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 e 2 = 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 P 2 = a 3 (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 N m 2 /kg 2 m = mass of objects r = distance between objects Action at a Distance

Sun’s Gravitational Force on Earth G = 6.67 x N m 2 /kg 2 M Earth = 5.98 x kg M sun = 1.99 x kg r ES = 1.50 x 10 11

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. 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.