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%
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)
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.
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:
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