Questions From Reading Activity?

Assessment Statements Gravitational Field, Potential and Energy Explain the concept of escape speed from a planet Derive an expression for the escape speed of an object from the surface of a planet Solve problems involving gravitational potential energy and gravitational potential.

Objectives  State the definitions of gravitational potential energy, and gravitational potential.  Understand that the work done as a mass m is moved across two points with gravitational potential difference ∆V is, W = mΔV

Objectives  Understand the meaning of escape velocity and solve related problems using the equations for escape speed from a body of mass M and radius R,

Objectives  Solve problems of orbital motion using the equation for orbital speed at a distance r from a body of mass M,  Understand the term weightlessness.

Newton’s Law of Universal Gravitation  Last year we learned,  This year we look at it from an energy standpoint

Gravitational Potential Energy  The gravitational force is an attractive force  Work must be done to separate two bodies in space a certain distance R  This work is converted to potential energy called the gravitational potential energy

Gravitational Potential Energy  For a satellite orbiting a body, its total energy is the sum of its kinetic and potential energy

Gravitational Potential Energy  For a satellite orbiting a body, its total energy is the sum of its kinetic and potential energy

Gravitational Potential Energy  If the satellite is in a stable, continuous orbit, the kinetic energy is equal to its potential energy

Gravitational Potential Energy  Newton’s Second Law tells us that the gravitational force will be balanced by the centripetal acceleration

Gravitational Potential Energy  Substituting into the traditional value for kinetic energy gives us

Gravitational Potential Energy  And total energy becomes

Gravitational Potential Energy  Graph of kinetic, potential, and total energy as a function of distance for a circular orbit

Gravitational Potential  The gravitational potential at any point P in the gravitational field is the work done per unit mass in bringing a small point mass m from infinity to point P  If the work done is W, then the gravitational potential is the ratio of the work done to the mass m

Gravitational Potential  The gravitational potential due to a single mass M a distance r from the center of M is  Gravitational potential is a scalar quantity  Its units are J/kg

Gravitational Potential  If we know the gravitational potential at some point P, then the potential energy of a mass m will be  And work will be defined as

Escape Velocity  Total energy of a mass m moving near a large mass M is given by  We assume the only force acting on m is the gravitational force created by M

Escape Velocity  We want to know if a mass m is launched from the surface of M, will it escape M’s gravitational field?

Escape Velocity  If total energy is greater than zero, m escapes  If total energy is less than zero, m will eventually return to the surface of M

Escape Velocity  The separation point is when V ∞ is equal to zero

Escape Velocity  This is the minimum velocity needed to exceed the gravitational attraction of M and is called the escape velocity  What happens if we double the value of m?

Orbital Motion  The law of gravitational attraction combined with Newton’s second law show that the orbit of any body due to gravitational attraction will follow the path of an ellipse or a circle (circles are ellipses with both foci at the same point).

Orbital Speed

Period of Motion  The period of a planet is proportional to the 3/2 power of the orbit radius  Kepler’s Third Law of Planetary Motion

Period of Motion  For two planets orbiting the same body, the ratio of their periods squared to their mean distance from the attracting body cubed, will be equal

Equipotential Surfaces  Gravitational potential is given by  An equipotential surface consists of those points that have the same potential

Equipotential Surfaces

 The magnitude of the gravitational field is the rate of change of with distance of the gravitational potential.

Equipotential Surfaces  Equipotential surfaces and field line are normal (perpendicular) to each other

Equipotential Surfaces  If we have a graph showing the variation with distance of the gravitational potential, the slope (gradient) of the graph is the magnitude of the gravitational field strength

Σary Review  Can you state the definitions of gravitational potential energy, and gravitational potential?  Do you understand that the work done as a mass m is moved across two points with gravitational potential difference ∆V is, W = mΔV ?

Σary Review  Do you understand the meaning of escape velocity and can you solve related problems using the equations for escape speed from a body of mass M and radius R ?

Σary Review  Can you solve problems of orbital motion using the equation for orbital speed at a distance r from a body of mass M ?  Do you understand the term weightlessness?

Assessment Statements Gravitational Field, Potential and Energy Explain the concept of escape speed from a planet Derive an expression for the escape speed of an object from the surface of a planet Solve problems involving gravitational potential energy and gravitational potential.

Part A, #1-15 Part B, #16-29 Homework