Gravitation PDF - Wiley

Module 5-3 Gravitation 5.3-1 Newton's Law of Gravitation 5.3-2 Gravitation and the Principle of Superposition 5.3-3 Gravitation Near Earth's Surface 5.3-4 Gravitation Inside Earth 5.3-5 Gravitational Potential Energy 5.3-6 Planets and Satellites: K...

Module 5-3 Gravitation 5.3-1 Newton's Law of Gravitation 5.3-2 Gravitation and the Principle of Superposition 5.3-3 Gravitation Near Earth's Surface 5.3-4 Gravitation Inside Earth 5.3-5 Gravitational Potential Energy 5.3-6 Planets and Satellites: Kepler's Laws 5.3-7 Satellites: Orbits and Energy 5.3-8 Einstein and Gravitation Copyright © 2014 John Wiley & Sons, Inc. All rights reserved. 5.3-1 Newton's Law of Gravitation Learning Objectives 13.01 Apply Newton's law of 13.03 Draw a free-body gravitation to relate the diagram to indicate the gravitational force between gravitational force on a two particles to their masses particle due to another and their separation. particle or a uniform, spherical distribution of 13.02 Identify that a uniform matter. spherical shell of matter attracts a particle that is outside the shell as if all the shell's mass were concentrated as a particle at its center. © 2014 John Wiley & Sons, Inc. All rights reserved. 5.3-1 Newton's Law of Gravitation (in 1665, aged 23) The same force, called Gravitational force: o Holds us to the Earth. Makes apple fall to the ground o Attracts and directs a passing space craft to a nearby planet o Holds Earth in orbit around the Sun o Holds the Sun together with the stars in our galaxy o Reaches out across intergalactic space to hold together the Local Group of galaxies o Holds together the Local Supercluster of galaxies o Is responsible for black holes Gravity is far-reaching and very important! © 2014 John Wiley & Sons, Inc. All rights reserved. 5.3-1 Newton's Law of Gravitation Gravitation is one of the Four basic forces directing interactions in our universe. (The others are electromagnetic force, strong nuclear force, and weak nuclear force) Gravitational attraction depends on the amount of “stuff” an object is made of. How much “matter” it contains. The force is always attractive, never repulsive Gravitation is the tendency for bodies to attract each other Newton realized this attraction was responsible for maintaining the orbits of celestial bodies Newton's law of gravitation defines in precise mathematics, the strength of this attractive force between particles For apple & Earth: 0.8 N; for 2 people: < 1 μN © 2014 John Wiley & Sons, Inc. All rights reserved. 5.3-1 Newton's Law of Gravitation The magnitude of the force is given by: Eq. (13-1) Where G is the gravitational constant: Eq. (13-2) The force always points from one particle to the other, so this equation can be written in vector form: Eq. (13-3) © 2014 John Wiley & Sons, Inc. All rights reserved. 5.3-1 Newton's Law of Gravitation The shell theorem describes gravitational attraction for objects Earth is a nesting of shells, so we feel Earth's mass as if it were all located at its center Gravitational force forms third-law force (i.e. Action-Reaction) pairs E.g., Earth-apple and apple-Earth forces are both 0.8 N Figure 13-2 © 2014 John Wiley & Sons, Inc. All rights reserved. 5.3-1 Newton's Law of Gravitation The difference in mass causes the difference in the apple:Earth accelerations: ~10 m/s2 vs. ~ 10-25 m/s2 Figure 13-3 Answer: All exert equal forces on the particle © 2014 John Wiley & Sons, Inc. All rights reserved. 5.3-2 Gravitation and the Principle of Superposition Learning Objectives 13.04 If more than one 13.05 If more than one gravitational force acts on a gravitational force acts on a particle, draw a free-body particle, find the net force by diagram showing those adding the individual forces forces, with the tails of the as vectors. force vectors anchored on the particle. © 2014 John Wiley & Sons, Inc. All rights reserved. 5.3-2 Gravitation and the Principle of Superposition Find the net gravitational force by the principle of superposition: the net is the sum of individual effects Add the individual forces as vectors: Eq. (13-5) For a real (extended) object, this becomes an integral: Eq. (13-6) If the object is a uniform sphere or shell we can treat its mass as being at its center instead © 2014 John Wiley & Sons, Inc. All rights reserved.