Today’s APOD

Review Chapter 1, Kepler’s LawsRead Chapter 2: Gravity & Motion2nd Homework due FridayKirkwood Obs. open tonight, 8:30-

10:30IN-CLASS QUIZ TODAY!!

The Sun Today

A100 Solar System

Extra Announcements

Caty can’t do office hours this week… (send email 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.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

P2 = a3 (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 forcesWithout friction…

a body at rest tends to remain at resta body in motion tends to remain in motion

Galileo experimented

with inclined planes

Isaac Newton, the Laws of Motion, and the Universal Law of

GravitationNewton

Born same year Galileo diedAttempts to understand motion of the

MoonLeads him to deduce the law of gravity (as we

still use it today!)Requires him to invent new mathematicsLeads 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 ideasWhat 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 structurea universal force that causes all objects to

pull on all other objects everywhereholds 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 GravityNewton

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 objectThis equation applies for any force,

gravitational or otherwise

F = maF = ma

F = ma

Newton’s Third Law of MotionWhen 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 motion2. The theory of universal gravitation3. 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

221

r

mGmF

F = ma

ASSIGNMENTSthis week

Review Chapter 1, Kepler’s LawsRead Chapter 2: Gravity & Motion2nd Homework due FridayKirkwood Obs. open tonight, 8:30-

10:30