Today’s APODAPOD  Review Chapter 1, Kepler’s Laws  Read Chapter 2: Gravity & Motion  2 nd Homework due Friday  Kirkwood Obs. open tonight, 8:30-10:30  IN-CLASS QUIZ TODAY!! The Sun Today A100 Solar System

Extra Announcements  Caty can’t do office hours this week…  (send with questions)  Nathalie will lecture on Friday  Postpone due date for HW2 until Monday, Sept. 29 (web problems, use alternate URL)  astro.unl.edu/naap/pos/animations/kepler.htmlastro.unl.edu/naap/pos/animations/kepler.html

Kepler’s 3 Laws of Planetary Motion  Planets move in elliptical orbits with the Sun at one focus of the ellipse  A planet’s orbital speed varies in such a way that a line joining the Sun and the planet will sweep out an equal area each month  P 2 = a 3 (the square of the period of a planet orbiting the sun is equal to the cube of the semi- major axis of the planet’s orbit) But WHY ????????

The Problem of Astronomical Motion  Galileo investigated this connection with experiments using projectiles and balls rolling down planks  He put science on a course to determine laws of motion and to develop the scientific method Astronomers of antiquity did not connect gravity and astronomical motion

inertia! Demonstrated the ideas of inertia and forces  Without friction…  a body at rest tends to remain at rest  a body in motion tends to remain in motion Galileo experimented with inclined planes

Isaac Newton, the Laws of Motion, and the Universal Law of Gravitation  Newton  Born same year Galileo died  Attempts to understand motion of the Moon  Leads him to deduce the law of gravity (as we still use it today!)  Requires him to invent new mathematics  Leads him to deduce the general laws of motion

A body continues in a state of rest or uniform motion in a straight line unless made to change that state by forces acting on it Galileo’s ideas of inertia became Newton’s First Law of Motion:

Newton’s First Law  Important ideas  What is a force? A push or a pull  The sum of all the forces on an object is the net force  If the forces all balance, the net force is zero, and the object’s motion will not change If the speed or direction of motion of an object changes, then a nonzero net force must be present

Astronomical Motion  Planets move along curved (elliptical) paths, or orbits  Speed and direction are changing Must there be a net force on the planets? Yes!

Gravity is that force  Gravity gives the Universe its structure  a universal force that causes all objects to pull on all other objects everywhere  holds the Earth in orbit around the Sun, the Sun in orbit around the Milky Way, and the Milky Way in its path within the Local Group

Everything attracts everything else!! Newton’s Law of Gravity

Orbital Motion and Gravity  Newton  Explained the Moon’s motion with force that pulls the Moon from a straight, inertial trajectory  Showed that the force must decrease with distance  defined the properties of gravity  wrote the equations of motion with gravity  The Moon moves “parallel” to the Earth’s surface at such a speed that its gravitational deflection toward the surface is offset by the surface’s curvature away from the projectile

Orbital Motion Using Newton’s First Law  At a sufficiently high speed, the cannonball travels so far that the ground curves out from under it.  The cannonball literally misses the ground!

Newton’s 2nd Law: Acceleration  Acceleration  An object increasing or decreasing in speed along a straight line is accelerating  An object changing direction, even with constant speed, is accelerating  Acceleration is produced by a force  Acceleration and force are proportional (double the force, double the acceleration

Newton’s Second Law: Mass  Mass is the amount of matter an object contains  Technically, mass is a measure of an object’s inertia  Mass is generally measured in kilograms  Mass should not be confused with weight, which is a force related to gravity – weight may change from place to place, but mass does not

Newton’s Second Law of Motion  The amount of acceleration (a) that an object undergoes is proportional to the force applied (F) and inversely proportional to the mass (m) of the object  This equation applies for any force, gravitational or otherwise F = ma

Newton’s Third Law of Motion  When two objects interact, they create equal and opposite forces on each other  This is true for any two objects, including the Sun and the Earth!

To explain the motion of the planets, Newton developed three ideas: 1.The laws of motion 2.The theory of universal gravitation 3.Calculus, a new branch of mathematics Newton solved the premier scientific problem of his time --- to explain the motion of the planets. “If I have been able to see farther than others it is because I stood on the shoulders of giants.” --- Newton’s letter to Robert Hooke, probably referring to Galileo and Kepler 2 21 r mGm F  F = ma

ASSIGNMENTS this week  Review Chapter 1, Kepler’s Laws  Read Chapter 2: Gravity & Motion  2 nd Homework due Friday  Kirkwood Obs. open tonight, 8:30-10:30