Astronomy Ch 2 - The Rise of Astronomy

Which of the following is a reason why Copernicus's theory was no better than Ptolemy's at predicting planetary positions.

Copernicus kept using circular orbits for the planets. - (Planetary orbits are actually shaped like ellipses)

Planets normally move from the west to the east with respect to the stars. Occasionally, they move east to west for a few weeks, which is called ___motion

retrograde

Simple geocentric models, such as the one by Eudoxus, explain the speed of a planet's movement across the sky but don't explain

retrograde

The path of Mars on the sky shown in the image is known as ___motion

retrograde

Half of the long dimension of an ellipse (a in the figure) is called the

semimajor axis

In a simple geocentric model, which celestial objects were thought to be closer to Earth than the Sun was?

the Moon, Mercury and Venus - (The faster an object moved, the closer it was thought to be to Earth)

If the angle between Alexandria, Earth's center, and Syene had been smaller than 7°, but the distance between the two cities was still 5,000 stadia, how would Eratosthenes's measurement have been different?

Earth's size would be bigger.

Which ancient Greek astronomer used shadows cast by the Sun to estimate the size of Earth?

Eratosthenes

True or false: Planets orbit the Sun on circular-shaped orbits.

False

True or false: The work of Islamic scholars had a big influence on the astronomical discoveries of the ancient Greek scientists.

False

True or false: An object with a large angular diameter will always have a large true diameter.

False - (angular diameter depends on both true diameter and distance. An object with a large angular diameter might be small but very close to the observer. For example, if you are wearing sunglasses, they might cover more than 100° of your view but are only a couple of inches wide.)

Aristarchus was a Greek astronomer who surmised that Earth orbited the Sun. Make the argument of Aristarchus's critics by matching steps with the scientific method.

Form a hypothesis - Earth moves around Sun Propose a test - An orbiting planet will see objects shift position depending on their distance (parallax) Collect new data - No parallax is observed Accept or deny the hypothesis -Earth must be stationary

Match the astronomers with their famous accomplishments.

Galileo - discovered the phases of Venus. Kepler - showed that planetary orbits are elliptical, not circular Copernicus - proposed a heliocentric model for the Solar System. Tycho Brahe - made the most accurate pretelescope measurements of planetary positions.

How did Galileo demonstrate that the sky was not perfect and unchanging, as people had believed it to be?

He observed sunspots, which look like blemishes and change their positions from day to day.

If the Moon were three times farther away from us than it now is, its angular size would be

three times smaller

Select all that correctly describe Ptolemy

He was an influential astronomer in the Roman Empire. He lived in the Egyptian city of Alexandria He wrote a book called Almagest that summarized ancient Greek knowledge of astronomy

Why did the Catholic Church put Galileo on trial?

His support of a heliocentric model was contrary to Church teachings.

If the Sun's true diameter were twice as large as it is now, it's angular size would be

twice as big

Eratosthenes's calculation made use of the fact that because the Sun is very far away from Earth, its rays of light are___as they arrive at Earth.

parallel

To calculate the size of Earth using the angles of shadows, Eratosthenes needed to know that rays of sunlight are___lines when they reach Earth and the___between Alexandria and Syene.

parallel distance

The orbital _____ of a planet is how long it takes to complete on orbit around

period

The orbital___of a planet is how long it takes to complete one orbit around the Sun.

period

In Ptolemy's model, Venus does not go through a complete set of phases (which it does in reality). Which other planet does not go through all the phases in Ptolemy's model but does in Copernicus's model?

Mercury

Which planet was discovered because of the effect its gravity had on the orbit of another planet?

Neptune - (Neptune's gravity caused Uranus to move in an unexpected manner)

The idea that scientific models must be as simple as possible and still explain what is known about a phenomenon is called

Ockham's razor

Select all the apparent planetary motions that are not a result of Earth's rotation.

Planets always stay very close to the ecliptic. Planets occasionally move backwards across the sky. Planets move west to east with respect to the stars.

Select Kepler's three laws of planetary motion from the following list.

Planets move faster in their orbits when close to the Sun and slower when far from it. Planets move in elliptical orbits with the Sun at one focus. p2 = a3

Match each model of the Solar System with its description.

Ptolemy's model - The Sun, Moon, planets, and stars all move around Earth on small circles (epicycles) attached to larger ones (orbits). Tycho's model - The Sun moves around Earth and other planets move around the Sun. Copernicus's model - Earth and all the other planets move around the Sun.

Select all the statements about Ockham's razor that are correct.

Scientific models should be as simple as possible in order to explain all the phenomena. It's okay to make a model more complex as long as it predicts results better than a simpler model could.

Select all the following situations that are similar to Copernicus's explanation for retrograde motion.

A runner on an inner track lapping a slower runner on an outer track. A fire truck overtaking and passing other vehicles on the road.

Using the equation from Kepler's third law, calculate the period of a planet's orbit (p) if its average distance from the Sun (a) is 16 A.U.

64 years

Arrange the steps of Eratosthenes's calculation of the size of Earth.

1. On the summer solstice, obtain the angle of a shadow cast at noon in Alexandria as 7 degrees. 2. Sun's rays arrive at Earth as parallel lines. Use the measurement to show the angular separation on Earth's surface of Alexandria and Syene as 7 degrees. There is no shadow cast in Syene. 3. Substitute values 4. Solve the equation to calculate the circumference of Earth

Place the celestial bodies in their order of increasing distance from Earth in the geocentric model of the Solar System.

1. The Moon 2. Mercury 3. Venus 4. The Sun 5. Mars 6. Jupiter, then Saturn

Although he did not believe in the heliocentric model (he proposed his own hybrid model), arrange the statements to summarize how Tycho Brahe contributed to the eventual understanding of the Solar System as heliocentric.

1. Tycho had an intense passion for studying astronomy 2. Tycho designed & built the most accurate observational tools up to that date 3. Tycho made the most precise measurements of planetary positions 4. Tycho's meticulous observations were used to show the true shape of planetary orbits 5. With the right orbital shape the heliocentric model accurately predicts planetary motions

Put the following discoveries in chronological order, starting with the work of Copernicus (at the top), followed by Tycho Brahe, Galileo, and Newton (at the bottom).

1. earth is the center of the solar system 2. exploding stars are not part of the solar system 3. jupiter has its own moons 4. the law of gravity

If a planet orbited the Sun at a distance of 4 AU, what would its orbital period be? Arrange the steps in order from start (top) to finish (bottom) to get the answer.

1. p squared = a to third power 2. p squared = 4 to the 3rd power 3. p squared = 64 4. square root of p squared = square root of 645. p = 8 years

Select all the evidence-based reasons the ancient Greeks had for thinking that Earth is round.

A traveler who moves south will see different stars than one who stays up north. The shadow of Earth on the Moon is round.

Match the ancient Greek astronomers with their famous work

Aristarchus - estimated the size and distance of the Sun and Moon. Aristotle - argued that Earth was spherical in shape. Eratosthenes - calculated the size of Earth

The ancient Greek astronomer___argued Earth was shaped like a sphere based on observations of lunar eclipses?

Aristotle

Which ancient Greek scientist was the first to use scientific observations to argue that Earth is round?

Aristotle - (Aristotle argued that Earth was round because its shadow on the Moon during a lunar eclipse is round.)

___is an ancient belief system that holds that the positions and patterns of celestial objects influence events on Earth. ___is a system of knowledge that attempts to explain the nature of celestial objects using the scientific method.

Astrology Astronomy

Match the scientific and technical advances with the discoveries they helped make.

Bigger telescopes - Nature of nebulae Study of heat - Power source of stars Photography - Permanent records of observations

How could you estimate the distance to the Sun like Aristarchus did?

By measuring the angles of a right triangle formed by the Sun, Earth, and the Moon.

Angular size

Can be measured in degrees Is a measure of how big an object looks - (Objects can appear big either because they really are big or because they are very close)

Renaissance scientists considered Copernicus's model more powerful than Ptolemy's because it

Could be used to estimate the relative sizes of the orbits of planets Required fewer special conditions, such as the alignment of Venus's and Mercury's spheres in Ptolemy's model

Which of the following is Ptolemy known for today?

Creating a detailed geocentric model of the Solar System

Match each piece of evidence for a spherical Earth on the left with the the way it was observed on the right.

Earth's Shadow is curved - Watch a lunar eclipse. Visible stars are different at different latitudes - Travelers move south on Earth's surface Tops of tall buildings remain visible even at great distances - Move away from a city

The apparent diameter or length an object extends across on the sky is called its___size

angular

Under what circumstance would a planet not always appear close to the ecliptic?

If its orbit did not lie in the same plane as those of the other planets.

Select all the answers that correctly explain why photography was such an important discovery for astronomers.

It allowed astronomers to see fainter objects than was possible before. It allowed astronomers to make permanent records of their observations.

Select all that correctly describe the Moon illusion.

It makes the Moon seem larger closer to the horizon. It's an optical illusion.

Select all the following statements that correctly describe Kepler's third law.

It tells us the relationship between a planet's orbital period and its semimajor axis. It is possible to calculate a planet's distance from the Sun if you know its orbital period.

In a solar system very similar to ours, an Earth-like planet orbits a star just like the Sun. This planet has an orbital period two-thirds that of Earth's. How will its average distance from the star be different?

It will orbit closer to its star than we do from the Sun. - (Yes, according to Kepler's third law, a planet with a shorter period will be closer.)

To calculate the true diameter of a planet, what information do you need?

Its angular diameter Its distance

Select all of the following that were important astronomical contributions made by Tycho Brahe.

Making very accurate measurements of planet positions Discovering that comets are in space, not in Earth's atmosphere Observing a supernova and showing it had a fixed position, so it was far beyond the planets

How does the heliocentric model of Copernicus explain the retrograde motion of Mars?

Mars takes longer to complete its orbit than Earth, so when we pass it, it falls behind us and appears to move backwards. - (In Copernicus's model, only one circular orbit is needed for each planet)

The figures are not to scale. If they were, then the Sun would be 400 times as far from Earth as the Moon. In this case in the right figure, the half-lit Moon and Sun would appear

Separated by almost 90° on the sky (Aristarchus argued that the Sun was much farther away than the Moon based on this argument.)

Select all the reasons that explain how Galileo's discovery of sunspots showed that the sky was not perfect and unchanging?

Sunspots look like blemishes, and the Sun was thought to be perfect. Sunspots change position from day to day, and even disappear.

Select all of the following objects that have an angular size of 1/2 degrees

The Moon (Although the Moon is much smaller than the Sun, it is the same angular size because it is also much closer than the Sun.) The Sun

Select all of the objects for which Aristarchus estimated the distance.

The Moon - (he calculated the Moon's distance as 70 times Earth's radius (it's closer to 60) The Sun - (he calculated the Sun's distance as 20 times the Moon's distance (it's closer to 400 times, but it's a very difficult measurement)

Match Galileo's discoveries with the reasons they support Copernicus's model of the Solar System.

The Moon has mountains - Objects in space were real and made of materials like Earth; they were not ethereal substances with exotic properties Jupiter has moons - Earth is not the center of the Solar System (or the Universe). Venus has phases like the Moon - Planets orbit the Sun, not the Earth

Select all of the objects for which Aristarchus estimated the size, relative to Earth.

The Sun (he estimated that the Sun was seven times wider than Earth much too small, but it was a hard measurement) The Moon (he estimated the Moon to be one-third Earth's size it is actually a little smaller).

Select the properties of Eudoxus (an ancient Greek) geocentric model of the solar system.

The Sun and Moon move around Earth. The planets move around Earth. Objects closest to Earth move fastest.

Select all the statements that correctly describe Galileo's important astronomical discoveries.

The Sun has sunspots. Jupiter has moons. Venus goes through phases like the Moon.

According to Aristarchus, if the Sun were just a few times farther from Earth than the Moon is, how would the Sun and the Moon look relative to each other at the time of third quarter?

The angle between them would be much less than 90°.

How would the angle between Alexandria, Earth's center, and Syene change if the distance between them were 1000 stadia instead of 5000 stadia?

The angle would be smaller.

Why do the planets always remain close to the ecliptic?

The planets all go around the Sun with orbits roughly all in the same plane.

Eratosthenes's calculation of the size of Earth required that the Sun be very far away from us because

The rays of sunlight only arrive at Earth in parallel lines if the Sun is far away from us - (Parallel rays of light make it possible to calculate the angle between Alexandria, Earth's center, and Syene)

The ancient Greek astronomer Aristarchus measured the angle, α, of the right triangle shown in the image to determine

The relative distances of the Sun and Moon. Using trigonometry, he estimated the Sun to be 20 times farther away from Earth than the Moon (it's really closer to 400, but it's a very difficult measurement to make, even today).

Copernicus found that a heliocentric model did a better job than a geocentric model in explaining

The retrograde motion of the planets The hundreds of years of new planetary observations since Ptolemy

In Ptolemy's model of the Solar System, what would be different about a planet with a large epicycle versus one with a small epicycle?

The size of the "zig-zag" during retrograde motion would be bigger and last longer for a larger epicycle.

Under what circumstances would you measure a large parallax for a star?

The star is very close to Earth. - (Smaller distances cause larger parallaxes.)

Select all of the following that are parts of Ptolemy's geocentric model.

The stars are farther away than the planets. Planets move on small circles called epicycles. The planets, the Sun, and the Moon move around Earth.

The Moon illusion is caused by

The way your brain subconsciously compares the size of the Moon to objects on the horizon

The ancient Greeks knew about parallax, so why did Aristarchus's critics think Earth was stationary?

They didn't realize that stars could be very, very far away. - (They didn't understand that stars could be so far away, making their parallax undetectable.) They observed no parallax motion of the stars.

Which of the following contributions to astronomy came from Islamic scholars?

They gave (Arabic) names, still used today, to many stars. They preserved and added to ancient Greek astronomical knowledge. They introduced the use of algebra.

Select all below that are contributions made by the ancient astronomers of East Asia.

They were the first astronomers to observe sunspots. They kept detailed records of exploding stars. They predicted the dates of eclipses.

True or false: Ancient Chinese astronomers discovered sunspots.

True - (Chinese astronomers observed them much earlier than did Galileo, who was the first person to observe them with a telescope)

True or false: Planets typically move from west to east against the backdrop of the stars.

True - (as planets move along their orbits, they slowly move west to east past the background of distant stars. This doesn't mean they rise in the west. The stars, planets, and the whole celestial sphere rise in the east and set in the west daily because of Earth's rotation.)

There were numerous models of the solar system. ___remained unconvinced of the validity of the ___ model because he could not detect any stellar parallax.

Tycho Copernican

Ptolemy's model uses epicycles to explain

a planet's retrograde motion

Copernicus's model could not predict planetary positions much more accurately than Ptolemy's model because Copernicus used ___orbits in his model, something Kepler later corrected.

circular

A small circular motion carried along a planet's larger circular orbit around Earth was called an ___in Ptolemy's model.

epicycle

The parallax of a star would be smaller if the star were

farther from Earth

According to Kepler's second law, planets move _____ in their orbits when closer to the Sun and ____ when they are farther away

faster slower

An ellipse

has both long and short axes has two foci

A___model places the Sun at the center of the Solar System, with the planets orbiting around it.

heliocentric

Copernicus's model is considered simpler than Ptolemy's because

it can explain retrograde motion with just one circular orbit for each planet - (remember Ptolemy's model had a large circular orbit and numerous smaller epicycles for each planet.)

If a comet orbits the Sun on a highly elongated elliptical orbit, then

it will spend most of its time far away from the Sun

Select all the answers that correctly finish the sentence: According to the angular size formula, an object will have a large angular size if it is

large and close small and very close

Select all the answers that correctly finish the sentence: According to the angular size formula, an object will have a small angular size if it is

large and very, very far away small and far away

True diameter is

measured in units of length different than angular diameter but related to it

The planet___was discovered because its___force caused irregularities in the orbit of the planet___

neptune gravitational uranus

Select the objects that complete the sentence: For a planetary orbit, ___ is found at one focus of the ellipse and ____ is found at the other focus.

nothing the Sun