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Transcript
Universal Gravitation Chapter 8 Isaac Newton and Gravity • Newton realized an apple falls because of force • Moon follows circular path, force needed • Newton first to realize gravity causes both. • Moon is actually “falling” towards earth • Tangential velocity (sideways) keeps it going around earth instead of into it Law of Universal Gravitation • Newton extended gravitation theory to all objects, • Realized gravitational attraction is property of all mass • Attractive force is directly proportional to product of two masses • Inversely proportional to square of distance between them Law of Universal Gravitation • F ~ m1 m2/d2 • Proportionality constant G must be used to make quantities equal • F = Gm1 m2/d2 • G = force between 2 1-kg masses, 1 m apart • Its value is G = 6.67 x 10-11 Nm2/kg2 • Henry Cavendish first to measure G Law of Universal Gravitation • Gravity very weak force • Force of attraction with earth is weight • Weight depends on distance from center of earth • On top of high mountain, you weigh less • Using G and radius of earth we can calculate mass of earth = 6 x 1024 kg An Inverse-Square Law • Force of gravity varies inversely with square of distance between objects • For a spherical body, distance is measured from its center • If distance is doubled, force is one-fourth as much; if tripled, force is one-ninth (1/3)2 • If distance is halved, force is 4 times as much; if distance is 1/3 as much, force is 9 times as great. An Inverse-Square Law • Other inverse-square relationships: light and sound intensity, magnetic and electric force. • Force of gravity weakens rapidly with distance due to spreading of force into surrounding space, but never really zero, even in deep space. Gravitational Fields • Gravitational force acts over a distance without contact • Caused by interaction with gravitational field • Field can be thought of as lines of force radiating from objects • Strength of field is force per unit mass exerted on object: g = F/m Gravitational Fields • Earth’s grav. field strength is actually acceleration due to gravity at any location • Combining g = F/m and F = G mM/R2, we find g = GMe/ R2, where Me = mass of the earth and R = distance from center of earth. • g for any planet can be found using this formula. Gravitation and the Universe • Planets, moons, stars are spherical due to gravity • All planets affect each other, can cause perturbations (wobbles) in orbits • Neptune and Pluto were discovered because of perturbations in Uranus’ orbit. • Perturbations of distant stars have led to discoveries of planets, double stars Gravitation and the Universe • “Big Bang” theory says universe hurled outward from big explosion • Universe is expanding, only pull of gravitation can stop it. • Unknown whether enough matter exists to stop expansion and begin contraction leading to “Big Crunch” and another big bang-expansion-contraction cycle. Gravitational Field Inside Earth • If hole were drilled through earth and you fell in, what would happen? • As you fall, mass below you pulls down, mass above you pulls up. • No force at center of earth, pull equal in all directions • You would accelerate with decreasing acceleration until you reached the center, then decelerate as you approach opposite surface. Satellites--Circular Orbits • In circular orbit, gravity always pulls perpendicular to velocity • Speed doesn’t change, only direction. • Time (period) for close orbit about 90 min., greater for higher orbits • If period of revolution is 24 hours, satellite remains over same point on earth-communication satellites do this (geosynchronous orbit) Satellites--Elliptical Orbits • If speed is faster than needed for circular orbit, elliptical orbit can result • Ellipse is oval with two focal points (foci) • Speed varies in elliptical orbit • Faster speed close to earth, slower when farther away • All planets follow elliptical orbits around sun Tides • Change in sea level due to difference in gravitational pull between earth and moon on opposite sides of earth. • Causes elongation of earth and moon along line of force, bulging on near and far side. • Earth turns underneath high water levels causing 2 high tides and two low tides per day. Tides • Sun also creates tides but effect is less than moon because distance difference is not as large a part of total distance. • Extra large spring tides caused by sunmoon alignment on same side of earth • Smaller neap tides occur when sun and moon are on opposite sides of earth Eclipses • When sun-moon-earth alignment is perfect, eclipses occur • When earth is between sun and moon, moon is in shadow and lunar eclipse occurs. • When moon is between sun and earth, parts of earth in moon’s shadow see solar eclipse. Black Holes • In stars, expansion forces due to nuclear fusion are balanced by contraction force of gravity. • When solar fuel runs out, stars collapse • Small stars will become dense, cool, black dwarfs. Black Holes • Large stars will continue collapse to enormous density with gravitational forces too strong for anything to escape • Even light, radio communications are trapped--nothing can escape black hole (except small amounts of radiation). • Edge of black hole is called event horizon Black Holes • Fabric of space-time is warped by tremendous gravity inside black hole • Mass of black hole is same as star that created it so gravity outside black hole is same as if original star were still there.