{"id":1481,"date":"2018-02-06T17:32:07","date_gmt":"2018-02-06T17:32:07","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/?post_type=chapter&p=1481"},"modified":"2019-01-17T18:37:34","modified_gmt":"2019-01-17T18:37:34","slug":"13-chapter-review","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-osuniversityphysics\/chapter\/13-chapter-review\/","title":{"raw":"13 Chapter Review","rendered":"13 Chapter Review"},"content":{"raw":"
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Key Terms<\/span><\/h3>\r\n
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action-at-a-distance force<\/strong><\/dt>\r\n \t
type of force exerted without physical contact<\/dd>\r\n<\/dl>\r\n
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aphelion<\/strong><\/dt>\r\n \t
farthest point from the Sun of an orbiting body; the corresponding term for the Moon\u2019s farthest point from Earth is the apogee<\/dd>\r\n<\/dl>\r\n
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apparent weight<\/strong><\/dt>\r\n \t
reading of the weight of an object on a scale that does not account for acceleration<\/dd>\r\n<\/dl>\r\n
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black hole<\/strong><\/dt>\r\n \t
mass that becomes so dense, that it collapses in on itself, creating a singularity at the center surround by an event horizon<\/dd>\r\n<\/dl>\r\n
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escape velocity<\/strong><\/dt>\r\n \t
initial velocity an object needs to escape the gravitational pull of another; it is more accurately defined as the velocity of an object with zero total mechanical energy<\/dd>\r\n<\/dl>\r\n
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event horizon<\/strong><\/dt>\r\n \t
location of the Schwarzschild radius and is the location near a black hole from within which no object, even light, can escape<\/dd>\r\n<\/dl>\r\n
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gravitational field<\/strong><\/dt>\r\n \t
vector field that surrounds the mass creating the field; the field is represented by field lines, in which the direction of the field is tangent to the lines, and the magnitude (or field strength) is inversely proportional to the spacing of the lines; other masses respond to this field<\/dd>\r\n<\/dl>\r\n
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gravitationally bound<\/strong><\/dt>\r\n \t
two object are gravitationally bound if their orbits are closed; gravitationally bound systems have a negative total mechanical energy<\/dd>\r\n<\/dl>\r\n
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Kepler\u2019s first law<\/strong><\/dt>\r\n \t
law stating that every planet moves along an ellipse, with the Sun located at a focus of the ellipse<\/dd>\r\n<\/dl>\r\n
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Kepler\u2019s second law<\/strong><\/dt>\r\n \t
law stating that a planet sweeps out equal areas in equal times, meaning it has a constant areal velocity<\/dd>\r\n<\/dl>\r\n
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Kepler\u2019s third law<\/strong><\/dt>\r\n \t
law stating that the square of the period is proportional to the cube of the semi-major axis of the orbit<\/dd>\r\n<\/dl>\r\n
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neap tide<\/strong><\/dt>\r\n \t
low tide created when the Moon and the Sun form a right triangle with Earth<\/dd>\r\n<\/dl>\r\n
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neutron star<\/strong><\/dt>\r\n \t
most compact object known\u2014outside of a black hole itself<\/dd>\r\n<\/dl>\r\n
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Newton\u2019s law of gravitation<\/strong><\/dt>\r\n \t
every mass attracts every other mass with a force proportional to the product of their masses, inversely proportional to the square of the distance between them, and with direction along the line connecting the center of mass of each<\/dd>\r\n<\/dl>\r\n
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non-Euclidean geometry<\/strong><\/dt>\r\n \t
geometry of curved space, describing the relationships among angles and lines on the surface of a sphere, hyperboloid, etc.<\/dd>\r\n<\/dl>\r\n
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orbital period<\/strong><\/dt>\r\n \t
time required for a satellite to complete one orbit<\/dd>\r\n<\/dl>\r\n
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orbital speed<\/strong><\/dt>\r\n \t
speed of a satellite in a circular orbit; it can be also be used for the instantaneous speed for noncircular orbits in which the speed is not constant<\/dd>\r\n<\/dl>\r\n
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perihelion<\/strong><\/dt>\r\n \t
point of closest approach to the Sun of an orbiting body; the corresponding term for the Moon\u2019s closest approach to Earth is the perigee<\/dd>\r\n<\/dl>\r\n
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principle of equivalence<\/strong><\/dt>\r\n \t
part of the general theory of relativity, it states that there no difference between free fall and being weightless, or a uniform gravitational field and uniform acceleration<\/dd>\r\n<\/dl>\r\n
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Schwarzschild radius<\/strong><\/dt>\r\n \t
critical radius (R<\/span>S<\/span><\/span><\/span><\/span><\/span><\/span><\/span>RS<\/span><\/span>) such that if a mass were compressed to the extent that its radius becomes less than the Schwarzschild radius, then the mass will collapse to a singularity, and anything that passes inside that radius cannot escape<\/dd>\r\n<\/dl>\r\n
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space-time<\/strong><\/dt>\r\n \t
concept of space-time is that time is essentially another coordinate that is treated the same way as any individual spatial coordinate; in the equations that represent both special and general relativity, time appears in the same context as do the spatial coordinates<\/dd>\r\n<\/dl>\r\n
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spring tide<\/strong><\/dt>\r\n \t
high tide created when the Moon, the Sun, and Earth are along one line<\/dd>\r\n<\/dl>\r\n
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theory of general relativity<\/strong><\/dt>\r\n \t
Einstein\u2019s theory for gravitation and accelerated reference frames; in this theory, gravitation is the result of mass and energy distorting the space-time around it; it is also often referred to as Einstein\u2019s theory of gravity<\/dd>\r\n<\/dl>\r\n
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tidal force<\/strong><\/dt>\r\n \t
difference<\/em>\u00a0between the gravitational force at the center of a body and that at any other location on the body; the tidal force stretches the body<\/dd>\r\n<\/dl>\r\n
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universal gravitational constant<\/strong><\/dt>\r\n \t
constant representing the strength of the gravitational force, that is believed to be the same throughout the universe<\/dd>\r\n<\/dl>\r\n<\/div>\r\n \r\n\r\n<\/div>\r\n
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Key Equations<\/span><\/h3>\r\n
\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Newton\u2019s law of gravitation<\/td>\r\nF<\/span>\u20d7\u00a0<\/span><\/span><\/span><\/span>12<\/span><\/span><\/span>=<\/span>G<\/span>m<\/span>1<\/span><\/span>m<\/span>2<\/span><\/span><\/span>r<\/span>2<\/span><\/span><\/span><\/span>r<\/span>\u02c6<\/span><\/span><\/span><\/span>12<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>F\u219212=Gm1m2r2r^12<\/span><\/span><\/td>\r\n<\/tr>\r\n
Acceleration due to gravity\r\n
<\/div>\r\nat the surface of Earth<\/td>\r\n
g<\/span>=<\/span>G<\/span>M<\/span>E<\/span><\/span><\/span>r<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>g=GMEr2<\/span><\/span><\/td>\r\n<\/tr>\r\n
Gravitational potential energy beyond Earth<\/td>\r\nU<\/span>=<\/span>\u2212<\/span>G<\/span>M<\/span>E<\/span><\/span>m<\/span><\/span>r<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>U=\u2212GMEmr<\/span><\/span><\/td>\r\n<\/tr>\r\n
Conservation of energy<\/td>\r\n1<\/span>2<\/span><\/span>m<\/span>v<\/span>2<\/span>1<\/span><\/span>\u2212<\/span>G<\/span>M<\/span>m<\/span><\/span>r<\/span>1<\/span><\/span><\/span><\/span>=<\/span>1<\/span>2<\/span><\/span>m<\/span>v<\/span>2<\/span>2<\/span><\/span>\u2212<\/span>G<\/span>M<\/span>m<\/span><\/span>r<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>12mv12\u2212GMmr1=12mv22\u2212GMmr2<\/span><\/span><\/td>\r\n<\/tr>\r\n
Escape velocity<\/td>\r\nv<\/span>esc<\/span><\/span><\/span>=<\/span>2<\/span>G<\/span>M<\/span><\/span>R<\/span><\/span><\/span><\/span>\u203e\u203e\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>vesc=2GMR<\/span><\/span><\/td>\r\n<\/tr>\r\n
Orbital speed<\/td>\r\nv<\/span>orbit<\/span><\/span><\/span>=<\/span>GM<\/span><\/span>E<\/span><\/span><\/span>r<\/span><\/span><\/span><\/span>\u203e\u203e\u203e\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>vorbit=GMEr<\/span><\/span><\/td>\r\n<\/tr>\r\n
Orbital period<\/td>\r\n\u03a4<\/span>=<\/span>2<\/span>\u03c0<\/span>r<\/span>3<\/span><\/span><\/span>GM<\/span><\/span>E<\/span><\/span><\/span><\/span><\/span><\/span>\u203e\u203e\u203e\u203e\u203e\u221a<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03a4=2\u03c0r3GME<\/span><\/span><\/td>\r\n<\/tr>\r\n
Energy in circular orbit<\/td>\r\nE<\/span>=<\/span>K<\/span>+<\/span>U<\/span>=<\/span>\u2212<\/span>G<\/span>m<\/span>M<\/span>E<\/span><\/span><\/span>2<\/span>r<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>E=K+U=\u2212GmME2r<\/span><\/span><\/td>\r\n<\/tr>\r\n
Conic sections<\/td>\r\n\u03b1<\/span>r<\/span><\/span>=<\/span>1<\/span>+<\/span>e<\/span>cos<\/span>\u03b8<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03b1r=1+ecos\u03b8<\/span><\/span><\/td>\r\n<\/tr>\r\n
Kepler\u2019s third law<\/td>\r\n\u03a4<\/span>2<\/span><\/span>=<\/span>4<\/span>\u03c0<\/span>2<\/span><\/span><\/span>G<\/span>M<\/span><\/span><\/span>a<\/span>3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u03a42=4\u03c02GMa3<\/span><\/span><\/td>\r\n<\/tr>\r\n
Schwarzschild radius<\/td>\r\nR<\/span>S<\/span><\/span>=<\/span>2<\/span>G<\/span>M<\/span><\/span>c<\/span>2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>RS=2GMc2<\/span><\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/section><\/div>\r\n<\/div>\r\n
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Summary<\/h3>\r\n<\/div>\r\n
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13.1<\/span>\u00a0<\/span>Newton's Law of Universal Gravitation<\/span><\/h4>\r\n