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)