The History of Astronomy. When did mankind first become interested in the science of astronomy? 1.With the advent of modern computer technology (mid-20.

The History of Astronomy

When did mankind first become interested in the science of astronomy?

1. With the advent of modern computer technology (mid-20th century)

2. With the development of the theory of relativity (early 20th century)

3. With the invention of the telescope (~ A.D. 1600)

4. During the times of the ancient greeks (~ 400 – 300 B.C.)

5. In the stone and bronze ages (several thousand years B.C.)

The Roots of Astronomy

• Already in the stone and bronze ages, human cultures realized the cyclic nature of motions in the sky.

• Monuments dating back to ~ 3000 B.C. show alignments with astronomical significance.

• Those monuments were probably used as calendars or even to predict eclipses.

Stonehenge

Stonehenge

• Constructed 3000 – 1800 B.C. in Great Britain

• Alignments with locations of sunset, sunrise, moonset and moonrise at summer and winter solstices

• Probably used as calendar.

Why is it so difficult to find out about the state of astronomical knowledge of

bronze-age civilizations?

1. Written documents from that time are in languages that we don’t understand.

2. There are no written documents documents from that time.

3. Different written documents about their astronomical knowledge often contradict each other.

4. Due to the Earth’s precession, they had a completely different view of the sky than we have today.

5. They didn’t have any astronomical knowledge at all.

Ancient Greek Astronomers

• Models were based on unproven “first principles”, believed to be “obvious” and were not questioned:

1. Geocentric “Universe”: The Earth is at the Center of the “Universe”.

2. “Perfect Heavens”: The motions of all celestial bodies can be described by motions involving objects of “perfect” shape, i.e., spheres or circles.

• Ptolemy: Geocentric model, including epicycles

1. Imperfect, changeable Earth,

2. Perfect Heavens (described by spheres)

Central guiding principles:

What were the epicycles in Ptolemy’s model supposed to explain?

1. The fact that planets are moving against the background of the stars.

2. The fact that the sun is moving against the background of the stars.

3. The fact that planets are moving eastward for a short amount of time, while they are usually moving westward.

4. The fact that planets are moving westward for a short amount of time, while they are usually moving eastward.

5. The fact that planets seem to remain stationary for substantial amounts of time.

Epicycles

The ptolemaic system was considered the “standard model” of the Universe

until the Copernican Revolution.

Introduced to explain retrograde (westward) motion of

planets

At the time of Ptolemy, the introduction of epicycles was considered a very

elegant idea because …

1. it explained the motion of the planets to the accuracy observable at the time.

2. it was consistent with the prevailing geocentric world view.

3. it explained the apparently irregular motion of the planets in the sky with “perfect” circles.

4. because it did not openly contradict the teaching of the previous authorities.

5. All of the above.

The Copernican Revolution

Nicolaus Copernicus (1473 – 1543):

Heliocentric Universe (Sun in the Center)

New (and correct) explanation for retrograde motion of the planets:

This made Ptolemy’s epicycles

unnecessary.

Retrograde (westward) motion of a

planet occurs when the Earth passes the planet

.

Described in Copernicus’ famous book “De Revolutionibus Orbium Coelestium” (“About the revolutions of celestial objects”)

Galileo Galilei (1564 – 1642)

Invented the modern view of science: Transition from a faith-based “science” to an

observation-based science.

Was the first to meticulously report telescope observations of the sky to support

the Copernican Model of the Universe.

Major discoveries of Galileo:

• Moons of Jupiter

(4 Galilean moons)

• Rings of Saturn

(What he really saw)

What he really saw: Two little “moons” on both sides of Saturn!

Knowing about the nature of Saturn’s rings, which problem would you anticipate for Galileo

concerning his observations of Saturn?

1. Nobody would believe it because everybody knew that Saturn has much more than just 2 moons.

2. Nobody would believe it because such a configuration is physically unstable.

3. The two little “moons” might seem to disappear when the rings are viewed edge-on.

4. All of the above.

Major discoveries of Galileo (II):• Surface structures on the moon;

first estimates of the height of mountains on the moon

Major discoveries of Galileo (III):

• Sun spots (proving that the sun is not perfect!)

Which “phases” of Venus would you expect to see in the Ptolomaic model?

1. All phases, just like the moon: full, crescent, gibbous, and new.

2. Only full and gibbous.3. Only new and crescent.4. Only new and full.5. Only crescent and gibbous.

• Phases of Venus, proving that Venus orbits the sun,

not the Earth!

Major discoveries of Galileo (IV):

In the Copernikan “Universe”, the orbits of planets and moons were …

1. Perfect Circles

2. Ellipses

3. Spirals

4. Epicycles

5. None of the above.

Johannes Kepler (1571 – 1630)• Used the precise observational tables of Tycho Brahe (1546 –

1601) to study planetary motion mathematically.

1.Circular motion and

• Planets move around the sun on elliptical paths, with non-uniform velocities.

• Found a consistent description by abandoning both

2.Uniform motion.

Kepler’s Laws of Planetary Motion

1.The orbits of the planets are ellipses with the sun at one focus.

c

Eccentricity e = c/a

e = 0 perfect circle

e = 1 straight line

Guess: Which of these Ellipses describes best Earth’s Orbit around the Sun?

e = 0.02 e = 0.1 e = 0.2

e = 0.4 e = 0.6

1) 2) 3)

4) 5)

Eccentricities of planetary orbits

Orbits of planets are virtually indistinguishable from circles:

Earth: e = 0.0167Most extreme example:

Pluto: e = 0.248

2. A line from a planet to the sun sweeps over equal areas in equal intervals of time.

Fas

t Slow

Are all four seasons equally long?

1. Yes.2. No, summer is the longest; winter is the

shortest.3. No, fall is the longest; spring is the shortest.4. No, winter is the longest; summer is the

shortest.5. No, spring is the longest; fall is the shortest.

Why is the summer longer than winter?

1. Because of the precession of the Earth’s axis of rotation.

2. Because of the moon’s 5o inclination with respect to the Ecliptic.

3. Because the Earth is rotating around its axis more slowly in the summer (→ longer days!).

4. Because the Earth is closest to the sun in January and most distant from the sun in July.

5. Because the Earth is closest to the sun in July and most distant from the sun in January.

Autumnal Equinox (beg. of fall)

Winter solstice (beg. of winter)

Summer solstice (beg. of

summer)

Vernal equinox (beg. of spring)

January

July

Fall

Winter Spring

Summer

3.A planet’s orbital period (P) squared is proportional to its average distance from the sun (a) cubed:

Py2 = aAU

3

(Py = period in years; aAU = distance in AU)

Kepler’s Third Law

Orbital period P known → Calculate average distance to the sun, a:

aAU = Py

2/3

Average distance to the sun, a, known → Calculate orbital period P.

Py = aAU3/2

It takes 29.46 years for Saturn to orbit once around the sun. What is its average distance from the sun?

1. 9.54 AU

2. 19.64 AU

3. 29.46 AU

4. 44.31 AU

5. 160.55 AU

Think critically about Kepler’s Laws: Would you categorize his achievements

as physics or mathematics?

1. Mathematics

2. Physics

Isaac Newton (1643 - 1727)

Major achievements:

1. Invented Calculus as a necessary tool to solve mathematical problems related to motion

• Adding physics interpretations to the mathematical descriptions of astronomy by Copernicus, Galileo and Kepler

2. Discovered the three laws of motion

3. Discovered the universal law of mutual gravitation

Newton’s Laws of Motion (I)

1. A body continues at rest or in uniform motion in a straight line unless acted upon by some net force.

An astronaut floating in space will float forever in a straight line unless some external force is accelerating him/her.

Velocity and Acceleration

Acceleration (a) is the change of a body’s velocity (v) with time (t):

a = v/t

Velocity and acceleration are directed quantities (vectors)!

a

v

Which of the following involve(s) a (non-zero) acceleration?

1. Increasing the speed of an object.2. Braking.3. Uniform motion on a circular path.4. All of the above.5. None of the above

Velocity and Acceleration

Acceleration (a) is the change of a body’s velocity (v) with time (t):

1. Acceleration in the conventional sense (i.e. increasing speed)

a = v/t

Different cases of acceleration:

Velocity and acceleration are directed quantities (vectors)!

3. Change of the direction of motion (e.g., in circular motion)

2. Deceleration (i.e. decreasing speed)

a

v

A ball attached to a string is in a circular motion as shown. Which path

will the ball follow if the string breaks at the marked point?

1) 2)

3)

4)

5) Impossible to tell from the given

information.

Newton’s Laws of Motion (II)

2. The acceleration a of a body is

inversely proportional to its mass m, directly

proportional to the net force F, and in the same direction as the net force.

a = F/m F = m a

Newton’s Laws of Motion (III)

3. To every action, there is an equal and opposite reaction.

The same force that is accelerating the boy forward, is accelerating the skateboard backward.

The Universal Law of Gravity

• Any two bodies are attracting each other through gravitation, with a force proportional to the product of their masses and inversely proportional to the square of their distance:

F = - G Mm

r2

(G is the Universal constant of gravity.)

According to Newton’s universal law of gravity, the sun is attracting the Earth with a force of 3.6*1022 N. What is the

gravitational force that the Earth exerts on the sun?

1. 02. 1.75*1018 N3. 3.6*1022 N4. 1.95*1029 N.5. Depends on the relative speed of the

Earth with respect to the sun.

Einstein and Relativity

Einstein (1879 – 1955): Newton’s laws of motion are only correct in the limit of low velocities, much

less than the speed of light.

→ Theory of Special Relativity

Also, revised understanding of gravity

→ Theory of General Relativity (GR)

Two postulates leading to Special Relativity (I)

1. Observers can never detect their uniform motion, except relative to other objects.

This is equivalent to:

The laws of physics are the same for all observers, no matter what their motion, as

long as they are not accelerated.

A physicist on a train that moves at 50 mph throws a ball straight up in the air. Where will

the ball land? (Neglect air resistance.)

1. Far ahead of the train.

2. It will come back to the same point on the train.

3. It will stay behind.

4. It will never fall back down.

1. 2.3.

4.

Two postulates leading to Special Relativity (II)

2. The velocity of light, c, is constant and will be the same for all observers, independent of their motion relative to the light source.

Effects of Special Relativity• Time dilation: Fast moving objects

experience less time.

Effects of Special Relativity

• Length contraction: Fast moving objects appear shortened.

• Time dilation: Fast moving objects experience less time.

How would the Smiley appear to you if he/she moved straight towards you with

50 % of the speed of light?

1. His face would appear stretched vertically

2. His face would appear stretched horizontally

3. His face would appear bigger overall.

4. His face would appear smaller overall.

5. His face would appear at the same size and shape it would have if he were not moving.

Effects of Special Relativity

• Length contraction: Fast moving objects appear shortened.

• The energy of a body at rest is not 0. Instead, we find E0 = m c2

• Relativistic aberration: Distortion of angles

• Time dilation: Fast moving objects experience less time.

’

Effects of Special Relativity

• Length contraction: Fast moving objects appear shortened.

• The energy of a body at rest is not 0. Instead, we find

E0 = m c2

• Relativistic aberration: Distortion of angles

• Relativistic Doppler shift: Change of wavelength (color) of light.

• Time dilation: Fast moving objects experience less time.

General RelativityA new description of gravity

Postulate:

Equivalence Principle:

“Observers can not distinguish locally

between inertial forces due to acceleration and

uniform gravitational forces due to the

presence of massive bodies.”

A thought experiment:

Imagine a light source on board a rapidly accelerated space ship:

As seen by a “stationary” observer

As seen by an observer on board the space ship

Light source

Time Time

a aa

a

g

For the accelerated observer, the light ray appears to bend

downward!

Now, we can’t distinguish between this inertial effect and the effect of

gravitational forces

Thus, a gravitational force equivalent to the inertial force

must also be able to bend light!

→ New description of gravity as curvature of space-time!

This bending of light by the gravitation of massive bodies has indeed been observed:

During total solar eclipses:

The positions of stars apparently close to the sun are shifted away from the position

of the sun.

General Relativity Effects

Spatial distortion of light → gravitational lensing

What is the shape of the orbits of the planets around the sun?

1. Perfect circles

2. Ellipses with the sun in the center

3. Ellipses with the sun in one focus

4. Ellipses with the sun being a point on the ellipse.

5. Epicycles (circles whose centers revolve around a perfect circle around the sun)

The Orbits of Planets

Ellipses with the Sun in one focus

Perihelion Precession