21

2d gt=

fv gt=

History of

Astronomy

Eratosthenes read of a well in Syene, Egypt which at noon on June 21 would reflect the sun overhead.

The distance between Alexandria and Syene is about 740 kilometers

A year later, Eratosthenes in Alexandria observed the shadow of a stick and measured the angle to be 7.2 deg,

X/740 = 360/7.2X=38,057 km or 22,940 mi

Eratosthenes ( 276 –194 B.C.) measured circumference of the Earth

90 deg

The distance to Mercury & Venus

a

Simple Trig: Sin (a)= A/B or A = (B) Sin(a)

A

B

When the planet Venus or Mercury are at greatest elongation, measure the angle between the Sun and the planet at Sunset. The distance of Earth to Sun is 1 A.U.

Using this method Mercury and Venus were .4 and .7 A.U. from the Sun respectively.

aA B

Claudius Ptolemy ~ 200 A.D.

Born in Alexandria, Egypt.

His model of the Solar system strived to explain the motion of the planets. He presumed that the Earth was at the

center of the Universe (geocentric) a theory that had been proposed by Aristotle.

Geocentric Theory

The planets & Sun revolve around the Earth. The circles are epicycles, where the planets appear to go into a loop and then continue onward.

He explained the motion of the planets this way!

Copernicus proposed the heliocentric model, with circular orbits, and uniform motion.

The model was less accurate for predicting positions, but more “physically realistic”

Copernicus: 1473 –1543

He also had a simple explanation for retrograde motion, the planet moved backwards for a short period of time.

Galileo Galilei1564-1642

•Galileo was among the first to turn a telescope to the sky.

•He developed the Scientific Method,

and the Law of Inertia.

• Galileo’s earlier work:

– 1590 Masses fall at same rate, heavier do not fall faster (unless affected by air resistance). First to experiment

– 1604 He observed a supernova

• Telescopes:– 1609 He hears of the invention of a

telescope, which uses eyeglass lenses.

– Works out details of better lenses and , builds improved ones himself.

Telescope DiscoveriesThe Moons of Jupiter

Clear example of four objects that do not orbit the Earth.

Telescope Discoveries

Sunspots

He showed they were really on the Sun.

But the Sun was made in the image of God!

On the Moon he saw mountains, valleys and (Earthlike) features .

Galileo’s Venus Observations• Detects the phases of Venus

– Phases show that Venus must orbit the Sun.

From our text: Horizons, by Seeds

Tycho Brahe (1546-1601)He was of Danish nobility. Lost his nose in duel (so he had a metal one made).

He built very accurate instruments for measuring sky positions. He hired Kepler to try to understand the motion of Mars and shortly thereafter he died.

Johannes Kepler (1571-1630)

He was born sickly and poor and, went to work with Tycho to escape 30 Years War.

Kepler proposed a geometrical heliocentric model with imbedded polygons ,but had to gave up (clever, but not better).

• He finally determined, that the planets

moved along elliptical paths, with the sun at one of the foci of the ellipse.

Since the planets’ orbits are close to circular, nothing is located at the other focus.

Properties of Ellipses• An ellipse is defined by two constants :

• (1) eccentricity e 0=circle, 1 = line

e=0.98

e=0

Same focus, at the sun

b a

a = Semi-major axis

b = Semi-minor axis ( we will not use)

(2) semi-major axis = a 1/2 length of major axis

Properties of Ellipses

Kepler’s Three Laws

•Law I–Planets orbit the Sun in ellipses with

the Sun at one focus of the ellipse.

Sun

Planet

Note: There is nothing at the other focus or in the center.

Kepler’s Law II

2) A line between a planet and the Sun sweeps out equal areas of the ellipse in equal amounts of time.

Kepler’s Laws• Law III

The orbital period of a planet squared is proportional to the length of the

semi-major axis cubed. P2 a3

If P is measured in earth years, and a is measured in AU, then the formula becomes

P2 a3

Using the Third Law

P2 a3

P must be in earth years, and a in AU.

A planet is located 4 au form the sun, what is the

period of the planet ?

2 3 24 , 64,

64, 8

P p

P P years

= =

= =

2 3 24 , 64,

64, 8

P p

P P years

= =

= =

Summary of Kepler’s Three Laws• I. The orbits of the planets are

ellipses with the sun at one focus.

• II The orbital path sweeps out equal areas in equal time.

• III The orbital period squared is proportional to the average distance cubed (usually expressed in earth years and A.U.s).

Isaac Newton (1642-1727)One of world’s greatest scientists, co-inventor of calculus.

He discovered the law of Universal Gravitation, Three Laws of Motion and he was able to explain Kepler’s Laws.

Personally rather obnoxious. Had poor relationships with women. Did most of his work before he turned 25!

Newton’s LawsThe First Law ( Inertia )

A body continues to move as it has been moving unless acted upon by an external force.

A body at rest

upon by some

stays at rest ,unless acted

force .

An astronaut, floating in space, will float in a straight line , unless some force acts upon him/her.

Newton’s Laws

The 2nd Law or a = F/mF = (mass) a

Forces acting on a body can produce an acceleration to a body.

Newton’s LawsFor every action there is

an equal and opposite reaction

The 3rd Law

Newton’s Law of Universal Gravitation

Every object in the universe attracts every other object with a force that is directly proportional to the product of its masses, and inversely proportional to the square of its distance.

M1 M2

d

M1 M2

2d

1 2 1 22 2

1

(2 ) 4

GM M GM MF

d d= =

1 22

GM MF

d=

M1 M2

d/21 2 1 2

2 24

( / 2)

GM M GM MF

d d= =

More distance less force - less distance, more force

2M1

M2

d1 2 1 22 2

(2 )2

G M M GM MF

d d= =

M1 M2

d1 22

GM MF

d=

2M1

2M2

d1 2 1 2

2 2

(2 )(2 )4

G M M GM MF

d d= =

More mass more force – less mass, less force

What is mass and weight ?

Weight is the attraction of gravity for an object. Mass is how much matter an object contains.

Mass does not depend on gravity. One kg on Earth is one kg everywhere in the universe.

Weight would be different for each planet, due to gravity.

Astronomers use the Kelvin scale, because it starts with 0 degrees, where there is no molecular motion .

•On the microscopic level , the average kinetic energy of the particles within a substance is called the temperature.

Temperature Scales

• Kinetic Energy– Energy due to motion

• Potential Energy– Stored energy

• Radiative Energy– Energy transported by light

Energy can change from one form to another.

Three Basic Types of Energy

Conservation of Energy

• Energy can be neither created nor destroyed.

• It merely changes it form or is exchanged between objects.

• The total energy content of the Universe was determined in the Big Bang and remains the same today.

• gravitational potential energy is the energy which an object stores due to its ability to fall.

• It depends on:

– the object’s mass (m)

– the strength of gravity (g)

– the distance which it falls (d)

Potential Energy

m

d

g

E=mgh

E = mcE = mc22

[ c = 3 x 108 m/s is the speed of light; m is in kg, then E is in joules]

Energy is stored in matter itself andthis mass-energy equation is how much energy would be released if an amount of mass, m were converted into energy.

The Acceleration of Gravity

• As objects fall, they accelerate.

• The acceleration due to Earth’s gravity is 10 m/s each second, or g = 10 m/s2,or 32 ft/s2.

• The higher you drop the ball, the greater its velocity will be at impact.

Ignoring air friction

Conservation of Angular Momentum

Angular momentum = rotational momentum

– Spinning objects rotate faster when radius shrinks, and rotate slower when their radius expands.

Experimental evidence indicates that angular momentum is rigorously conserved in our Universe: it can be transferred, but it cannot be created or destroyed.

When an ice skater goes into a spin, if the skater moves their arms inward, the rate of spin increases, and if the arms are move outward, the rate of spin slows down.

When they bring their arms in, this shortens the distance from the mass in the arms to the rotation axis, so the velocity of that mass must increase accordingly for the product of the two to remain the same.

This is conservation of angular momentum.