ASTRONOMY 202 Spring 2007: Solar System Exploration

Instructor: Dr. David Alexander Web-site: www.ruf.rice.edu/~dalex/ASTR202_S07

Class 11: ’s Laws [2/9/07]  Announcements

 Gravitational acceleration

 Mass, weight and fun on elevators

 One good apple • Newton’s 3 Laws of Motion • Conservation of Momentum • Conservation of Angular Momentum

Chapter 4 Newtonian Gravitation • Universal Law of Gravitation • ‘Falling’ Orbits • Generalizing Kepler’s Laws • Tricking gravity

 Tidal Forces and Orbital Energy Announcements

 Homework 4 available online – due Mon Feb 12

 Guidelines for Discussion papers online

• Discussion paper due Mon Feb 19

 Observing night planned for sometime next week, weather permitt ing Gravitational Potential Energy

The amount of gravitational potential energy released as an object falls depends on its mass, the strength of gravity, and the distance it falls.

On the surface of the Earth : P = mgh

Mass -Energy

E = mc 2

The energy produced in the center of stars is generated entirely from matter. Conservation of Energy

We can change the form of energy from one to another but the total quantity of energy never changes.

This is called the law of conservation of energy and is one of the cornerstones of science. Gravitational Acceleration

Acceleration due to gravity: g = 9.81 m/s 2

This value holds at the surface of the Earth.

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Momentum and Force

Momentum – the product of an objects mass and velocity: p = mv

Force – the thing that causes a change of momentum: F = ma - strictly speaking this should be net force Mass and Weight

Mass on Earth = 100 kg Mass on Moon = 100 kg Weight at surface of Earth = 100 kg Weight at surface of Moon = 16 kg Newton ’s Laws of Motion

If I have seen further it is by standing on the shoulders of giants. Letter to Robert Hooke, February 5, 1675

Philosophiae Naturalis Principia Mathematica (1687), Sir (1642-1727)

Newton invented several years prior to Leibniz but did not publish his results.

Newton modified the conventional to provide an off-axis focus.

2.5 m Isaac Newton Telescope La Palma, Newton ’s First Law

I. In the absence of a net (overall) force acting upon it an object moves with constant velocity

Thus, objects at rest will tend to stay at rest while an object in motion stays in motion with no change in velocity. This is called an object’s . Newton ’s Second Law

II. The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.

Force = rate of change of momentum or Units? Force = mass x acceleration (F=ma)

Thus, objects of different mass will accelerate differently when subjected to the same force.

Also applies to angular motion

Inward force implies inward acceleration Newton ’s Third Law

III. For any force, there is an equal and opposite reaction force or For every action there is an equal and opposite reaction

Thus, forces always come in equal and opposite pairs.