Chapter 2

Suppose that instead of being inclined to Earth's orbit around the Sun, the Moon's orbit was in the same plane as Earth's orbit around the Sun. In this hypothetical situation, approximately how many solar eclipses would occur each year?

12

How many arcseconds are in a full circle?

1296000"

What is the Moon's angular size in arcseconds?

1800"

In reality, the Moon's orbit about Earth is tilted (by about 5°) with respect to Earth's orbit about the Sun. As a result, the actual number of solar eclipses that occur each year is approximately _____.

2

Which position in this diagram represents Earth on the day that we have the longest amount of daylight in the continental United States?

2

There are 360∘∘ in a full circle. How many arcminutes are in a full circle?

21600′′

Which position in this diagram represents Earth at the beginning of spring for the Southern Hemisphere?

3

The Moon's angular size is about 1/2 degrees. What is this in arcminutes?

30'

What do astronomers mean by a constellation?

A constellation is a region in the sky as seen from Earth.

Today, astronomers can detect and measure stellar parallax for thousands of the nearest stars, providing us with direct evidence that Earth really does orbit the Sun. Moreover, as the Parallax Angle animation shows (return to the main "Parallax" screen, and select the "Parallax and Distance" button), these measurements allow us to calculate distances to these relatively nearby stars. If we hope to use parallax to measure distances to even more-distant stars, which of the following telescopes would be most useful?

A telescope that orbits the Sun in the outer solar system

Which of the following celestial objects do not rise in the east and set in the west? (Assume that all of these objects are visible from your location on Earth, and that none of them are circumpolar.)

All of these objects rise in the east and set in the west.

Assume that all the shaded regions have exactly the same area. Rank the segments of the comet's orbit from left to right based on the length of time it takes the comet to move from Point 1 to Point 2, from longest to shortest.

Although Kepler wrote his laws specifically to describe the orbits of the planets around the Sun, they apply more generally. Kepler's second law tells us that as an object moves around its orbit, it sweeps out equal areas in equal times. Because all the areas shown here are equal, the time it takes the comet to travel each segment must also be the same.

Why does the local sky look like a dome?

Because we see half of celestial sphere at any time.

If you could change the layout of the solar system, which of the following would cause a lunar eclipse to occur at least once every month in this hypothetical situation?

Change the Moon's orbital plane so it is in the same plane as Earth's orbit around the Sun.

During the period each year when we see Mars undergoing apparent retrograde motion in our sky, what is really going on in space?

Earth is catching up with and passing by Mars in their respective orbits.

When we see Saturn going through a period of apparent retrograde motion, it means:

Earth is passing Saturn in its orbit, with both planets on the same side of the Sun.

Earth is closer to the Sun in January than in July. Therefore, in accord with Kepler's second law:

Earth travels faster in its orbit around the Sun in January than in July.

Each choice below describes how a few astronomical phenomena are related to time periods. Which list is entirely correct?

Earth's rotation defines a day. The cycle of the Moon's phases takes about a month. Earth's orbit defines a year. Earth's cycle of axis precession takes 26,000 years.

The dwarf planet Eris orbits the Sun every 557 years. What its average distance (semimajor axis) from the Sun?

Eris's semimajor axis = 67.7 a.u.

As you saw in Part C, stellar parallax exists only because Earth orbits the Sun. Therefore, if the ancient Greeks had measured stellar parallax, they would have known that their belief in an Earth-centered universe was wrong. Why didn't the ancient Greeks measure stellar parallax?

Even for the nearest stars, parallax angles are too small to measure with the naked eye.

Again, assume that all the shaded areas have exactly the same area. This time, rank the segments of the comet's orbit based on the speed with which the comet moves when traveling from Point 1 to Point 2, from fastest to slowest.

From Parts A and B, you know that the comet takes the same time to cover each of the four segments shown, but that it travels greater distances in the segments that are closer to the Sun. Therefore, its speed must also be faster when it is closer to the Sun. In other words, the fact that that the comet sweeps out equal areas in equal times implies that its orbital speed is faster when it is nearer to the Sun and slower when it is farther away.

What is a first quarter moon?

Half with the right side illuminated

If we have a new moon today, when we will have the next full moon?

In about 2 weeks

How does Earth's varying distance from the Sun affect our seasons?

It doesn't; Earth's orbital distance plays no significant role in the seasons.

What is stellar parallax?

It is the slight back-and-forth shifting of star positions that occurs as we view the stars from different positions in Earth's orbit of the Sun.

According to Kepler's third law,

Jupiter orbits the Sun at a faster speed than Saturn.

Consider again the diagrams from Parts D and E, which are repeated here. Again, imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. This time, rank the positions (A-D) from left to right based on how fast the asteroid is moving at each position, from fastest to slowest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Just as you found for the comet in Parts A through C, the asteroid must be traveling at a higher speed during parts of its orbit in which it is closer to the Sun than during parts of its orbit in which it is farther away. You should now see the essence of Kepler's second law: Although the precise mathematical statement tells us that an object sweeps out equal areas in equal times, the key meaning lies in the idea that an object's orbital speed is faster when nearer to the Sun and slower when farther away. This idea explains why, for example, Earth moves faster in its orbit when it is near perihelion (its closest point to the Sun) in January than it does near aphelion (its farthest point from the Sun) in July.

Imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. Rank the positions based on the area that would be swept out by a line drawn between the Sun and the asteroid during the one-week period, from largest to smallest.

Kepler's second law tells us that the asteroid will sweep out equal areas in equal time intervals. Therefore, the area swept out in any one week period must always be the same, regardless of the asteroid's location in its orbit around the Sun.

Again, assume that all the shaded areas have exactly the same area. This time, rank the segments of the comet's orbit from left to right based on the distance the comet travels when moving from Point 1 to Point 2, from longest to shortest. I

Kepler's second law tells us that the comet sweeps out equal areas in equal times. Because the area triangle is shorter and squatter for the segments nearer to the Sun, the distance must be greater for these segments in order for all the areas to be the same.

Suppose it is full moon. What phase of Earth would someone on the Moon see at this time?

New Earth

The following figures are the same as those from Part A. This time, imagine that each person places an identical glass of water outside. Consider only the effects of the season — meaning the amount of daylight and the height of the Sun's path through the sky — on the water temperature. Rank the figures based on the highest (warmest) temperature the glass of water would reach during a 24-hour period, from highest to lowest. To rank items as equivalent, overlap them.

Notice that the answer is the same here as it was for Part A. This is because (just as in Part A) the key factor is whether the person is in summer or winter. The water will heat up more on a summer day than on a winter day because there are more hours of daylight and because the Sun is higher in the sky.

Consider again the diagrams from Part D, which are repeated here. Again, imagine that you observed the asteroid as it traveled for one week, starting from each of the positions shown. This time, rank the positions from left to right based on the distance the asteroid will travel during a one-week period when passing through each location, from longest to shortest. If you think that two (or more) of the diagrams should be ranked as equal, drag one on top of the other(s) to show this equality.

Notice the similarity between what you have found here and what you found for the comet in Part B. Kepler's second law tells us any object will sweep out equal areas in equal times as it orbits the Sun, which means the area triangles are shorter and squatter when the object is nearer to the Sun, so that the object covers a greater distance during any particular time period when it is closer to the Sun than when it is farther away.

During the time that a planet is in its period of apparent retrograde motion:

Over many days or weeks, the planet moves westward relative to the stars, rather than the usual eastward relative to the stars

In winter, Earth's axis points toward the star Polaris. In spring, the axis points toward

Polaris

Choose the correct definition of precession, and the correct explanation how does it affect what we see in our sky.

Precession is the change of direction in which Earth's axis points. The celestial poles slowly move relative to the stars. In about 13000 years the star Vega will be the North star instead of Polaris.

If you are located in the Northern Hemisphere, which of the following correctly describes a relationship between the sky and your location?

The altitude of the north celestial pole equals your latitude.

Notice that the parallax is greater (the apparent movement is larger) for the person than for the trees, and that the mountains do not appear to shift at all. Why?

The amount of parallax depends on an object's distance, with greater parallax for nearer objects.

What is the celestial sphere?

The celestial sphere is a representation of how the entire sky looks as seen from Earth.

Which of the following statements about the celestial sphere is not true?

The celestial sphere is another name for our universe.

A total solar eclipse is when

The moon lies directly in the path between the sun and earth

Why is there not a solar eclipse at every new moon?

The orbital plane of the Moon is tilted slightly (by about 5 degrees) to the ecliptic plane.

What is the ecliptic?

The path the Sun appears to trace around the celestial sphere each year

Each of the following figures shows a person (not to scale) located on Earth at either 40°N or 40°S latitude. Rank the figures based on how much time the person spends in daylight during each 24-hour period, from most to least. To rank items as equivalent, overlap them.

The person's distance from the equator is the same in all cases (40° latitude either north or south), so the only thing that affects the amount of daylight is time of year, with longer days in summer and shorter days in winter. The three figures that have the long daylight hours show the person in summer, while the three figures with the short daylight hours show the person in winter.

What conditions must exist for a lunar eclipse to occur?

The phase of the Moon must be full and the Moon must be passing through Earth's orbital plane.

What conditions must exist for a solar eclipse to occur?

The phase of the Moon must be new and the Moon must be passing through Earth's orbital plane.

On the main screen of the interactive figure, select "Parallax", then select the "Introduction to Parallax" button. Click the play button to watch the animation, and watch how the motion of the photographer (lower window) affects what the camera sees (upper window). Which of the following statements correctly describes what is really happening? (Note: You need not continue with the next button to answer this question.)

The photographer is moving, but the person being photographed and the trees are staying still.

Beijing and Philadelphia have about the same latitude but different longitudes. What can be said about the tonight's night sky in these two places?

The sky will look about the same.

Which of the following best describes why we have seasons on Earth?

The tilt of Earth's axis causes different portions of the Earth to receive more or less direct sunlight at different times of year.

When I looked into the dark lanes of the Milky Way with my binoculars, I saw what must have been a cluster of distant galaxies. Which of the following explanation is CORRECT about this statement?

This statement does not make sense, because we cannot see through the band of light we call the Milky Way to external galaxies; the dark fissure is gas and dust blocking our view.

Although all the known stars rise in the east and set in the west, we might someday discover a star that will rise in the west and set in the east. Choose the correct explanation why does the statement above make sense (or is clearly true) or does not make sense (or is clearly false).

This statement does not make sense. The stars appear to rise and set because of Earth's rotation. So, during the day, all the stars must move in the same direction.

I live in the United States, and during my first trip to Argentina I saw many constellations that I'd never seen before.

This statement makes sense, because the constellations visible in the sky depend on latitude. Since Argentina is in the Southern Hemisphere, the constellations visible there include many that are not visible from the United States.

Based on what you have learned from your rankings in Parts A and B, why is it generally hotter in summer than in winter?

We have more hours of daylight in summer. The Sun is higher in the sky in summer.

Stellar parallax occurs in much the same way as parallax on Earth, with greater parallax for stars that are nearer. Return to the main "Parallax" screen, and from here select the "Stellar Parallax" button, and watch how the motion of the star changes in the "View from Earth" window. Which statement best summarizes why stellar parallax occurs?

We view nearby stars from different positions in Earth's orbit at different times of year.

Suppose you live in the United States and you see a crescent moon in your evening sky tonight. What will a friend in South America see tonight?

Your friend will also see a crescent moon.

About how many stars are visible to the naked eye on a clear, dark night away from city lights?

a couple thousand

We cannot see a new moon in our sky because _________.

a new moon is quite near the Sun in the sky

The dwarf planet Eris orbits the Sun every 557 years. How does its average distance compare to that of Pluto?

aEris/aPluto = 1.72

Stars that are visible in the local sky on any clear night of the year, at any time of the night, are called _________.

circumpolar

If a star's distance from Earth increased, its parallax shift would __________

decrease

Based on their inability to detect stellar parallax, the ancient Greeks concluded that _________.

either Earth is the center of the universe or stars are extremely far away

Lunar eclipses can occur only when the phase of the Moon is _________.

full

Horizon

is the boundary line dividing the ground and the sky.

Zenith

is the highest point in the sky, directly overhead.

Meridian

is the semicircle extending from the horizon at north through the zenith to the horizon at south.

We describe a location on Earth's surface by stating its _________.

latitude and longitude

Two stars that are in the same constellation

may actually be very far away from each other.

The fact that we always see the same face of the Moon tells us that the Moon

rotates with the same period that it orbits Earth.

This multiple exposure photograph shows the apparent retrograde motion of Mars. To make this picture, the photographer needed to combine individual photos of Mars taken over a period of:

several months

How can we describe the location of an object in the local sky?

specifying its altitude and azimuth

The Moon always shows nearly the same face to Earth because ________.

the Moon rotates once in the same amount of time that it takes the Moon to orbit Earth once

If there is going to be a total lunar eclipse tonight, then you know that:

the Moon's phase is full.

This diagram represents a simplified model of the celestial sphere. The unlabeled circle that is highlighted in purple represents:

the celestial equator

If our year were twice as long (that is, if Earth took twice as many days to complete each orbit around the Sun), but Earth's rotation period and axis tilt were unchanged, then _________.

the four seasons would each be twice as long as they are now

This diagram represents a person's local sky. What does the red semicircle represent?

the meridian

The point directly over your head is called _________.

the zenith

A week after full moon, the Moon's phase is:

third quarter.

When it is summer in Australia, the season in the United States is

winter