astro exam 2 (Unit 5 Tycho Brahe, Unit 6 Johannes Kepler, Unit 7 Galileo)

Tycho Brahe (1546-1601)

although he never used telescopes, he is considered one of the greatest observational astronomers of all time; he made very accurate
observations of planetary motions, especially Mars, which enabled Kepler to develop his three laws of planetary motion

discovered a new star in the constellation of Cassiopeia

published a book called De Stella Nova

colorful life: lost nose is a duel, did not marry mother of his eight children, kept a pet elk

Tycho Brahe’s Observations

observed a comet in 1577 and also failed to find any parallax, implying it must be beyond the moon

excelled at building ingenious instruments that greatly improved the accuracy of naked eye astronomical observations

achieved an unprecedented precision of about one arc minute in his stellar and planetary positions

The Tychonic System

wanted to produce a definitive catalog of planetary positions that could be used to decide between the systems of Ptolemy and Copernicus

in this system, the planets orbit the sun, but the sun orbits the earth

his observations were so good that he could make none of these three systems work, in desperation he invited Johannes Kepler to join him

Kepler (1571-1630)

he showed that the Sun-centered (heliocentric) model of the Universe worked better if the planets were in elliptical orbits about the Sun instead of circular orbits and put forth his three laws of planetary motion

Kepler’s model of the Solar System

he published “Mysterious Cosmographicum”

the distances between the six planets could be represented by the 5 pythagorean solids, nested such that each planet is on the inner sphere of a polyhedron whose outer sphere contains the next planet

however, he could not make his model fit the observations of the time, so he sent his book to Tycho

Kepler and Tycho

worked together in Prague

their relationship was strained, but they needed each other

Kepler’s Three Laws of Planetary Motion

1. Planetary orbits are ellipses (not circles as the Greek demanded). this was a great revelation given the importance that the Greeks placed on the circle

2. a planet in its orbital plane sweeps out equal areas in equal amounts of time. this means that the closer a planet is to the sun, the faster it moves

3. the equation P²=D³ applies, where P is the period of a planet’s revolution around the sun in years and D is the planet’s distance from the sun in AU, with AU being the Earth-Sun distance

ellipse

the locus points such that the sum of the distances from two points to any point on the ellipse is fixed, d1 + d2 = constant

Kepler’s First Law

Planetary orbits are ellipses with the Sun at one focus

Kepler’s Second Law

A line joining a planet and the Sun sweeps out euqal areas during equal intervals of time

Kepler’s Third Law

the square of the period of an orbit is proportional to the cube of the semi-major axis

Do Kepler’s laws of planetary motion apply to all bodies moving in a gravitational field?

yes, planets, asteroids, spacecraft, etc.

reception of Kepler’s laws

his work was not immediately accepted

many important contemporaries ignored his work

he died a relative anonymity in 1630

Galileo (1564-1642)

he did important experiments which helped reveal the laws of falling bodies; he also made observations with a telescope (he put together the first refracting telescope used for astronomical observation) which supported the heliocentric theory

bears more responsibility for the birth of modern science than any other individual

tried for heresy by the Inquisition in 1633 due to his public defense of heliocentric

performed and recorded many experiments to support his theories

first to correctly define the law of inertia

law of inertia

‘An object at rest remains at rest. Left on its own, an object in motion will continue moving along a straight line with constant speed until an outside force acts to change its motion.’

crucial to understand why object do not experience any obvious effects from Earth’s motion

did Galileo invent the telescope?

no, but he built his own greatly improving the design

Galileo’s Discoveries: the moons of Jupiter

Viewed with the telescope, Jupiter appeared as a bright disk, with four small stars around it. The stars were not left behind as Jupiter moved across the sky, but appeared to orbit around it. This showed that there is no single center to the universe.

actually were the moons of Jupiter

Galileo’s Discoveries: the rings of Saturn

Viewed with the telescope, Saturn appeared to have ears that appeared and disappeared over time, implying that Saturn was imperfect not spherical and changed with time. Later, Christiaan Huygens figured out that Saturn has a ring.

Galileo’s Discoveries: the phases of Venus

Ptolemaic and Copernican systems made different predictions about th phases of the inner planets

Viewed with the telescope, Venus showed phases exactly as predicted in the Copernican system, falsifying the Ptolemaic system

Galileo’s Discoveries: Moon Craters

Viewed with the telescope, the surface of the Moon revealed mountains, valleys, and craters

This implied the Moon was also imperfect

Galileo’s Discoveries: Sunspots

Viewed with the telescope, the Sun showed dark spots that appeared, disappeared, and changed shape. Another imperfection in the heavens

Galileo discovered the sun rotates on an axis just like earth

Galileo’s Discoveries: Thousands of Stars

the telescope revealed thousands of stars that were too faint to see with the naked eye

he identified the diffuse emission known as the Milky Way as a large collection of countless faint stars

What did Galileo’s observations reveal?

a fascinating changing Universe full of nuance and detail, very far from the Aristotelian concept of immutable perfection

On what would Ptolemy and Copernicus likely have agreed?

All orbits and epicycles must be composed of perfect circles

In Copernicus's theory, retrograde planetary motion is explained as

a result of Earth's motion: as Earth passes another planet, that planet appears to move backward as seen against the background stars.

True or False? Ptolemy said that the stars rise and set because of the rotation of the Earth, while Copernicus said that the stars are fixed on rotating spheres.

False

True or False? To explain why we don’t see the parallax of stars, Copernicus claimed that stars are too far away, while Ptolemy maintained that the Earth doesn't move.

True

True of False? With regards to the phenomenon of retrograde motion, Ptolemy needed epicycles to explain it; in Copernicus’s model it is naturally a result of Earth overtaking an outer planet since the Earth travels faster. 

True

True or False? With regards to the phases of Venus, Ptolemy's model of the Universe shows that all phases of Venus should be visible, whereas Copernicus's model shows that only the crescent phase will be visible. 

False

True or False? The elongation of Mercury and Venus are explained in the Copernicus system because they orbit the Sun inside the orbit of the Earth. Ptolemy explained this phenomenon by tying their orbits to the Sun’s orbit around the Earth.

True

Tycho Brahe's main contribution to astronomy was that

he made highly accurate measurements of the positions of the planets

The semi-major axis of a dwarf planet in the Kuiper Belt is 80 AU. How long does it take to complete one orbit around the Sun?

715 yrs

Kepler's second law states that

the line joining a planet to the Sun sweeps out equal areas in equal intervals of time.

When does the Earth move the fastest in its orbit around the Sun?

when it is closest to the Sun in January

Suppose you are on the moon and you drop a rock and a feather at the same time. You will find that

the two fall at the same speed, but this speed is slower than a rock would fall on Earth.

A ball is moving at 20 m/s. If no forces act on it, then 5 seconds later the ball's speed will be

20 m/s

true or false? Galileo perfected the telescope that had been invented by Lippershey, and was the first to use it for astronomical observations.

true

Tycho "achieved an unprecedented precision of about 1 arcminute". What does this mean? 

Tycho's measurements of the position of a planet or star was wrong by no more than 1 arcminute.