Astronomy Midterm 1

What is meant by "reflecting" and "refracting" telescopes?

A reflecting telescope uses a mirror as the primary light collector, reflecting light into the spectrometer and detector. A refractor uses lenses to focus light.

What are the three basic components of a modern astronomical instrument? Describe each in one to two sentences.

A visible-light/infrared telescope is made from either a mirror or a lens that collects the light from an astronomical source. A spectrometer or other wavelength-sorting device separates the light into wavelengths. A detector is an instrument that is sensitive to certain wavelengths of light and makes a permanent record of the light that comes into the telescope and through the spectrometer.

What is a wave? Use the terms wavelength and frequency in your definition.

A wave is a repeating disturbance that travels outward, like ripples moving through water. The distance between crests (or troughs) of the wave is the wavelength, and the number of crests that move past a given location each second (or other unit of time) corresponds to the frequency of the wave.

Explain why astronomers use the term "blueshifted" for objects moving toward us and "redshifted" for objects moving away from us.

Objects moving toward us appear to have their light shifted to a shorter wavelength. In the visible spectrum, the short wavelength end of the spectrum is blue (or violet), so we use "blueshifted" as shorthand for "shifted to a shorter wavelength." The color red is at the longest wavelength end of the visible spectrum, so objects moving away from us that have their light shifted to longer wavelengths are similarly called "redshifted."

Why did Pythagoras believe that Earth should be spherical?

He believed circles and spheres were perfect forms and that Earth should, naturally, take one of these shapes.

Suppose you lived in the crater Copernicus on the side of the Moon facing Earth. A. How often would the Sun rise? B. How often would Earth set? C. During what fraction of the time would you be able to see the stars?

A. The Sun would rise once every solar month, or 29.5 days; B. Earth's position would remain roughly fixed in the sky, so it would never rise or set; C. You would be able to see stars all the time if you looked in a direction away from the Sun, since there is no air and hence no "blue sky" on the Moon.

If the Moon rises at a given location at 6:00 p.m. today, about what time will it rise tomorrow night?

About 6:50 p.m.; the Moon rises about 50 minutes later each day.

Discuss how latitude and longitude on Earth are similar to declination and right ascension in the sky.

Latitude and longitude make up a coordinate system that enables a person to uniquely specify a given place on a map of the spherical surface of Earth. Right ascension and declination serve a similar purpose to specify a given place on the celestial sphere. Both latitude and declination start measuring from an equator, Earth's equator in the former case and the celestial equator in the latter case. Both longitude and right ascension are measured from an arbitrarily chosen great circle that intersects the equator in their system.

Explain the origin of the leap year. Why is it necessary?

Since the solar year is 365.25 days, if we allow for only 365 days in a year, our calendar will be off by one full day after four years have passed. So every four years we add an additional day to take off the four 0.25 days. If we use the calendar to keep track of seasons for the purposing of planting crops, this could lead to big problems over time, so the leap year was introduced so that certain dates on the calendar would always correspond with the same seasons.

Explain how tidal forces are causing the Moon to slowly recede from Earth.

The Earth-Moon system must conserve total angular momentum, so as Earth loses angular momentum due to its rotation slowing, the Moon increases its angular momentum by drifting slightly farther away from Earth.

Show that the Gregorian calendar will be in error by 1 day in about 3300 years.

The Gregorian year averages 365.242500 days in length. The tropical year is 365.242199 days. The Gregorian year is thus too long by 0.000301 day/year. This error accumulates to a full day in 1/0.000301 = 3300 years.

Describe one visible-light or infrared telescope that astronomers are planning to launch into space in the future.

The James Webb Space Telescope will be have a mirror 6 m in diameter made up of 36 small hexagons. The telescope should have the sensitivity needed to detect the very first generation of stars, formed when the universe was only a few hundred million years old.

What distinguishes one type of electromagnetic radiation from another? What are the main categories (or bands) of the electromagnetic spectrum?

The different bands of the spectrum each have a characteristic wavelength or frequency range. In order from lowest to highest frequency, the main bands are: radio, microwave, infrared, visible, ultraviolet, X-ray, and gamma ray.

Look at the image of Cygnus A (Figure 6.18 Radio Image) and read its caption again. The material in the giant lobes at the edges of the image had to have been ejected from the center at least how many years ago?

The jets are 160,000 light-years long, meaning that even if the material moved at the speed of light (impossible, but this assumption gives us a lower limit), the material would have taken 160,000 years to go from the center to the lobes. Therefore, that material was ejected at least 160,000 years ago.

What are the two ways that the tilt of Earth's axis causes the summers in the United States to be warmer than the winters?

The tilt during northern summer results in more direct sunlight for land in the Northern Hemisphere, so more solar energy per square meter reaches us, making Earth's surface warmer. Also, the amount of daylight is longer for Northern Hemisphere sites during summer months, allowing the Sun to illuminate this part of Earth for a longer time, resulting in further warmth.

Explain the results of Rutherford's gold foil experiment and how they changed our model of the atom.

When Rutherford fired a stream of alpha particles at a thin sheet of gold foil, most of them passed through completely unaffected, as if going through space empty of any charge or mass. But a small number of alpha particles rebounded almost directly backward. The results suggested that the positive charge of the atom is not spread out over a large area, as had been thought previously, but instead is concentrated in an extremely small nucleus.

What is the momentum of an object whose velocity is zero? How does Newton's first law of motion include the case of an object at rest?

Zero. Momentum is mass × velocity. If velocity is zero, so is momentum.

Why was Brahe reluctant to provide Kepler with all his data at one time?

Brahe didn't want Kepler to discover the general rules of how the planets moved, thereby robbing Brahe of the glory.

What is the phase of the Moon during a total solar eclipse? During a total lunar eclipse?

During a solar eclipse, the Moon is new. During a lunar eclipse, the Moon is full.

What are two lines of evidence you could use to indicate that the phases of the Moon are not caused by the shadow of Earth falling on the Moon?

First, during waxing crescent phase, the Moon is visible just above the western horizon, not far from the location where the Sun has set. Meanwhile, Earth's shadow is in the opposite direction from the Sun, toward the East, nowhere near the Moon. Second, if you examine the shape of the shadow during the Moon's gibbous phase, it is a crescent, which is not a shadow that can be cast by a spherical object such as Earth.

Explain three lines of evidence that indicate that the seasons in North America are not caused by the changing Earth-Sun distance as a result of Earth's elliptical orbit around the Sun.

First, the orbit of Earth is elliptical by only a few percent, not enough of a distance difference to cause a significant difference in temperature as we experience due to seasonal shifts. Second, our closest approach to the Sun occurs in January, one of the coldest months in the Northern Hemisphere. Third, the Northern and Southern Hemispheres experience opposite seasons simultaneously (in June, it is summer in the north and winter in the south), which is not possible if changing distance to the Sun is the cause. If it were, both hemispheres would experience the same seasons at the same time.

If the major axis of an ellipse is 16 cm, what is the semimajor axis? If the eccentricity is 0.8, would this ellipse be best described as mostly circular or very elongated?

The semimajor axis is 1/2 the major axis, so 8 cm. An ellipse with an eccentricity of 0.8 would be best described as very elongated.

What is the origin of the terms "a.m." and "p.m." in our timekeeping?

These terms refer to the Sun's crossing of the meridian, a line in the sky that extends from the southernmost point on the horizon, through the zenith, to the northernmost point on the horizon. The Sun crosses the meridian at "local noon," which is approximately noon on our clocks (not counting daylight saving time), so prior to that time, the Sun hasn't crossed the meridian. We refer to that as "ante meridiem" (ante means "before"), and we call the time after the Sun crosses the meridian "post meridiem" (post means "after").

One year in the future, when money is no object, you enjoy your birthday so much that you want to have another one right away. You get into your supersonic jet. Where should you and the people celebrating with you travel? From what direction should you approach? Explain.

When you cross the international date line from west to east, the date drops back by one day. Thus, you could party in Tokyo on your birthday, then fly quickly to San Francisco and do it all over again (except, alas, there is no supersonic service from Tokyo to San Francisco).

List the largest-aperture single telescope currently in use in each of the following bands of the electromagnetic spectrum: radio, X-ray, gamma ray.

Radio, Arecibo telescope; X-ray, Chandra X-Ray Observatory; gamma-ray, Fermi Gamma-ray Space Telescope.

Why do we say that Neptune was the first planet to be discovered through the use of mathematics?

Careful observations of Uranus showed that the planet was not exactly where Newton's laws predicted it to be in the night sky from day to day. Using mathematics, Kepler's laws, and Newton's laws, mathematicians were able to calculate that the gravitational influence of a planet outside the orbit of Uranus could account for Uranus' observed orbital discrepancies and predict where this planet should be located. Johann Galle discovered the planet Neptune in just that location.

Explain why more stars are circumpolar for observers at higher latitudes.

Circumpolar stars tend to be higher declination stars that move in very small circles in the sky centered on the celestial poles. At higher latitudes, when the celestial pole is higher in the sky, these small circular paths are more likely to be completely above the horizon. As latitude increases and the altitude of the pole above the horizon increases, so does the size of the circular motion for stars that will remain above the horizon, and so more stars are circumpolar from higher latitudes.

Explain what dispersion is and how astronomers use this phenomenon to study a star's light.

Dispersion is the splitting of light into its component wavelengths. By splitting the star's light, and producing a spectrum, we can determine what spectral lines are present in the star's spectrum. Absorption lines in the spectrum tell us what elements the star is made of. We can also measure the amount of light emitted at each wavelength, determining the star's temperature from where the maximum number of photons are emitted (Wien's law).

On the day of the vernal equinox, the day length for all places on Earth is actually slightly longer than 12 hours. Explain why.

Due to atmospheric refraction, the Sun remains visible for a short time even though from a geometric point of view, it is technically below the horizon, so sunrise occurs a few minutes earlier than it otherwise would, and sunset a few minutes later, extending the day length.

Describe what an observer at the crater Copernicus would see while the Moon is eclipsed on Earth. What would the same observer see during what would be a total solar eclipse as viewed from Earth?

During a lunar eclipse, the observer would see Earth pass across and fully cover the disk of the Sun. During the time of a solar eclipse (as seen from Earth), the observer on the Moon would see the Moon's shadow pass over Earth. In the penumbral region, the ground would slightly darken. The umbra of the Moon would look like a small, dark spot and would pass across the face of Earth.

What is a charge-coupled device (CCD), and how is it used in astronomy?

A CCD is a modern detector. Photons of radiation that hit a CCD's surface release a stream of charged particles (electrons) that are then counted at the end of the exposure. The number of electrons released is proportional to the amount of light hitting each pixel of the CCD. They are used in astronomy as reliable and sensitive light detectors.

What is a constellation as astronomers define it today? What does it mean when an astronomer says, "I saw a comet in Orion last night?"

A constellation is a well-defined area of the sky with borders, much like states have borders on a map of the United States. Seeing a comet in Orion means the comet was seen in the sky within the defined borders of the constellation Orion.

When astronomers discuss the apertures of their telescopes, they say bigger is better. Explain why.

A larger aperture collects more light because there's a larger area onto which the light falls. Therefore, a larger aperture can detect fainter sources than a smaller one. Also, the diameter of the aperture is inversely proportional to the resolution; a larger aperture makes images with a higher resolution (finer detail) than a smaller one.

What are advantages and disadvantages of apparent solar time? How is the situation improved by introducing mean solar time and standard time?

Apparent solar time tells you precisely where the Sun is in the sky for your specific location, but the precise time changes continuously as your longitude changes. It would be difficult to track these changes in real time and plan ahead for real-life events, such as classes, meetings, and dates. Mean solar time allows everyone within a given band of longitude to agree on the same time standard so that events can be scheduled more easily for everyone.

Explain how we use spectral absorption and emission lines to determine the composition of a gas.

As light passes through a gas, each specific element (or type of molecule) in a gas will leave a unique pattern of absorption lines. Likewise, if a gas is heated, each specific element will emit a unique pattern of emission lines. We know which patterns go with which elements (or molecules) and so we can use these "spectral fingerprints" to deduce the composition of the gas.

Explain how a rocket can propel itself using Newton's third law.

As the rocket pushes exhaust gases backward from the rear, the exhaust gases equally push the rocket forward.

What kind of visible-light and infrared telescopes on the ground are astronomers planning for the future? Why are they building them on the ground and not in space?

Astronomers are planning much bigger visible-light and infrared telescopes for the future, with primary mirrors around 30 m in diameter, to improve on the 10-m telescopes available today. Such large primary mirrors are too costly to try to put in space, so they are being built on the ground.

Explain why astronomers long ago believed that space must be filled with some kind of substance (the "aether") instead of the vacuum we know it is today.

Astronomers thought that light, like other waves, needed some medium through which to propagate (like sound moves through air, water, or solids), and since we get light from distant planets and stars, they thought space must therefore be filled with a substance like the aether to be a medium for traveling light waves. We now know light does not require a medium to propagate.

Why do the heights of the tides change over the course of a month?

Both the Sun and Moon affect Earth's tides, though the Sun's effect is less than half that of the Moon. When the Moon and Sun are lined up, during either full or new moon, the tidal effects augment one another, resulting in higher tide amplitudes than normal. During quarter phases, the Sun's and Moon's effects partially cancel, resulting in below-average tide amplitudes.

Why is the warmest day of the year in the United States (or in the Northern Hemisphere temperate zone) usually in August rather than on the day of the summer solstice, in late June?

Earth has some thermal inertia. It takes some time for Earth's temperature to rise in response to the increased energy it receives from the Sun, in the same way the hottest part of the day is usually much later than the maximum solar energy received at noon.

Why are lunar eclipses more common than solar eclipses?

Earth's shadow is much larger than the Moon's shadow on Earth, so it is far more likely for the Moon to intersect Earth's shadow than for any given location on Earth to intersect the Moon's shadow.

Name the two spectral windows through which electromagnetic radiation easily reaches the surface of Earth and describe the largest-aperture telescope currently in use for each window.

Electromagnetic radiation from the visible/IR band and the radio band penetrates Earth's atmosphere. The Gran Telescopio Canarias, with its 10.4-m primary mirror, is the largest single visible light or infrared telescope, and the Arecibo telescope is the largest single-dish radio telescope.

Explain how electrons use light energy to move among energy levels within an atom.

Electrons in stable orbits are only allowed to have specific energies within an atom. They can absorb or emit photons that have energies corresponding to differences between these specific energy levels of electrons within the atom. If an electron absorbs a photon, it can move up to a higher energy level. If the electron emits a photon, it can move down to a lower energy level.

Where in an atom would you expect to find electrons? Protons? Neutrons?

Electrons would be found in an orbit around the nucleus, surrounding it. Protons and neutrons are found within the nucleus.

Explain how emission lines and absorption lines are formed. In what sorts of cosmic objects would you expect to see each?

Emission lines are formed when an atom's electron moves from a higher to a lower energy level, and that atom then emits a photon with a particular wavelength that corresponds to the energy difference between the two levels. You can see this in a low density gas cloud heated by light from a nearby star. Absorption lines are caused when light passes through a cloud and some photons with energies corresponding to differences in energy levels in a given element are "consumed" by atoms to push their electrons to higher energy states. This can occur when observing a continuous light source through a gas cloud or a planetary atmosphere that intercepts some of the photons that pass through it.

The Great Pyramid of Giza was constructed nearly 5000 years ago. Within the pyramid, archaeologists discovered a shaft leading from the central chamber out of the pyramid, oriented for favorable viewing of the bright star Thuban. Thinking about Earth's precession, explain why Thuban might have been an important star to the ancient Egyptians.

Five thousand years ago, Thuban occupied a position in the sky very close to the north celestial pole, so for the ancient Egyptians, it served a purpose similar to the one Polaris serves for us.

What is the semimajor axis of a circle of diameter 24 cm? What is its eccentricity?

For a circle, the semimajor axis is the radius, so 12 cm. For a circle, the eccentricity is zero.

Regions north of the Arctic Circle are known as the "land of the midnight Sun." Explain what this means from an astronomical perspective.

For latitudes north of the Arctic Circle, there are some days during the year, around the time of the summer solstice, when the day length is a full 24 hours, so the Sun can be above the horizon at midnight at some times.

Explain what Joseph Fraunhofer discovered about stellar spectra.

Fraunhofer discovered that the dark lines in stellar spectra were absorption line patterns that were unique to different atoms or molecules in the gas through which the light passes.

Which is more dangerous to living things, gamma rays or X-rays? Explain.

Gamma rays are more energetic since they have a shorter wavelength (higher frequency), so they can potentially do more damage to biological organisms; however, this does not imply that X-rays are necessarily "safe"—they must still be used sparingly and cautiously.

Compare the density, weight, mass, and volume of a pound of gold to a pound of iron on the surface of Earth.

Gold is denser than iron, both have the same weight (a pound each), both have the same mass, but iron has a greater volume than gold.

In countries at far northern latitudes, the winter months tend to be so cloudy that astronomical observations are nearly impossible. Why can't good observations of the stars be made at those places during the summer months?

Good observations are difficult to obtain due to the short night. Even while the Sun is below the horizon, the time during which it is more than about 18° below the horizon is extremely short, making observations of faint objects difficult due to the twilight sky.

Suppose astronomers find an earthlike planet that is twice the size of Earth (that is, its radius is twice that of Earth's). What must be the mass of this planet such that the gravitational force (Fgravity) at the surface would be identical to Earth's?

Gravitational force at the surface is inversely proportional to the square of the radius of the planet and directly proportional to the mass of the planet; therefore, the planet must have a mass of 22 or 4 times that of Earth.

What fraction of the Moon's visible face is illuminated during first quarter phase? Why is this phase called first quarter?

Half of the visible face of the Moon is illuminated, not a quarter of it. The phase is called first quarter because the Moon at this time has completed the first quarter of its phase cycle (solar month).

How did Hipparchus discover the wobble of Earth's axis, known as precession?

He compared his careful observations of the stars with those of earlier observers and noticed that the positions of the fixed stars had changed slightly and systematically over the course of about 150 years, consistent with the direction of the celestial pole changing relative to the stars.

What did Galileo discover about the planet Jupiter that cast doubt on exclusive geocentrism?

He discovered four visible moons orbiting Jupiter, meaning that Earth clearly is not the central focus of all motion in the universe. He showed the moons can orbit Jupiter while Jupiter moves around the Sun, so it is possible that our Moon can orbit Earth as Earth revolves around the Sun.

What did Galileo discover about Venus that cast doubt on geocentrism?

He discovered that Venus shows a full range of phases, from new to crescent to gibbous, and these phases are only possible if Venus orbits so that sometimes it is on the near side of the Sun with respect to us and sometimes on the far side of the Sun (where he presumed it went to full phase, although he could not see it). Thus, Venus must orbit the Sun and not Earth.

Why did Ptolemy have to introduce multiple circles of motion for the planets instead of a single, simple circle to represent the planet's motion around the Sun?

He had to account for the observed occasional retrograde motion of the planets.

How did Aristotle deduce that the Sun is farther away from Earth than the Moon?

He noticed during solar eclipses that the Moon passes in front of the Sun, and the opposite case never happens.

What are two ways in which Aristotle deduced that Earth is spherical?

He noticed that the shadow Earth casts on the Moon during a lunar eclipse is always circular, which is only possible if a spherical body casts the shadow. He also noted that as travelers go farther south, fewer stars are circumpolar and more stars are visible to them overall.

Why did Copernicus want to develop a completely new system for predicting planetary positions? Provide two reasons.

He wanted to improve upon the predictions of planetary positions because the geocentric model often gave inaccurate results. He also thought his system was simpler and more elegant—that the existing system was needlessly and implausibly complicated.

How does the mass of an astronaut change when she travels from Earth to the Moon? How does her weight change?

Her mass does not change because that measures the amount of "stuff" that makes up her body. Her weight will decrease because that is a measure of the amount of gravitational force she is experiencing; on the Moon, her weight would be about 1/6 what it is on Earth.

What were four of Galileo's discoveries that were important to astronomy?

His observation of the phases of Venus, which supported the heliocentric model; his observations of Jupiter's moons, which showed not everything orbits Earth; his observations of features on the surface of the Moon, which showed it has similarities to Earth; and his discovery that the Milky Way is simply a mass of unresolved stars.

Explain why hotter objects tend to radiate more energetic photons compared to cooler objects.

Hotter objects have more electrons in higher energy levels, so they not only emit more photons, but those photons are, on average, more energetic.

If there is gravity where the International Space Station (ISS) is located above Earth, why doesn't the space station get pulled back down to Earth?

If the space station were not moving, it would do just that, but when the space station was first assembled at a certain height above Earth, it was provided an appropriate speed for that height in a direction parallel to the surface of Earth. As such, instead of falling toward Earth, it is continuously falling around Earth. Since friction with Earth's atmosphere slows down the ISS, it requires occasional upward pushes, or boosts, to stay in orbit.

If you were to drive to some city south of your current location, how would the altitude of the celestial pole in the sky change?

If you are in the Northern Hemisphere, the north celestial pole should be lower in altitude. In the Southern Hemisphere, the south celestial pole should be higher in altitude.

The term solstice translates as "Sun stop." Explain why this translation makes sense from an astronomical point of view.

If you observe the sunset on the horizon, you will notice that during spring and early summer, the sunset position of the Sun moves slowly northward, slowing as June 21 nears. On June 21, the Sun's setting position stops moving north and, on later days, begins moving south, so "Sun stop" is referring to the halt of the Sun's migration along the horizon.

Explain the difference between radiation as it is used in most everyday language and radiation as it is used in an astronomical context.

In everyday usage, the term radiation can refer to highly energetic photons or to particles emitted from a radioactive substance, which are normally harmful to life forms. In an astronomical context, radiation is simply light of any kind emitted by an object, and it is not necessarily harmful in any way.

Why did Kepler need Tycho Brahe's data to formulate his laws?

In science, laws of nature are often developed by carefully analyzing data collected from observations of various phenomena. In this case, Kepler used Brahe's data regarding the observed positions of the planet Mars in order to determine that Mars moved in an elliptical, not circular, orbit.

Explain, according to both geocentric and heliocentric cosmologies, why we see retrograde motion of the planets.

In the geocentric model, Mars orbits outside of the Sun on its deferent path, but it also moves in a circular motion on its epicycle as it follows the deferent. If the planet moves faster "backward" on the epicycle than it moves forward on the deferent, then it can appear to move in a retrograde manner while still retaining the overall pattern of prograde motion in the sky. In the heliocentric model, Mars moves somewhat slower than Earth. During periods of time when Earth passes Mars, Mars appears to move backward on the sky relative to the background stars. This is confirmed by the fact that Mars appears at its brightest during this motion (due to it being at its closest approach to Earth) and is also on the opposite side of the sky from the Sun during retrograde motion.

The Sun was once thought to be a planet. Explain why.

In the geocentric system, all of the objects that moved in the sky relative to the fixed stars were considered to be "wanderers," and the Sun was no exception, so it was classified as a planet.

If a star rises at 8:30 p.m. tonight, approximately what time will it rise two months from now?

In two months, Earth will have moved 1/6 of the way around its orbit, so the star will rise 1/6 of a day earlier, or about 4:30 p.m.

Is it possible to escape the force of gravity by going into orbit around Earth? How does the force of gravity in the International Space Station (orbiting an average of 400 km above Earth's surface) compare with that on the ground?

It is not possible to escape the force of gravity by going into orbit. The space station is about 6800 km from the center of Earth, only about 86% farther away than the surface of our planet. The force of gravity in the International Space Station (ISS) is only slightly less than the gravity at the surface of Earth. People (and sandwiches) "float" in the ISS because they, and the station itself, are falling around Earth.

If Sirius rises at 8:00 p.m. tonight, at what time will it rise tomorrow night, to the nearest minute? Explain.

It will rise at 7:56 p.m. on the following night. The sidereal day is the time it takes for a star to return to the same position in our sky, and that is 23 hours and 56 minutes, or 4 minutes less than 24 hours.

Suppose Earth took exactly 300.0 days to go around the Sun, and everything else (the day, the month) was the same. What kind of calendar would we have? How would this affect the seasons?

It would still be the case that the lunar cycle would not evenly divide into the solar cycle, so we would still have to use a solar calendar for simplicity. The seasons would be shorter since the overall year is shorter.

Make a list of each main phase of the Moon, describing roughly when the Moon rises and sets for each phase. During which phase can you see the Moon in the middle of the morning? In the middle of the afternoon?

New moon rises at sunrise and sets at sunset. Waxing crescent rises midmorning and sets between sunset and midnight. First quarter rises at noon and sets at midnight. Waxing gibbous rises midafternoon and sets between midnight and sunrise. Full moon rises at sunset and sets at sunrise. Waning gibbous rises between sunset and midnight and sets midmorning. Third quarter rises at midnight and sets at noon. Waning crescent rises between midnight and sunrise and sets midafternoon. You can see the Moon midmorning during third quarter and waning crescent. You can see the Moon mid-afternoon during waxing crescent and first quarter.

What was the great insight Newton had regarding Earth's gravity that allowed him to develop the universal law of gravitation?

Newton speculated that Earth's gravity might extend out into space to help keep the Moon in its orbit around Earth. On a deeper level, he was able to see that the same rules of nature developed on Earth could also apply in the heavens (beyond Earth).

Write out Newton's three laws of motion in terms of what happens with the momentum of objects.

Newton's first law says that the momentum of an object remains constant in both magnitude and direction unless acted upon by a force. Newton's second law says that the rate of change of the momentum of an object is equal to the force that produced that change. Newton's third law says that momentum is conserved when two or more objects interact with each other.

Which of these properties of an object best quantifies its inertia: velocity, acceleration, volume, mass, or temperature?

Mass best quantifies its inertia.

Describe how Bohr's model used the work of Maxwell.

Maxwell's theory of electromagnetism says that when a charged particle changes speed or direction, it should radiate an electromagnetic wave and lose energy. As electrons orbit the nucleus, they change their direction regularly and therefore should radiate energy and soon fall into the nucleus. Bohr proposed that in certain permitted orbits around the nucleus, the electrons can orbit without giving off waves and losing energy, which was a radical notion and part of the revolution of quantum mechanics.

In a part of Earth's orbit where Earth is moving faster than usual around the Sun, would the length of the sidereal day change? If so, how? Explain.

No, the sidereal day length depends only upon Earth's rotation speed, which is uniform. It will always be approximately 23 hours and 56 minutes, no matter what time of year it is.

Is your textbook the kind of idealized object (described in section on radiation laws) that absorbs all the radiation falling on it? Explain. How about the black sweater worn by one of your classmates?

No, the textbook reflects light of different colors unlike a blackbody, which reflects no light. A black sweater is a somewhat better approximation of a blackbody since it absorbs almost all light and reflects very little light. But since it reflects enough light so that everyone can see your sweater, it is not a true blackbody.

A car accident occurs around midnight on the night of a full moon. The driver at fault claims he was blinded momentarily by the Moon rising on the eastern horizon. Should the police believe him?

No. He should not be believed since the full moon is always high in the sky near midnight. When full, the Moon rises as sunset and sets at sunrise.

On a globe or world map, find the nearest marked latitude line to your location. Is this an example of a great circle? Explain.

No. The center of all latitude circles (except the equator) is not the center of Earth. A great circle must be centered on the center of Earth.

Explain how the Doppler effect works for sound waves and give some familiar examples.

Sound waves emitted by an object moving toward you are compressed and observed to have a higher pitch, or frequency. For objects moving away, the sound has a lower pitch. We hear this in cars or trains passing by us—first moving toward us and then away from us.

What are the differences between light waves and sound waves?

Sound waves move much more slowly than light and require some sort of medium to propagate (like air, water, or any solid). Light moves much more quickly (at the fastest speed possible in the universe) and does not require a medium. It can propagate through empty space.

Why do you think so many people still believe in astrology and spend money on it? What psychological needs does such a belief system satisfy?

Student answers will vary. One concept is that people are comforted by the idea of a higher power controlling some aspects of their lives or fate so they don't have to take full responsibility. Also, such a "cosmic" system can give meaning to everyday triumphs and challenges; it can explain events in life that people find confusing, unfair, or difficult.

What was the problem with the Hubble Space Telescope and how was it solved?

The HST's primary mirror was constructed with a flaw in its shape, so that the images it produced initially were warped and out of focus. The problem was solved by a space mission in which astronauts visited the telescope in its orbit and added small and carefully designed mirrors to correct the flaw.

How many degrees does the Moon move per day relative to the fixed stars? How many days does it take for the Moon to return to its original location relative to the fixed stars?

The Moon moves about 12° per day. It takes the Moon about 30 days to return to its original position relative to the fixed stars (actually 27.3 days).

In a lunar eclipse, does the Moon enter the shadow of Earth from the east or west side? Explain.

The Moon orbits Earth in the same direction of Earth's rotation, which is from west to east, so the Moon would enter Earth's shadow from the west side.

Explain why some solar eclipses are total and some are annular.

The Moon's orbit around Earth is slightly elliptical. When the Moon is farther from Earth, the cone of its umbra does not quite reach Earth's surface, resulting in an annular eclipse. When the Moon is closer to Earth, we can experience a total solar eclipse.

Why don't lunar eclipses happen during every full moon?

The Moon's orbital plane is tilted about 5° with respect to Earth's orbital plane (the ecliptic), so most of the time during full phase, the Moon is either above or below the ecliptic, not in Earth's shadow.

How many degrees does the Sun move per day relative to the fixed stars? How many days does it take for the Sun to return to its original location relative to the fixed stars?

The Sun moves about 1° per day. It takes about 360 days (actually 365.25 days) to return to its original location.

The Hooker telescope at Palomar Observatory has a diameter of 5 m, and the Keck I telescope has a diameter of 10 m. How much more light can the Keck telescope collect than the Hooker telescope in the same amount of time?

The amount of light a telescope can collect increases with the square of the aperture. Therefore, increasing the aperture diameter by a factor of two increases the area of light collection by a factor of four. The Keck telescope is four times more sensitive than the Hooker telescope.

What is the right ascension and declination of the autumnal equinox?

The autumnal equinox occurs half a year after the vernal equinox, so in that time, the Sun will have moved 180° around the celestial sphere to a right ascension of 180° or 12 hours. The declination will be zero since the Sun is again crossing the celestial equator.

Explain why the Gregorian calendar modified the nature of the leap year from its original definition in the Julian calendar.

The average year length using the Julian method is 11 minutes off from a true year, and this is a large enough error to add up over a century or more, so the frequency of the leap day had to be slightly modified to correct for this error.

Is the ecliptic the same thing as the celestial equator? Explain.

The celestial equator is the projection of Earth's equator onto the sky whereas the ecliptic is the Sun's apparent annual path in the sky. These two circles are separated by an angle of 23.5° (see Figure 2.7 The Celestial Tilt).

A certain material has a mass of 565 g while occupying 50 cm3 of space. What is this material? (Hint: Use Table 3.1 Densities of Common Materials)​

The density of the material is 565g/50cm3 = 11.3 g/cm3. This material is lead.

According to Kepler's second law, where in a planet's orbit would it be moving fastest? Where would it be moving slowest?

The planet would move fastest when it is closest to the Sun (at perihelion) and slowest when farthest from the Sun (at aphelion).

Hipparchus could have warned us that the dates associated with each of the natal astrology sun signs would eventually be wrong. Explain why.

The precession of Earth changes the dates for which the Sun crosses through each of the zodiacal constellations over the course of 26,000 years.

Give four ways to demonstrate that Earth is spherical

The shadow cast on the Moon is always round in shape. Ships sailing away on the ocean appear to sink into the ocean due to the curvature of Earth's surface, rather than simply getting smaller and smaller. Orbiting satellites taking photographs of Earth show that Earth looks round from every direction. The Sun is at different altitudes in the sky for different longitudes (it would be in the same place for everyone if Earth were flat, for example), and the Sun's position in the sky depends upon the time.

If identical spacecraft were orbiting Mars and Earth at identical radii (distances), which spacecraft would be moving faster? Why?

The spacecraft moving around Earth would be moving faster. Because Earth has a greater mass, it has a greater gravitational pull on the spacecraft; so for a similar orbit, the one orbiting Earth has to be moving faster to keep from being pulled to the ground.

Explain the origin of the magnitude designation for determining the brightness of stars. Why does it seem to go backward, with smaller numbers indicating brighter stars?

The system originated with Hipparchus, who ranked the brightest stars as being "first magnitude," fainter stars being of the "second magnitude," then "third magnitude," and so on as the stars grew progressively fainter.

Explain how tidal forces are causing Earth to slow down.

The tidal bulges of Earth want to continue to point toward the Moon, which orbits Earth every 27.3 days. Earth, however, spins faster than this, about once per day. Friction between the rapidly spinning Earth and slowly moving tidal bulges results in a slight slowing of Earth's spin.

Explain why there are two high tides and two low tides each day. Strictly speaking, should the period during which there are two high tides be 24 hours? If not, what should the interval be?

The tidal force of the Moon creates bulges on both the near and far sides of Earth, so there are two high tide bulges. As Earth rotates, a person would be carried through both of these bulges during any given 24-hour period (actually, more like 24 hours and 50 minutes due to the changing position of the Moon in the sky).

Consider a calendar based entirely on the day and the month (the Moon's period from full phase to full phase). How many days are there in a month? Can you figure out a scheme analogous to leap year to make this calendar work? Can you also incorporate the idea of a week into your lunar calendar?

There are 29.5 days in a month. The only way to make a calendar work that is consistent with the solar cycle would be to have 12 months in most years but occasionally add in a thirteenth "leap" month in order to keep the calendar in sync with the seasons, since 12 months of 29.5 days is short of 365 days.

Explain three lines of evidence that argue against the validity of astrology.

There are no known forces that could explain why the positions of planets should affect a person's personality or fate. The dates that supposedly correspond to a person's natal astrology sun sign have shifted significantly since the first astrological charts, and no corrections or adjustments have been made to the predictive methods, implying that they are not logical or true. Statistical tests of astrology, such as seeing whether people in certain occupations were born in just one or two sun signs, show that people are distributed randomly in their astrological characteristics.

The secret recipe to the ever-popular veggie burgers in the college cafeteria is hidden in a drawer in the director's office. Two students decide to break in to get their hands on it, but they want to do it a few hours before dawn on a night when there is no Moon, so they are less likely to be caught. What phases of the Moon would suit their plans?

There is no Moon in the predawn morning sky when the phase is between new moon and gibbous (a few days past first quarter). Of course, you'd have to be a lunatic to commit a crime like this!

Explain how the zodiacal constellations are different from the other constellations.

These constellations intersect with the ecliptic, the Sun's apparent annual path in the sky. So from Earth, the Sun appears to move through the zodiacal constellations, but not the others.

What kind of motion for a star does not produce a Doppler effect? Explain.

Transverse (sideways) motion (perpendicular to your line of sight to the object) does not produce a Doppler shift since there is no motion either toward or away from the observer.

Why is Tycho Brahe often called "the greatest naked-eye astronomer" of all time?

Tycho Brahe made large and elaborate measurement devices on his island, but none of them were telescopes (Tycho was "pre-telescopic"). He and his helpers used equipment to make precise measurements of the positions of planets moving through space, but the equipment did not have lenses.

Describe a practical way to determine in which constellation the Sun is found at any time of the year.

Use a star chart to determine which zodiacal constellation rises at sunset (or, if it is easier, which zodiacal constellation crosses the meridian near midnight). Then, the constellation on the opposite side of the sky (with dates 6 months different from the constellation you observed) is likely the constellation in which the Sun will be found.

What phases would Venus show if the geocentric model were correct?

Venus would only show crescent phases because the illuminated side would only ever partially be visible from Earth.

What were two arguments or lines of evidence in support of the geocentric model?

We do not feel any motion. There is no wind or vibration indicating that Earth is moving. Also, because we do not see stellar parallax, the simplest explanation is that there is no movement of Earth around the Sun.

If spectral line wavelengths are changing for objects based on the radial velocities of those objects, how can we deduce which type of atom is responsible for a particular absorption or emission line?

We look for patterns of wavelengths associated with each element rather than a single specific line, so even if a particular line has been shifted in an unknown direction, we look for other lines in the pattern that may be similarly shifted in order to identify an element or molecule.

What is the phase of the Moon if it . . . A. rises at 3:00 p.m.? B. is highest in the sky at 7:00 a.m.? C. sets at 10:00 a.m.?

A. waxing gibbous; B. third quarter, assuming 7:00 a.m. = sunrise; C. waning gibbous.

With what type of electromagnetic radiation would you observe: A. A star with a temperature of 5800 K? B. A gas heated to a temperature of one million K? C. A person on a dark night?

A. visible light; B. X-ray; C. infrared

Where are you on Earth if you experience each of the following? (Refer to the discussion in Observing the Sky: The Birth of Astronomy as well as this chapter.) A. The stars rise and set perpendicular to the horizon. B. The stars circle the sky parallel to the horizon. C. The celestial equator passes through the zenith. D. In the course of a year, all stars are visible. E. The Sun rises on September 21 and does not set until March 21 (ideally).

A. Earth's equator (0° latitude); B. either the North or the South Pole (90° North or South latitude); C. Earth's equator (0° latitude); D. Earth's equator (0° latitude); E. the North Pole (90° North latitude).

Which major planet has the largest . . . A. semimajor axis? B. average orbital speed around the Sun? C. orbital period around the Sun? D. eccentricity?

A. Neptune; B. Mercury; C. Neptune; D. Mercury. (This question asked only about planets, not dwarf planets, just in case Pluto or Eris fans are objecting.)

Which has more mass: an armful of feathers or an armful of lead? Which has more volume: a kilogram of feathers or a kilogram of lead? Which has higher density: a kilogram of feathers or a kilogram of lead?

An armful of lead would have more mass. A kilogram of feathers would have a greater volume. A kilogram of lead would have a higher density.

What is an asterism? Can you name an example?

An asterism is a small, easily recognizable group of stars within a larger constellation. Examples include the Little Dipper inside Ursa Minor and the Big Dipper inside Ursa Major.

What two factors made it difficult, at first, for astronomers to choose between the Copernican heliocentric model and the Ptolemaic geocentric model?

Both gave inaccurate predictions of planetary positions and motions from complicated models. In those days, little weight was given to observational experimental methods of validating one model or the other.

Why is it difficult to observe at infrared wavelengths? What do astronomers do to address this difficulty?

Both telescopes and Earth itself emit a lot of infrared radiation that is difficult to separate from the radiation coming from astronomical sources. To solve the problem, astronomers either shield the detector from its surroundings by cooling it or they make infrared observations from high in the atmosphere or from space.

Which type of wave has a longer wavelength: AM radio waves (with frequencies in the kilohertz range) or FM radio waves (with frequencies in the megahertz range)? Explain.

AM radio waves have a lower frequency. According to the wave equation, waves with a lower frequency must have a larger (longer) wavelength. To put it another way, frequency is inversely proportional to wavelength.

As friction with our atmosphere causes a satellite to spiral inward, closer to Earth, its orbital speed increases. Why?

According to Kepler's third law, P2 ∝ a3, where a is the semimajor axis (essentially the distance from the center of Earth in our case). If the satellite spirals in (because of air friction), a decreases and, hence, so does P. Thus, a decrease in a means an increase in V.

Explain how we can deduce the temperature of a star by determining its color.

According to Wien's law, the peak wavelength of a blackbody spectrum is inversely related to its temperature. The color of a star is indicative of where the peak wavelength of its spectrum is located, so color can indicate to us the temperature of a star. Bluer stars are hotter, whereas red stars are cooler.

Explain why the year 1800 was not a leap year, even though years divisible by four are normally considered to be leap years.

According to the Gregorian calendar reform, having a leap year every four years wasn't quite accurate enough, since Earth's orbital period is slightly different from 365.25 days. So, the rule is that century leap years occur only in years divisible by 400, which 1800 is not.

Your great-great-grandfather, who often exaggerated events in his own life, once told your relatives about a terrific adventure he had on February 29, 1900. Why would this story make you suspicious?

According to the Gregorian calendar, the century year 1900 (not being divisible by 400) had no leap year, and thus no February 29. (However, if your great-great-grandfather was living at the time in Russia or some other country that had not converted from the Julian to the Gregorian calendar, his story could be correct.)

Why are the largest visible-light telescopes in the world made with mirrors rather than lenses?

Because the light does not pass through the mirror so flaws inside the mirror do not affect the path of the light as they do with lenses. Only the front surface must be perfectly manufactured. It is also easier to support a mirror, because it can be held in place from the back. For these reasons, it's much easier and cheaper to manufacture a suitable large mirror than a suitable large lens.

What is the altitude of the Sun at noon on December 22, as seen from a place on the Tropic of Cancer?

Between 44° and 45°.

In what ways did the work of Copernicus and Galileo differ from the views of the ancient Greeks and of their contemporaries?

Copernicus and Galileo believed that Earth spins on its axis and revolves around the Sun as one of the planets, both contradicting the idea that Earth is motionless at the center of the solar system. In addition, Galileo thought that the best way to understand nature is through experiments, rather than just pure thought, as the ancient Greeks did. Galileo also had a telescope with which to examine the heavens, which the ancient Greeks did not have.

Although the Copernican system was largely correct to place the Sun at the center of all planetary motion, the model still gave inaccurate predictions for planetary positions. Explain the flaw in the Copernican model that hindered its accuracy.

Copernicus assumed all motion must be uniform circular motion. Because planets orbit the Sun in elliptical paths with varying speeds, there is no way to reproduce that motion faithfully with the planets in circular motion at constant speed around the Sun.

State Kepler's three laws in your own words.

Kepler's first law says that all planetary orbits are ellipses with the Sun at one focus. Kepler's second law says that planets sweep out equal areas of their orbits in equal amounts of time. Kepler's third law says that the square of the average distance a planet is from the Sun is proportional to the period of its orbit cubed.

Why do astronomers place telescopes in Earth's orbit? What are the advantages for the different regions of the spectrum?

Light from some bands of the electromagnetic spectrum does not penetrate Earth's atmosphere, so direct detection of those bands requires putting telescopes in space. For this reason, X-ray and gamma-ray space-based observatories are essential. Even in bands that do penetrate the atmosphere, like millimeter wavelengths, "pollution" from terrestrial sources can swamp faint astronomical signals, making it advantageous to place telescopes in space at these bands also. Infrared radiation is absorbed by water in Earth's atmosphere, so the higher up the telescope can be located, the less absorption by water it will have to deal with.

Explain why light is referred to as electromagnetic radiation.

Light is an example of electromagnetic radiation, which encompasses a broad spectrum of waves. Light is a traveling wave of oscillating electric and magnetic fields.

The term equinox translates as "equal night." Explain why this translation makes sense from an astronomical point of view.

On the date of the equinox, everyone on Earth experiences an equal-length day and equal-length night of roughly 12 hours each.

What is the right ascension and declination of the Sun at noon on the summer solstice in the Northern Hemisphere?

On the day of the summer solstice, the Sun will have moved halfway from the vernal equinox (0 hours) toward the autumnal equinox (12 hours). Since right ascension is measured in the direction of the apparent motion of the Sun, the Sun will be halfway between these points, at a right ascension of 6 hours (or 90°). The declination is 23° N of the celestial equator, just as the Tropic of Cancer is 23° N of Earth's equator.

What are the three isotopes of hydrogen, and how do they differ?

Ordinary hydrogen has a single proton for a nucleus. Deuterium is hydrogen with a proton and a neutron in its nucleus. Tritium is hydrogen with a proton and two neutrons in its nucleus.

Pluto's orbit is more eccentric than any of the major planets. What does that mean?

Pluto's orbit is less circular (or more elongated) than the others planets' orbital paths.

Describe the techniques radio astronomers use to obtain a resolution comparable to what astronomers working with visible light can achieve.

Radio astronomers use interferometry, in which the measurements of several telescopes are combined in order to produce a result that is comparable to that generated by a single telescope as large as the distance between the separate telescopes. In this way, the resolution of the observation is greatly increased, approaching the resolution of visible-light and infrared telescopes.

Radio and radar observations are often made with the same antenna, but otherwise they are very different techniques. Compare and contrast radio and radar astronomy in terms of the equipment needed, the methods used, and the kind of results obtained.

Radio astronomy passively detects incoming radio energy from an astronomical source. It requires three basic components: a telescope, a spectrometer, and a detector. It can detect sources all the way to the edge of the visible universe. Radar, on the other hand, is an active technique. Radio waves are emitted from the instrument on Earth, bounce off a source, and are detected upon their return. Therefore, a radio emitter is required in addition to a detector. It can only be used to detect very close astronomical bodies, such as planets or asteroids.

Draw a picture that explains why Venus goes through phases the way the Moon does, according to the heliocentric cosmology. Does Jupiter also go through phases as seen from Earth? Why?

Refer to Figure 2.18 Phases of Venus for the picture of Venus going through its phases. Jupiter, which is farther from the Sun than Earth is, does not experience phases because it is always fully illuminated as seen from Earth.

During a retrograde loop of Mars, would you expect Mars to be brighter than usual in the sky, about average in brightness, or fainter than usual in the sky? Explain.

Retrograde motion is seen due to the faster-moving Earth passing Mars in orbit, so the two planets must be next to each other (closer to each other than usual). Thus, Mars should appear brighter than usual.

Earth's shadow is much larger than the Moon's shadow on Earth, so it is far more likely for the Moon to intersect Earth's shadow than for any given location on Earth to intersect the Moon's shadow.

Since Earth's shadow is much larger than the Moon's shadow, it takes longer for the Moon to traverse the shadow cone of Earth than it does for any given location on Earth to traverse the much smaller shadow cone of the Moon.

Two asteroids begin to gravitationally attract one another. If one asteroid has twice the mass of the other, which one experiences the greater force? Which one experiences the greater acceleration?

Since Newton's law of gravity says the force is proportional to the product of the two masses, both masses experience the same force. This is also consistent with Newton's third law of motion. But the asteroid with the lesser mass would feel the greater acceleration, according to Newton's second law.

Explain how Kepler was able to find a relationship (his third law) between the orbital periods and distances of the planets that did not depend on the masses of the planets or the Sun.

Since all the planets orbit the Sun, the Sun's mass is the same for all the planets in Kepler's third law. The individual masses for each of the planets, M2, are so small (even Jupiter's) compared to the Sun that they are insignificant in calculating a3 = (M1 + M2) × P2 and can be treated as if they were zero and not significantly change the answer.

By what factor would a person's weight be increased if Earth had 10 times its present mass, but the same volume?

Since the force is directly proportional to mass, the person would weigh 10 times his or her present weight. If the volume is the same, the distance of the person from Earth's center would not change.

The day on Mars is 1.026 Earth-days long. The Martian year lasts 686.98 Earth-days. The two moons of Mars take 0.32 Earth-day (for Phobos) and 1.26 Earth-days (for Deimos) to circle the planet. You are given the task of coming up with a Martian calendar for a new Mars colony. What might you do?

Since the lunar cycles do not divide evenly into the annual cycle, a solar calendar would be best for keeping track of the seasons.

What is the right ascension and declination of the vernal equinox?

Since the vernal equinox marks the starting point of our measurement of right ascension (much like the Greenwich meridian marks the starting point for longitude), it has a right ascension of zero. On the vernal equinox, the Sun is crossing the celestial equator heading north, so it is at a declination of zero.

To calculate the angular momentum of an object, which properties of an object do you need to know?

You need to know the object's mass, velocity, and distance from the spin axis.

When Earth's Northern Hemisphere is tilted toward the Sun during June, some would argue that the cause of our seasons is that the Northern Hemisphere is physically closer to the Sun than the Southern Hemisphere, and this is the primary reason the Northern Hemisphere is warmer. What argument or line of evidence could contradict this idea?

The diameter of Earth is only about 8000 miles. The difference in distance to the Sun between the hemispheres is less than this, on the order of 1000 miles. This is extremely small compared with the average Earth-Sun distance of 93 million miles. If the few percent distance variation of our elliptical orbit is not enough to cause seasons, then a 1000-mile difference could not possibly be the cause.

Why does the Moon create tidal bulges on both sides of Earth instead of only on the side of Earth closest to the Moon?

The differential force of gravity exerted by the Moon has the effect of stretching Earth out along a line connecting Earth and the Moon, so both sides of Earth bulge out. Another way of saying this is that the near side of Earth feels a stronger pull than the center of Earth, and the center of Earth feels a stronger pull than the far side, so the near side is pulled toward the Moon somewhat and the far side is left behind somewhat, elongating Earth.

Compare the eye, photographic film, and CCDs as detectors for light. What are the advantages and disadvantages of each?

The eye has the advantage of being readily available—no extra equipment is required. However, the eye is connected to an imperfect recording and retrieving device (the human brain), and it has a short integration time. Photograph plates can make a permanent record of an astronomical image and have much longer integration times than the eye, but they are extremely inefficient, retaining only 1% of the light that falls on them. CCDs, on the other hand, retain 60-70% or more of the incident light and provide more accurate measurements of brightness than photographic plates. Their output can be sent directly to computers for storage and analysis.

The gas pedal, the brakes, and the steering wheel all have the ability to accelerate a car—how?

The gas pedal can increase the speed, the brakes can decrease the speed, and the steering wheel can change the direction; all represent changes to the velocity of the car.

Consider three cosmological perspectives—the geocentric perspective, the heliocentric perspective, and the modern perspective—in which the Sun is a minor star on the outskirts of one galaxy among billions. Discuss some of the cultural and philosophical implications of each point of view.

The geocentric perspective implies that humanity holds some kind of special or privileged place in the cosmos—that the universe is centered on us somehow. In the heliocentric perspective, our system of planets is still the center of things, with the Sun the center of that and not Earth. Earth thus becomes only one planet among the others. Our modern understanding shows that our solar system, our planet, and all of us do not exist in a particularly special or privileged location and, further, there really is no such location.

Explain what the ionosphere is and how it interacts with some radio waves.

The ionosphere is a layer of charged particles at the top of our atmosphere, mostly ionized by interactions with sunlight and the solar wind. Some longer wavelength radio waves (such as AM radio) cannot penetrate this region and so the ionosphere scatters these waves in many directions. Under the right conditions, the ionosphere sometimes acts like a radio mirror, reflecting these waves back to the surface (hence the reason you can hear some powerful AM radio stations from more than 1,000 miles away at night).

What is the latitude of the North Pole? The South Pole? Why does longitude have no meaning at the North and South Poles?

The latitude of the North Pole is 90° N, and the South pole is 90° S. Longitude is meaningless since there is no east-west direction at the poles.

In a part of Earth's orbit where Earth is moving faster than usual around the Sun, would the length of the solar day change? If so, how? Explain.

The length of the solar day will increase slightly. Typically, as Earth spins, it moves a little bit in its orbit around the Sun, so it takes a little extra time for some point on Earth to see the Sun directly overhead: 4 minutes extra compared to Earth's rotation period of 23 hours and 56 minutes. If Earth is moving faster in its orbit, the change in position of the Sun in the sky relative to the fixed stars will be greater, meaning it will take longer for the Sun to return to its overhead position from the previous day.

Why is it difficult to construct a practical calendar based on the Moon's cycle of phases?

The monthly cycle of the Moon (29.5 days) does not evenly divide into the seasonal solar cycle of 365.25 days, so there is no easy way to construct a practical calendar that keeps track of the seasons using only the lunar cycle as a guide.

During summer in the Northern Hemisphere, the North Pole is illuminated by the Sun 24 hours per day. During this time, the temperature often does not rise above the freezing point of water. Explain why.

The north polar region receives sunlight indirectly, at an angle that causes the sunlight to be spread out over a large area, so each square meter of the surface gets very little energy from the Sun.

Parallaxes of stars were not observed by ancient astronomers. How can this fact be reconciled with the heliocentric hypothesis?

The parallax is the shift of an object in the sky when seen from two separated vantage points. It depends inversely on the distance to the object. Stars are so far away, compared to the size of Earth's orbit, that their parallax angle could not be measured to the necessary precision attainable at the time.

Explain why glass prisms disperse light.

When light passes through one edge of a prism, it goes from the air into glass, bending the light. The light bends (refracts) differently for different wavelengths, dispersing the colors. When the light comes out of the other side of the prism, it goes from glass into air, but since the other side of the prism is at a different angle, the dispersing effect continues. So the prism refracts different wavelengths of light at different angles, and "white light" is turned into a rainbow.

Explain why we have to observe stars and other astronomical objects from above Earth's atmosphere in order to fully learn about their properties.

While we can see the visible light of planets, stars, and galaxies from the ground, much of the electromagnetic radiation emitted by these objects is not emitted in the visible part of the spectrum. Some of the radiation is emitted in a part of the spectrum that doesn't penetrate Earth's atmosphere easily (like ultraviolet, X-rays, gamma rays, and some parts of the infrared and radio bands of the spectrum). In order to observe the radiation emitted at all different wavelengths by astronomical objects, we have to also observe them from above the atmosphere.

Why is it dangerous to be exposed to X-rays but not (or at least much less) dangerous to be exposed to radio waves?

X-rays are much more energetic with wavelengths much smaller than most biological organisms, so they and can do damage to cells and biological organisms. Radio waves are much longer than most biological organisms and much less energetic, so there is very little interaction between organic material and radio waves.

Ursa Minor contains the pole star, Polaris, and the asterism known as the Little Dipper. From most locations in the Northern Hemisphere, all of the stars in Ursa Minor are circumpolar. Does that mean these stars are also above the horizon during the day? Explain

Yes, they are always above the horizon; but during the day, the sunlight makes them invisible to us.

Is it possible for two different atoms of carbon to have different numbers of neutrons in their nuclei? Explain.

Yes, what determines the element is the number of protons in the nucleus, so any nucleus that has six protons is carbon, regardless of whether it has six, seven, or eight neutrons.

A body moves in a perfectly circular path at constant speed. Are there forces acting in such a system? How do you know?

Yes; there must be a force pulling toward the center of the circle. According to Newton's first law, there must a force present to keep the object moving in a circle rather than a straight line.

Evil space aliens drop you and your fellow astronomy student 1 km apart out in space, very far from any star or planet. Discuss the effects of gravity on each of you.

You and the classmate, both having mass, will begin to move toward one another via your mutual gravitational attraction. Using Newton's second law, the person with less mass will accelerate faster.

From where on Earth could you observe all of the stars during the course of a year? What fraction of the sky can be seen from the North Pole?

You can observe all of the stars from the equator over the course of a year, although high-declination stars will be difficult to see so close to the horizon. Only half the sky can be seen from the North Pole, and that half does not change throughout the year.

Suppose you are on a strange planet and observe, at night, that the stars do not rise and set, but circle parallel to the horizon. Next, you walk in a constant direction for 8000 miles, and at your new location on the planet, you find that all stars rise straight up in the east and set straight down in the west, perpendicular to the horizon. How could you determine the circumference of the planet without any further observations? What is the circumference, in miles, of the planet?

You could deduce that you have walked 1/4 of the way around the planet, from the pole to the equator, so you could multiply 4 by the distance you traveled to determine the circumference: 4 × 8000 miles = 32,000 miles.

To calculate the momentum of an object, which properties of an object do you need to know?

You need to know the object's mass and velocity.