1. Origin of the Law of Gravitation 2. Newton's Law of Universal Gravitation Chapter 14 3. The Gravitational Gravitation Constant 4. Gravitation Near the Earth's surface 5. The two shel Theorems 6. Gravitational Potential Energy 下一页
Chapter 14 Gravitation 1. Origin of the Law of Gravitation 2. Newton’s Law of Universal Gravitation 3. The Gravitational Constant G 4. Gravitation Near the Earth’s surface 5. The Two Shell Theorems 6. Gravitational Potential Energy
14-1 Origin of the law of gravitation 1. In 16th century Copernicus(1473v 1543) proposed a heliocentric( sun-centered )scheme, in which the earth and other planets move about sun 2. Kepler(1571v1630) proposed three law which we discuss in Section 14-7) that describe Planet's motions However, Keplers Laws were only empirical without any basis in terms of forces
14-1 Origin of the law of gravitation 1. In 16th century Copernicus ( 1473~1543 ) proposed a heliocentric ( sun-centered ) scheme, in which the Earth and other planets move about sun. 2. Kepler ( 1571~1630 ) proposed three law ( which we discuss in Section 14-7) that describe Planet’s motions. However, Kepler’s Laws were only empirical without any basis in terms of forces
14-2 Newton 's law of universa gravitation 1. Guided by Kepler's 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
14-2 Newton’s law of universal gravitation 1. Guided by Kepler’s 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 nnn F=G (14-1) Here G called the gravitational constant. G=667×10-N·m2(kg)2 We can represent eq(14-1)in vectors form m1m, 12 -C r2 and 21 G=221Eq(143) where r2 and r are unit vectors
Mathematically, the law of gravitation has the following form (14-1) Here G, called the gravitational constant. We can represent Eq(14-1) in vector’s form. where and are unit vectors. 2 1 2 r m m F = G 11 2 2 G = 6.6710 N m /(k g) − → = − 2 21 21 1 2 21 r r m m F G → = − 2 12 12 1 2 12 r r m m F G and 21 r 12 r Eq(14-3)
12 12 ,21=12-7i 2 21 12 12 Fig(14-2) The negative sign in Eq(14-3)shows that F points in a direction opposite to ri2, which indicates that the gravitational force is attractive
The negative sign in Eq(14-3) shows that points in a direction opposite to , which indicates that the gravitational force is attractive. 12 1 2 12 12 12 , r r r r r r = = − m1 m1 m1 m2 2 m2 m → F12 → F12 → F12 → F21 → F21 12 r → 12 r → 21 r 21 2 1 21 21 21 , r r r r r r = = − Fig(14-2)
Sample Problem 14-2 A properly suited astronaut (ma=105Kg is drifting through the asteroid be(小行星带)ona mining expedition(矿业探险). At a particular instant he is located near two asteroid s of masses m1=346Kg(1=215m) and m2=184Ko ([2=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
Sample Problem 14-2 A 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 g 1. The first laboratory determination of Gwas done by Cavendish in 1798 This experiment was selected as one of the top 10 beautiful experiments in Phys 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
14-3 The gravitational constant G 1.The first laboratory determination of G was 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
Cavendish, Henry(1731-1810) English chemist and physicist who 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
English chemist and physicist who 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)
Cavendish Laboratory CAVENDISH PROFESSORS at Cambridge Univ PHYSICS (1871- present) 1871-1879 少2∠x 1879-1884 p、;乙 1884-1919 1919-1937 名 1938.15304 1954-1971 1971-1982 Prof Sir Brian Pippard 1983-1995 Prof Sir Sam Edwards 1995 Prof. Richard Friend 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
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 Laboratory at Cambridge Univ. (1871~ present)
14-4 Gravitation near the earth's surface 1. If we combine the law of gravitation and Newton 's second law, we can obtain the acceleration of free fall body near Earth's surface The distance of the body from the earth s center is r M.m F=mgo 0=G2(145) ME is the mass of the earth go is the free-fall acceleration due only to the gravitational pull of the Earth
14-4 Gravitation near the Earth’s surface 1. If we combine the law of gravitation and Newton’s second law, we can obtain the acceleration of freefall body near Earth’s surface. The distance of the body from the Earth’s center is r. 2 r M m F G E = F = mg0 ｝ 0 2 r M g G E = ME is the mass of the Earth; is the free-fall acceleration due only to the gravitational pull of the Earth 0 g (14-5)
