GENERALGENERAL SCIENCESCIENCE

MIKE ST. MIKE ST. JOHNJOHN

WEEK ONEWEEK ONE

ErathostenesErathostenes

BORN 275BC DIED 194 BCBORN 275BC DIED 194 BCCALCULATED THE CALCULATED THE

CIRCUMFERENCE OF THE CIRCUMFERENCE OF THE EARTH TO BE 39000 KM EARTH TO BE 39000 KM COMPARED TO ACTUAL OF COMPARED TO ACTUAL OF 40075 KM %ERROR OF 2.7%40075 KM %ERROR OF 2.7%

804.65 km

The Formula UsedThe Formula Used

D D = = AA d = distance between

d a Syene and Alexandria

A = 360 degrees

a = shadow angle of vertical stick

D = circumference of the earth (to be determined)

Ptolemy 87 – 150 ADPtolemy 87 – 150 AD

EccentricEccentric

EpicycleEpicycle

Planetary ModelPlanetary Model

Ptolemaic UniversePtolemaic Universe

Ptolemaic UniversePtolemaic Universe

CopernicusCopernicus1473-15431473-1543

There is no one centre in the There is no one centre in the universe.universe.

The Earth's centre is not the The Earth's centre is not the centre of the universe.centre of the universe.

The centre of the universe is The centre of the universe is near the sun.near the sun.

Little CommentaryLittle Commentary

Commentary ContinuedCommentary Continued

The distance from the Earth to The distance from the Earth to the sun is imperceptible the sun is imperceptible compared with the distance to compared with the distance to the stars.the stars.

The rotation of the Earth The rotation of the Earth accounts for the apparent daily accounts for the apparent daily rotation of the stars.rotation of the stars.

ContinuedContinued

The apparent annual cycle of The apparent annual cycle of movements of the sun is caused movements of the sun is caused by the Earth revolving round it.by the Earth revolving round it.

The apparent retrograde motion The apparent retrograde motion of the planets is caused by the of the planets is caused by the motion of the Earth from which motion of the Earth from which one observes.one observes.

Data on Planetary OrbitsData on Planetary Orbits

Copernican UniverseCopernican Universe

Copernican UniverseCopernican Universe

Tycho Brahe 1546 - 1601Tycho Brahe 1546 - 1601

SextantSextant

Mural QuadrantMural Quadrant

Tychonic UniverseTychonic Universe

Johannes Kepler 1571-1630Johannes Kepler 1571-1630

Kepler’s LawsKepler’s LawsI. The orbits of the planets are I. The orbits of the planets are

ellipses, with the Sun at one ellipses, with the Sun at one focus of the ellipse.focus of the ellipse.

II. The line joining the planet to II. The line joining the planet to the Sun sweeps out equal areas the Sun sweeps out equal areas in equal times as the planet in equal times as the planet travels around the ellipse.travels around the ellipse.

Kepler’s LawsKepler’s Laws

III. The ratio of the squares of III. The ratio of the squares of the revolutionary periods for the revolutionary periods for two planets is equal to the ratio two planets is equal to the ratio of the cubes of their semimajor of the cubes of their semimajor axes:axes:

Kepler’s First LawKepler’s First Law

focusfocus

Kepler’s Second LawKepler’s Second Law

EQUAL AREAS IN EQUAL TIME

Kepler’s Third LawKepler’s Third Law

Galileo Galilei 1564-1642Galileo Galilei 1564-1642

SectorSector

TelescopeTelescope

MoonMoon

SaturnSaturn

Galileo and GravityGalileo and Gravity

Legend has it that Legend has it that Galileo Galileo went to thewent to the Tower of Pisa Tower of Pisa toto test Gravity. The test Gravity. The

experiment which experiment which would hit the would hit the ground first the ground first the

heavier or lighter heavier or lighter cannonball cannonball

Gravity Gravity

Galileo reasoned that gravity must Galileo reasoned that gravity must accelerate an object at a constant rate. He accelerate an object at a constant rate. He conducted experiments to test this conducted experiments to test this hypothesis. This time he used a very long hypothesis. This time he used a very long ramp and a ball.ramp and a ball.

Galileo Gravity DemonstratorGalileo Gravity Demonstrator

Galileo thought that it would take twice as Galileo thought that it would take twice as long for the ball to roll down the whole long for the ball to roll down the whole ramp as it would from the quarter mark.ramp as it would from the quarter mark.

Mathematics The Language of Mathematics The Language of ScienceScience

Scientist use metric units in their Scientist use metric units in their calculationscalculations

Basic Measurement Units are:Basic Measurement Units are:Mass:Mass: kilogramskilogramsLength:Length: metersmetersTime:Time: secondsseconds

Scalar Versus VectorScalar Versus Vector

Scalar quantity just has magnitudeScalar quantity just has magnitudeExamples:Examples: 50 mph50 mph 8 meters8 meters

Vector quantity has both magnitude and Vector quantity has both magnitude and directiondirection

Examples:Examples: 50 mph in a Northerly 50 mph in a Northerly DirectionDirection 8 meters South8 meters South

Isaac Newton 1642 -1727Isaac Newton 1642 -1727

““If I have been ableIf I have been able to see further, it wasto see further, it was only because I stood only because I stood on the shoulders of on the shoulders of giants.”giants.”                                                                 —                                                                —Sir Isaac Newton Sir Isaac Newton

Newton’s First Law of MotionNewton’s First Law of Motion

An object at rest will stay at rest an object An object at rest will stay at rest an object in motion will stay in motion unless acted in motion will stay in motion unless acted upon by a force.upon by a force. That property about That property about the object that resist motion is called the object that resist motion is called inertia.inertia.

Newton’s Second Law of MotionNewton’s Second Law of Motion

Force = (mass) (acceleration) or F=maForce = (mass) (acceleration) or F=maUnits:Units: massmass kilogramskilograms

accelerationacceleration m/sm/s22

ForceForce NewtonsNewtons

Newton’s Third Law of MotionNewton’s Third Law of Motion

For every action there is an equal and For every action there is an equal and opposite reaction.opposite reaction.

Which Will Hit the Ground First?Which Will Hit the Ground First?

Motion in the x and y Motion in the x and y direction direction

are independent. The key is are independent. The key is that both objects started at the that both objects started at the same height above the ground. same height above the ground.

Newton and GravityNewton and Gravity

Newton thought that the same force that causes Newton thought that the same force that causes an apple to fall to the ground is the same as the an apple to fall to the ground is the same as the force that keeps the moon orbiting the earth.force that keeps the moon orbiting the earth.

Newton’s Universal Law of Newton’s Universal Law of GravitationGravitation

F = F = G mG m1 1 mm22

dd22

F: ForceF: Force G: Gravitational G: Gravitational

ConstantConstant mm11: mass of first : mass of first

objectobject mm22: mass of second : mass of second

objectobject d: distance between d: distance between

the objectsthe objects

How Much is the Force of Attraction How Much is the Force of Attraction between the Sun and the Earth?between the Sun and the Earth?

2x1030 kg

6x1024 kg 1.5x1010 m

F = (6.67x10-11 Nm2/kg2) (2x1030 kg) (6x1024 kg)

(1.5x1010 m)2

F = 3.56x1024 Newtons