7
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If the Earth's tilt were 13.5 degrees instead of 23.5 degrees, the path of the Sun would be:
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Not as far north in summer nor as far south in winter.
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Just as the Sun sets, the shadows are:
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Always the same length BUT pointed to a different compass point according to the season.
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Cooler days in winter are due to:
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Less direct Sunlight, therefore less heating and fewer hours of sunlight
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About how many stars are in our home galaxy, also known as the Milky Way Galaxy?
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over 100,000,000,000
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How long does it take light to cross the diameter of our Milky Way Galaxy?
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80,000 years
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The apparent visual magnitude of star A is 2 and the apparent visual magnitude of star B is 1. Based on this information which statement below must be true?
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Light output and distance cannot be determined from a star's apparent visual magnitude alone.
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Quiz2
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Quiz2
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The entire electromagnetic spectrum can be divided into seven bands: radio, microwave, infrared, visible, ultraviolet, X ray, and gamma ray (from longest to shortest wavelength). To which of these two bands is Earth's atmosphere the most transparent?
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visible and radio
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Rank the following colors of visible light in order of increasing wavelength:
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Blue, green, yellow, red
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Rank the following colors of visible light in order of increasing frequency:
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Red, Yellow Green Violet
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Rank the following types of electromagnetic radiation in order of decreasing wavelength: infrared, gamma-ray, radio, ultraviolet, visible.
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Radio, Infrared, Visible, Ultraviolet, Gamma Rays
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What is the wavelength of radio waves transmitted by a radio station with a frequency of 1220 million cycles per second?
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0.246 m
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Which power of a telescope might be expressed as "0.5 seconds of arc"?
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resolving power
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In which device do astronomers take advantage of chromatic aberration?
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the prism
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Which power of a large ground-based optical telescope is severely limited by Earth's atmosphere on a cloudless night?
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light gathering and resolving power
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What do the newer light-sensitive electronic CCD chips do better than the older photographic plates coated with light-sensitive chemicals?
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They have a greater sensitivity to light.
They can detect both bright and dim objects in a single exposure. Photometry can be done with the CCD images. The CCD images are easier to manipulate. |
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Why do nocturnal animals usually have large pupils in their eyes?
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To gather more light, so they can see better at night.
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Which is not an advantage of a larger telescope objective?
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A larger objective gives higher magnification.
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The visible part of the electromagnetic spectrum can be divided into seven color bands: red, orange, yellow, green, blue, indigo, and violet (from long to short wavelength). A single photon of which of these colors has the greatest amount of energy?
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violet
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Of the two telescopes shown here, which will allow you to see dimmer objects?
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The telescope on the left.
(Bigger circumference) |
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Which theoretical power of an optical telescope is determined by the diameter of the primary mirror or lens?
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light gathering power and resolving power
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Radio telescopes are often connected together to do interferometry. What is the primary problem overcome by radio interferometry?
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poor resolving power
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Why do radio telescopes have such poor resolution?
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because radio waves have such a long wavelength
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What can radio telescopes do that optical telescopes cannot?
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Find the location of cool hydrogen gas and see through dust clouds.
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What advantage do the builders of large telescopes today have over the previous generation of telescope builders?
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Large mirrors can now be made thinner and lighter than before.
Tracking celestial objects today is computer controlled and can take advantage of simpler, stronger mounts. High-speed computing today can be used to reduce the effect of Earth's atmosphere. Tracking celestial objects today is computer controlled and can take advantage of simpler, stronger mounts and high-speed computing today can be used to reduce the effect of Earth's atmosphere. |
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Quiz3
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Quiz 3
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What kind of spectrum would be observed when observing radiation from a hot solid or gas under high pressure?
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continuous
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What kind of spectrum would be observed when observing radiation through a cool gas?
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absorption
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What kind of spectrum would be observed when observing radiation from a hot gas?
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emission
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What kind of spectrum would you observe from molten lava?
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continuous
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What kind of spectrum would you observe if you looked through gases boiling out of molten lava?
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absorption
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What is true of a neutral atom?
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It has the same number of protons and electrons.
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What is true of an ion?
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It has gained or lost electrons.
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What is true of an excited atom?
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It has an electron at a higher energy level.
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If the lines in a stellar spectrum are blueshifted, which of the following is true?
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The star is moving toward us.
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If the lines in a stellar spectrum are redshifted, which of the following is true?
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The star is moving away from us.
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(c) If the lines in a stellar spectrum show no Doppler shift, which of the following is true?
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The star could be moving perpendicular to a line between Earth and the star.
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Human body temperature is about 310 K (98.6°F). At what wavelength do humans radiate the most energy?
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9350
infrared |
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Describe what an absorption spectrum looks like.
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A continuous spectrum with specific colors of light missing.
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The light bulb here serves as the blackbody. Which of these are characteristic of blackbodies?
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They are very hot.
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A star has an emission spectrum, since it is a blackbody surrounded by a thinner atmosphere.
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False
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If the temperature of star B is twice the temperature of star A, what can we say about the energy emitted by the surface of star B compared to the energy emitted by star A?
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Each square meter emits sixteen times as much energy per second.
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Suppose that you take the spectra of several stars and identify the 656 nm line of hydrogen. You then measure against the reference spectrum on the same image and find that some of the 656 nm lines are shifted due to the Doppler effect. Of the following shifted locations of this line, which one is that of a star that is moving away from us at the highest speed?
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star E at 659 nm
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What is true of stellar spectra?
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They are dark-line.
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(What do stellar spectra tell us about a star?
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temperature
composition |
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What information do we get from stellar spectra?
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It tells us only about a star's surface.
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Of the following sequence of spectral types, which star has the highest surface temperature: A, B, F, K, G?
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B
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What property of a star can broaden the width of its spectral lines?
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rapid rotation of the star
high-density atmosphere high-temperature atmosphere high-density and high-temperature atmosphere |
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What determines the wavelengths of the photons an atom will absorb or emit?
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the difference in energy between electron energy levels
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If a star has a surface temperature of 12,000 K, at what wavelength will it radiate the most energy?
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242 nm
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In the Bohr model, where are the electrons located?
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In orbits around the nucleus
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In atomic excitation, electrons jump between which two orbits?
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From a lower orbit to a higher one
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A photon is emitted during which atomic process?
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De-excitation
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Infrared observations of a star show that it is most intense at a wavelength of 680 nm. What is the temperature of the star's surface?
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4410 k
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Light and sound waves from a moving source are ________ in the direction of movement.
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compressed
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The light or sound waves from a moving object increase in frequency when
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it is moving toward an observer
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What does an observer moving at the same speed with a sound source measure?
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There is no change in wavelength or frequency
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Quiz 4
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Quiz 4
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Which of the following is true for an object moving in a circle at a constant speed?
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The acceleration is not zero, and there must be a force acting on the object in the same direction as the acceleration.
The acceleration is not zero, and there must be a force acting on the object in the same direction as the acceleration. |
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What did Newton determine necessary for the force exerted by the sun on the planets to yield elliptical orbits?
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The force must be attractive and the force must vary inversely with distance squared.
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If we drop a feather and a hammer at the same moment and from the same height, we see the hammer strike the ground first, whereas on the moon both strike the ground at the same time. Why?
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The amount of force on Planet Q is 1/25 the force on Earth.
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Which statement below best describes the difference between your mass and your weight?
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Your mass is a measure of the amount of matter that you contain and your weight is a measure of the amount of gravitational pull that you experience.
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What is significant about the May 29, 1919 solar eclipse?
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The bending of light by gravity was observed, thus verifying general relativity.
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Einstein formulated the General Theory of Relativity.
What is equivalent in the Equivalence Principle? |
force from gravity and acceleration from motion
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When can you detect your motion during an elevator ride?
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at the beginning and end only
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Why do you feel at little heavier at the beginning of a ride up an elevator and lighter at the end?
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Because at the beginning the elevator accelerates up, and at the end it accelerates down.
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How is the Equivalence Principle demonstrated in an elevator?
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At the beginning of the trip, you really canÂt be sure whether you are being forced up or pulled down.
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Why are Astronauts in space weightless?
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Actually, they are not weightless; they are in perpetual free-fall toward the Earth, but traveling fast enough in their orbit to continuously "miss the Earth."
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Which is an unchanging measurement of the amount of matter an object is made of?
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mass
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Which is the measurement of the force that gravity exerts on an object?
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weight
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Which measurement would be different for you on the moon?
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weight
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What is velocity?
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speed with an indication of direction
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What is speed?
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unchanging in uniform circular motion
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What is 186,000 miles per second?
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a speed
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Compared with the strength of Earth's gravity at its surface, how much weaker is gravity at a distance of 13 Earth radii from Earth's center?
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169 times
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How much weaker is gravity at 40 Earth radii?
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1600 times
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What does mutual gravitation mean?
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Gravitation is an action-and-reaction pair of forces that two masses exert on one another.
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What does universal gravitation mean?
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All objects in the universe exert gravitation on one another.
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What is true about the gravitational force that Earth exerts on the moon?
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It is the same as the gravity that the moon exerts on Earth.
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Why does the moon orbit Earth and not vice-versa?
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Earth has more inertia.
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Which of the following is true in general relativity?
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Gravity is a curvature in space caused by mass.
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If radio waves from a distant galaxy passed by the sun, what would happen?
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They would pass through the curved space near the sun and be deflected.
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Quiz 5
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Quiz 5
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A 1 megaton nuclear weapon produces about 4 1015 J of energy. How much mass must vanish when a 6 megaton weapon explodes?
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0.267 kg
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How much energy is produced when the sun converts 7 kg of hydrogen into helium? (Hint: How does this problem differ from when the sun converts 7 kg of mass into energy?)
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4.52e+15 J
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Rank the following layers of the solar interior in order from the outermost to the innermost: convective zone, core, radiative zone.
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outermost convective zone
convective zone radiative zone radiative zone innermost core core |
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Rank the following layers of the sun in order of increasing temperature: convective zone, core, radiative zone.
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least
convective zone radiative zone greatest core |
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What happens to the neutrinos that are produced in the proton-proton chain?
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They head out of the sun at nearly the speed of light.
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What is a solar prominence?
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It is solar material from the chromosphere following the arches of the sun's magnetic field.
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What does the spectrum of a solar prominence reveal?
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that it is much cooler than its surroundings
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What does the shape of a solar prominence suggest?
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that it is following the solar magnetic field
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Why does fusion require a high temperature?
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to overcome the repulsive force between the protons
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The sunÂs atmospheric layers are all less dense than its interior. Based on this figure, which layer of the sun is responsible for the absorption lines in the solar spectrum?
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photosphere
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Based on this figure, which atomic element has the greatest binding energy per nuclear particle?
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iron
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Which is not considered a layer of the solar interior?
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photosphere
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How are astronomers able to explore the layers of the solar interior?
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from Doppler shifts on the solar surface
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This diagram explains the structure of solar granules. Why is the center of a granule brighter than its edges?
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The temperature is higher at the center.
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How are astronomers able to explore the layers of the sun below the photosphere?
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By measuring and modeling the modes of vibration of the sun's surface.
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Where in the sun does nuclear fusion occur?
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the core
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Why does fusion occur in the layer(s) that it does?
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Only the core is hot enough.
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Rank the following stars from the above H-R diagram in order of brightness from dimmest to brightest: Barnard's Star, Canopus, Rigel A, Sirius B, Sun.
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dimmest
Barnard's Star Sirius B Sun Canopus Rigel A Brightest |
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Rank the following stars from the above H-R diagram in order of brightness from brightest to dimmest: Aldebaran A, Altair, Antares, Polaris, Procyon B.
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Brightest
Antares Polaris Aldebaran A Altair Procyon B Dimmist |
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Rank the following stars from the above H-R diagram in order of temperature from hottest to coolest: Aldebaran A, Altair, Antares, Mira, Rigel A.
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Hottest
Rigel A Altair Aldebaran A Mira Antares Cooler |
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In addition to the H-R diagram, what other information is needed to find the distance to a star whose parallax angle is not measurable?
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the star's spectral type and luminosity class
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What is the distance to a star that has an apparent visual magnitude of 3.5, and an absolute visual magnitude of -1.5?
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100 pc
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What is the distance to a star that has a parallax angle of 0.5 arc seconds?
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2 parsecs
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How can a cool star be more luminous than a hot star?
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It can be more luminous if it is larger.
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How do astronomers determine the distance to nearby stars?
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by observing their shifting motion against the further background stars
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Why are parallax measurements from Earth limited to closer stars?
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because parallax must be measured in front of a farther background
because our baseline is limited to about 2 AU because the atmosphere obscures the images of stars, limiting how precisely their position can be measured |
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In a given volume of space, the Red Dwarf (or lower main sequence) stars are the most abundant, however, on many H-R diagrams very few of these stars are plotted. Why?
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They have very low luminosity and are difficult to detect, even when nearby.
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Randomly set the distances for bike and truck. Now, looking ONLY at "What the Observer Sees", which is more intrinsically bright?
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cant tell
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Move both bike and truck to distance of 100 units. Which statement is false?
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We can't tell which has greater intrinsic brightness.
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When the bike is moved from a distance of 400 units to 100 units, how does its apparent brightness change?
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16 times as bright
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Which luminosity class has stars of the lowest density, some even less dense than air at sea level?
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supergiant
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To which luminosity class does the mass-luminosity relation apply?
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main sequence
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If a star has an apparent magnitude equal to its absolute magnitude, how far away is it in parsecs?
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10 pc
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How far away is it in light-years?
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32.6 ly
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Quiz 7
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7
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At what wavelength can we observe the Hot Coronal Gas component of the interstellar medium?
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x ray
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(a) Rank components of the interstellar medium in the above table in order of increasing temperature.
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least
molecular clouds HI clouds intercloud medium coronal gas reatest |
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Rank the components of the interstellar medium in the above table in order of decreasing density.
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Greatest
Molecular Cloud HI Cloud Intercloud Medium Coronal Gas Least |
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What is coronal gas?
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highly ionized hot gas in the interstellar medium
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What produces the coronal gas?
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energy from hot stars and supernova explosions
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Why does the Sun appear redder at the horizon?
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Because it passes through more atmosphere, and the blue light is scattered more.
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Given that blue light scatters more, what best explains why the Sun appears yellow instead of blue when it's directly overhead?
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The Sun radiates much more yellow light than blue light.
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Which is the same as an HII region?
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emission nebula
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Which looks blueish in color?
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reflection nebula
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Which looks pinkish in color?
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emission nebula
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Which is scattering longer wavelength light?
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reflection nebula
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Why can the 21 cm radio emission line of neutral hydrogen be observed in the interstellar medium but not in the laboratory?
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The density in the laboratory is too high.
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What effect does interstellar dust have on the light from distant stars?
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It causes extinction.
It scatters away the shorter wavelengths. |
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How does light from distant stars look different than expected?
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It looks dimmer.
It looks redder. |
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Hot emission nebulae are somewhat red, and cool reflection nebulae are blue. Why are these colors different from what Wien's law tells us about the radiation emitted by a black body?
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The gases in an emission nebula do not emit light like a black body.
We see reflection nebulae by reflected light, not emitted light. The dust grains in reflection nebulae scatter shorter wavelengths of visible light better than longer wavelengths. The gases in an emission nebula do not emit light like a black body and we see reflection nebulae by reflected light, not emitted light. |
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Which is not a reason that interstellar lines are so narrow?
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They have passed through much dust.
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What is a forbidden spectral line?
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a line from a transition that is almost never observed in laboratories on Earth
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What does the observation of forbidden lines in interstellar clouds tell astronomers?
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Interstellar clouds are of very low density
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Why are interstellar absorption lines so much thinner than stellar absorption lines?
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Most interstellar gas is at a lower temperature than that of stellar atmospheres and the density of interstellar gas is less than that of stellar atmospheres.
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What type of hydrogen emits 21 cm radiation?
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cool atomic hydrogen
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What is the dark area in the above picture?
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a dark nebula
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In the above picture the dark area is doing which of the following?
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blocking out light from nearby stars
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What is the pink area in the above picture?
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emission nebula
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Which process is how Earth receives its energy from the Sun?
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Radiation
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What heat transfer process is responsible for the granular effect of the Sun's surface?
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Convection
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What is the primary heat transfer method of an electric stove?
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Conduction
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Which is the cause of the contraction of a cloud of interstellar gas?v
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gravity
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Which does not resist the contraction of interstellar gas?
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thermal energy
rotation turbulence |
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Examine this model of main-sequence stars of different masses. How does a 7-solar-mass star differ from a 1-solar-mass star like the sun?
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The convective and radiative zones are switched.
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At any layer in a star, the weight pressing down is _____ the pressure in the gas.
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equal to
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What is the state described in the previous question called?
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hydrostatic equilibrium
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Which must be true for the state described in the previous questions to be maintained?
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The inner layers of the star must be hotter than the outer layers.
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As cold gas in interstellar space contracts, which of the following occurs?
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It heats up.
Its molecules pick up speed. Gravitational energy is converted to thermal energy. |
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What is a protostar's energy source?
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gravitational energy
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What happens to the temperature and density inside a collapsing protostar?
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Temperature and density both increase.
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What are small nebulae that fluctuate in brightness called?
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Herbig-Haro objects
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Which is evidence that protostars are surrounded by disks?
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small nebulae that fluctuate in brightness
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What would happen in the interior of a normal star if gravity were to shrink the star's size a small amount?
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The interior temperature would increase.
The rate of fusion would increase. The gas pressure would increase The interior temperature would increase and the rate of fusion would increase. |
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Which is not a way that a giant molecular cloud can be triggered to collapse?
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turbulence
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Which is a way that a giant molecular cloud can be triggered to collapse?
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the spiral structure of the Milky Way Galaxy
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Which method of energy transport is NOT important inside most stars?
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conduction
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According to the figure shown here, the protosun was cooler yet much more luminous than the sun is now. How can this be true?
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The protosun was much larger.
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Quiz 10
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10
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Which of the following is an accurate description of the Schwarzschild radius?
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It is the radius to which an object must shrink to become a black hole and is the radius of the event horizon surrounding a black hole singularity.
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What is the probable next step in a star's evolution after the white dwarf stage?
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black dwarf
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How many of the objects from the previous question have been observed?
red dwarf neutron star white black dwarf |
none
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What is the reason for the answer to the above question?
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There has not been enough time for these objects to form.
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If a nebula is 3 light-year(s) in diameter and is expanding at a velocity of 18 km/s, typical of planetary nebulae, how old is it? (Hint: 1 ly = 9 1012 km, and 1 y = 3.15 107 s.)
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23800 years
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What is the lower limit for the mass of neutron stars?
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about 1.4 solar masses
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How can a black hole emit X-rays?
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X-rays emitted just before material crosses the event horizon can escape the gravitational pull.
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Why can't the lowest-mass stars become giants?
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They are not massive enough to fuse helium.
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What kind of spectrum does a planetary nebula produce?
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emission
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Where does a planetary nebula get its energy to produce a spectrum?
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from the white dwarf at its center
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What prevents neutron stars from contracting to a smaller size?
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degenerate neutrons
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Which stars have high rates of mass loss due to intense stellar winds?
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high-mass stars
newly forming stars stars approaching death high-mass and newly forming stars |
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This diagram illustrates the interior structure of which of the following?
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supergiant star
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High mass stars live longer than low mass stars.
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False
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The more massive the star, the more dense its end state.
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True
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Low mass stars explode as supernovae.
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False
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Why does the short length of pulsar pulses eliminate normal stars as possible pulsars?
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An object cannot emit pulses that are shorter than the time it takes light to cross its diameter.
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Why didn't astronomers realize at first how large the galaxy is?
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interstellar dust obscuring starlight
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Who was the first astronomer to get a reasonable idea of the size and shape of the galaxy?
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Shapley
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What must be measured to determine distance by the Cepheid variable star method?
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the apparent magnitude and the period of pulsation of the variable star
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What is the approximate diameter of the disk component of the Milky Way Galaxy?
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75,000 ly
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What are spiral tracers?
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objects used to map spiral arms
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Which is not an example of a spiral tracer?
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O and B associations
young open clusters high-mass variable stars all of the above are spiral tracers |
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What is true about the age of most spiral tracers?
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They are young.
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What is the reason for the answer to the previous question?
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Spiral arms are places of star formation.
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If the sun is 5 billion years old, how many times has it orbited the galaxy?
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21 orbits
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Which is observational evidence that the center of the galaxy contains a supermassive black hole?
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x-ray emissions
high orbital speeds of stars very large mass |
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Why do some clusters lose stars more slowly than others?
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different ages
different masses of stars in clusters different amounts of gravity holding the clusters together |
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Which type of cluster is more likely to have stars "wander away"?
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an open cluster
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How is the rate of star loss affected by the age of a cluster?
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Younger clusters lose stars faster.
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What is the reason for the answer to the previous question?
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More massive stars will burn out early in the cluster's life.
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Where in the galaxy are "high-velocity" stars found?
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in the halo
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Why are "high-velocity" stars named so?
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When they cut through the orbits of stars in the disk, they appear to have very high velocities.
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How do the metal abundances of high-velocity stars compare to those of the sun?
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They are lower.
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What is the reason for the answer to the previous question?
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They formed before the sun.
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With the 100 inch telescope, Harlow Shapley could not resolve variable stars in the more distant globular clusters of the Milky Way. What basic assumption did Shapley make about the far-away globular clusters that allowed their distances to be found?
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Far-away globular clusters have the same average size as nearby globular clusters.
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The abundance of metal in older stars is ______ in younger stars.
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less than
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What is the reason for the answer to the previous question?
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There were no heavy elements available when the older stars were forming.
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What main conclusion did the Herschels draw from their star counts?
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The Milky Way is a disk of stars with the sun near the center.
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Galaxies with active star formation also have which of the following?
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plenty of gas and dust
O and B associations emission nebula a bluish tint |
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How are the shapes of galaxies affected by collisions?
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They are twisted and distorted by tidal forces.
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Which is a more likely evolution of galaxies?
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neither is very likely
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What is the most likely way that one type of galaxy may be formed from others?
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mergers
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What type of galaxy is the most likely result of the process of the previous question>
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elliptical
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Which of the following is NOT a distance indicator used in galactic astronomy?
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white dwarfs
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What parameter must we know to determine the linear diameter and luminosity of a particular galaxy?
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the distance to the galaxy
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Why is a supernova type Ia standard candle better to use in measuring very long distances than either the brightest globular cluster or Cepheid Variable star standard candles?
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Supernovae type Ia are more luminous.
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In a few billion years, our own Milky Way may merge with the Andromeda Galaxy. Which type of galaxy is most likely to result from such a merger?
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an elliptical galaxy
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What is the Hubble Law a relationship between?
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the distance and recessional velocity of a galaxy
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What must actually be measured to use the Hubble law to determine the distance to a galaxy?
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a galaxy's redshift
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What must be known to estimate the distance to a galaxy with the Hubble law?
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he Hubble constant
the recessional velocity |
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Rank the subclasses of spiral galaxies in order of how tightly wound they are: Sa, Sb, Sc.
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SA SB SC
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Rank the subclasses of spiral galaxies in order of the size of their nuclei, from smallest to largest: Sa, Sb, Sc.
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SC SB SA
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What is the Milky Way in our sky?
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It is bright band of light that goes around the entire sky.
It is the disk of the galaxy of which we are a part. |
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Would people living on a planet orbiting a star in an E0 type galaxy see a Milky Way?
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No, their galaxy has no disk.
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Which type of galaxy has the largest range in both size and mass?
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elliptical
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What did William Parsons (Lord Rosse) think the spiral nebulae were?
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island universes
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What conditions can create broad emission lines of highly ionized elements?
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High-temperature gas must be present.
Low-density gas must be present. The gas must be rotating at high speeds. High-temperature and low-density gas must be present. |
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This image shows four quasars around a galaxy. The redshift of each of the four quasars is 0.0394 and greater than that of the galaxy. How should we interpret this photo?
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The galaxy acts as a gravitational lens and the four quasar images are of the same quasar.
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The name "quasar" is derived from the description "quasi-stellar radio source." In this image the quasar (center) appears star-like. How are quasars very different from stars?
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Quasars have highly redshifted spectral lines.
Quasars have emission line spectra. No quasars are nearby. Quasars have highly redshifted spectral lines and emission line spectra. |
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What observational evidence leads us to believe that AGNs contain supermassive black holes?
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The gas in the disk is orbiting at high speeds and short-duration fluctuations in brightness limit the size of the object at the center of an AGN.
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What is at the center of Seyfert galaxies?
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supermassive black holes
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Careful measurements of this image of the quasar 3C273 and its spectrum reveal that the H-delta line of the Balmer series is shifted from a wavelength of 410 nm to 474 nm. What is the redshift (z) of this quasar?
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z = 0.16
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