复旦大学《大学物理》课件（英文）-第14章 Gravitation(1).pdf

Chapter 14 Gravitation1.Origin of the Law of Gravitation2.Newtons Law of Universal Gravitation3.The Gravitational Constant G 4.Gravitation Near the Earths surface5.The Two Shell Theorems6.Gravitational Potential Energy14-1 Origin of the law of gravitation1.In 16th century Copernicus(14731543)proposed a heliocentric(sun-centered)scheme,in which the Earth and other planets move about sun.2.Kepler(15711630)proposed three law(which we discuss in Section 14-7)that describe Planets motions.However,Keplers Laws were only empirical without any basis in terms of forces.14-2 Newtons law of universal gravitation1.Guided by Keplers laws,Newton proposed a force law for gravitation:Every particle in the universe attracts every other particle with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.The direction of the force is along the line joining the particles.Mathematically,the law of gravitation has the following form(14-1)Here G,called the gravitational constant.We can represent Eq(14-1)in vectors form.where and are unit vectors.221rmmGF=2211)/(1067.6kgmNG=212212121rrmmGF=122122112rrmmGFand21r12rEq(14-3)The negative sign in Eq(14-3)shows that points in a direction opposite to ,which indicates that the gravitational force is attractive.2112121212,rrrrrr=1m1m1m2m2m2m12F12F12F21F21F12r12r21r1221212121,rrrrrr=Fig(14-2)Sample Problem 14-2A properly suited astronaut(ma=105Kg)is drifting through the asteroid belt(小行星带)on a mining expedition（矿业探险）.At a particular instant he is located near two asteroids of masses m1=346Kg(r1=215m)and m2=184Kg(r2=142m)two asteroids form an angle of 120 degree.At that instant,what is the magnitude and direction of the gravitational force on the astronaut due to these two asteroids?14-3 The gravitational constant G1.The first laboratory determination of Gwas done by Cavendish in 1798.2.It is difficult to improve substantially on the precision of the measured value of G because of its small magnitude.3.This difficulty of measuring G is unfortunate,because gravitation has such an essential role in theories of the origin and structure of the universe.This experiment was selected as one of the top 10 beautiful experiments in Phys.English chemist and physicistwho was shy and absent-minded.He was terrified of women,and communicated with his female servants by notes.He performed numerous scientific investigations,but published only twenty articles and no books.Cavendish,Henry(1731-1810)The Cavendish Laboratory was founded in 1871,along with the appointment of James Clerk Maxwell as the first Cavendish Professor.It has a distinguished intellectual history,with 29 Nobel prizewinners who worked for considerable periods within its facilities,and is associated with many notable discoveries,including the electron and the structure of DNA.Cavendish Laboratoryat Cambridge Univ.(1871 present)14-4 Gravitation near the Earths surface1.If we combine the law of gravitation and Newtons second law,we can obtain the acceleration of free-fall body near Earths surface.The distance of the body from the Earths centeris r.2rmMGFE=0mgF=20rMGgE=EMis the mass of the Earth;is the free-fall acceleration due only to the gravitational pull of the Earth0g(14-5)Look at the spacecraft:The acceleration from the gravitational force of Earth at that place is not zero!高度/Km08.836.640035700As we will prove in Sec14-5,for spherical mass distributions we can regard the object as a point mass concentrated at its center.It is an exact relationship.Any assumption in above deduction?The Earth is regarded as a mass point at its center.So Eq.(14-5)requires the Earth is spherical and that its density depends only on the radial distance from its center2.The real Earth differs from our model in three way(a)The Earth is not uniform；(b)The Earth is approximately an ellipsoid(椭球)；flattened at the poles and bulging at the equator(c)The earth is rotating.3.How does spin of the Earth affect the measure value g of gravitational acceleration g0?Fig 14-7 shows the rotating Earth from an inertial frame positioned in space above the north pole.A crate of mass m rests on a platform scale(台秤)at the equator.Because of the Earths spin,the crate is in uniform circular motion with radiusand period of rotation T(=24 hours).From Fig14-7(14-16)EEcRmRmvmaNmg220/=)(20ERgmN=(a)(b)N0mgNorth polecratescaleRERFig 14-7where N is the normal force on the crate due to the platform scale(equal to the scale reading mg,and g is the measure value of gravitational acceleration g0),The g is smaller than by only ,or.220/034.0smRggE=0g2/034.0sm0mgmg ERgmNg20=If N=mg,14-5 The two shell theorems1.Shell theoremA uniformly dense spherical shell attracts an external particle as if the mass of the shell were concentrated at its center.The shell theorem indicates:A spherically symmetric body attracts particle outside as if its mass were concentrated at its center.2.Shell theoremA uniformly dense spherical shell