Gravitation and the Clockwork Universe

Apollo 11 Lunar Lander

How can satellites orbit celestial objects without falling?

The Ancient Greeks Model of the Universe

Geocentric View

Ancient Astronomers Saw Lights that Wandered About the Sky

Claudius Ptolemy's View of the Universe

Geocentric View

Nicolas Copernicus (1473 – 1543)

Copernicus worked out the details of the heliocentric model of the universe.

Occam’s razor

Too simple to be wrong

The Retrograde Motion Was an Optical Illusion

A Comparison of the Average Sun – Planet Distances

Tycho Brahe

Greatest naked eye observer

Trusted the geocentric view

His observations confirmed the heliocentric theory

Measured the positions of the stars and planets accurately.

Tycho argued that nearby stars should shift their position as the Earth revolved around the Sun.

Tycho Brahe looked for stellar parallax

Tycho Brahe and Johannes Kepler teamed up.

An Ellipse

Focus

Foci

Major axis

Minor axis

Eccentricity

e = 1 => line

e = 0 => circle

e2 = 1-(b/a)2

Kepler’s Three Laws

The orbit of a planet is an ellipse with the Sun at one foci

A line joining a planet and the Sun sweeps out equal areas in equal times

The harmonic law P2 = a3 (a is the semi-major axis)

The Harmonic Law

The square of the sidereal period of a planet is directly proportional to the cube of the semi-major axis of the orbit.

Galileo Galilei (1564 – 1642)

Objects fall with constant acceleration

Galileo Discovered Four Moons Orbiting Jupiter

Ganymede

IO

Europa

            

Callisto

Objects Accelerate as they Fall

Speed increases at a constant rate.

Falling bodies move with constant acceleration..

Experimented by rolling balls down various inclines.

a = dv/dt

Sir Isaac Newton (1642 – 1727)

Newton laid the foundation for differential and integral calculus. His work on optics and gravitation make him one of the greatest scientists the world has known.

Law of Gravity

F = Force

G = Gravitational constant of the universe

6.67 x 10-11 N•m2/kg2

m = mass of objects

r = distance between objects

Action at a Distance

Sun’s Gravitational Force on Earth

G = 6.67 x 10-11 N•m2/kg2

MEarth = 5.98 x 1024 kg

Msun = 1.99 x 1030 kg

rES = 1.50 x 1011

Skating - The laws of Motion

Neglect air resistance

Neglect friction

•At rest on a level surface:–If you just wait, you stay stationary–If you’re pushed, you start moving in that direction

Moving on a level surface:–If you just wait, you coast steadily in straight line–If you’re pushed, you change direction or speed

Physics Concept

• Inertia

– A body at rest tends to remain at rest– A body in motion tends to remain in motion

Newton’s First Law

An object that is free of external influences moves at a constant velocity.

Physical Quantities• Position – an object’s location

• Force – a push or a pull• Acceleration – its change in velocity with time

• Velocity – change in position with time

• Mass – measure of its inertia

• Speed = distance/time

Mass and Inertia• Mass is the measure of an object’s inertia.

• Mass is how much matter is contained within the object.

• The kilogram (kg) is the basic unit of measure for mass.

• Inertia is the object’s resistance to a change in it’s motion.

Newton’s Second Law

The force exerted on an object is equal to the product of that object’s mass times its acceleration. The acceleration is in the same direction as the force.

force mass acceleration

F = ma

Falling Balls

Check Your Understanding• Suppose that I throw a ball upward into the air. After

the ball leaves my hand, is there any force pushing the ball upward?

• Out in deep space, far from any celestial object, would an astronaut weigh anything? Would the astronaut have mass?

• If you weight on the moon is one-sixth of what it is on Earth, what is the moon’s acceleration due to gravity?

w = mg

Weight vs. Mass

• Weight – earth’s gravitational force on object

Relative Motion

The further a satellite is from the Earth the weaker the Earth’s pull, therefore it should travel slower so gravity can pull it back.