The number of degrees in a full circle is
How many arcseconds are there in a full circle?
360 x 3600
In angular measurements used in astronomy, how many right angles are there in a full circle?
One arcsecond is equal to
One arcminute is equal to
On a particular night, Jupiter subtends an angle of 42 arcseconds as seen from Earth. This angle is
roughly three-quarters of an arcminute.
Astronauts on the Moon look back at Earth, a distance of about 400,000 km away. If the cities of Washington, D.C., and New York are separated by about 300 km, what will be the angle between them when viewed from the Moon?
Two very bright fireworks are exploded at the same time during the July 4 celebrations, one in New York, the other in Los Angeles (4000 km apart). How far apart in angle will these flashes appear to astronauts on the Moon, who are 400,000 km from Earth?
At what distance would a friend have to hold a dime (about 1 cm diameter) for it to subtend an angle of 2 arcseconds?
The number five hundred thousand is written in powers-of-ten notation as
5 × 105.
10^5 × 10^8 =
One billionth divided by one millionth is equal to
By what approximate factor in powers-of-ten notation is a human being (height about 2 m) larger than the nucleus of a hydrogen atom, or proton (diameter about 10^-15 m)?
2 × 10^15
One astronomical unit, or one AU is defined as the
mean distance between the Sun and Earth.
A light-year is a measure of
If you were able to travel out into space until the angular distance between Earth and the Sun was 1 second of arc, how far would you be from the Sun? (Assume that Earth-Sun line is at right angles to your line of sight.)
The distance to the star τ Scorpii has been measured as 230 pc. Expressed in light-years, this is approximately
The time taken for light to travel to Earth from a galaxy that is 10 Mpc away is
3.26 × 10^7 years.
The following distance units, arranged in size from smallest to largest, are
km, AU, ly, pc
A star rises at 8 P.M., moves across the sky (crossing high overhead), and then sets at
The phrase “diurnal motion” refers to the
gradual motion of the constellations from east to west across the sky each night, resulting in different constellations being visible at 4 A.M. than at 10 P.M. on any given night.
What basic pattern do stars seem to trace out in our sky if you watch (or photograph) stars near the north celestial pole for a period of several hours?
circles, with the north celestial pole at the center
With respect to the stars, the rotation of Earth carries you toward the
Which of the following lines or points is always directly over your head, no matter where on Earth you go?
Diurnal motion of objects in the sky is caused by the
rotation of Earth on its axis.
The nightly motion of objects across our the sky is caused by the
rotation of Earth on its axis.
The ecliptic is defined as the
line traced in our sky by the Sun over one year against the background stars.
The ecliptic crosses the celestial equator at
two points, known as equinoxes.
Earth would not have seasons if
its axis of rotation were perpendicular to its orbital plane.
Summertime in the northern hemisphere is when
more direct sunlight shines on this hemisphere.
It is warmer in summer than winter because
the Sun is higher in the sky and the days are longer.
One required condition for seasons to occur is that a planet’s
spin axis be tilted with respect to the perpendicular to its orbital plane.
The equinoxes are located at the intersections of the
ecliptic and the celestial equator.
When the Sun is at one of the equinoxes,
day and night are of equal length everywhere on Earth.
If you observe from a location north of the equator the Sun’s position on the horizon as it rises each morning throughout the year you will find that
the rising position moves progressively northward from December through June.
The Sun rises due east in the sky when viewed from any site
on Earth only on the first day of spring and the first day of fall.
The Arctic Circle is at a latitude of
The Arctic Circle is defined as a line on Earth where the Sun
can be seen for 24 hours on at least one day of the year.
the slow coning motion of the spin axis of Earth, similar to that of a spinning top.
What is the significance of Polaris, the North Star?
Polaris is almost on the curve traced out by the rotation axis as a result of the precession of the rotation direction.
The position in Earth’s orbit around the Sun which presently corresponds to Winter Solstice will instead correspond to Summer Solstice in about
Precession of Earth’s axis of rotation is caused by
the gravitational pull of the Moon and the Sun on the equatorial bulge of Earth.
The reason for the slow movement of the vernal equinox through our sky against the background stars over long periods of time is the
precession of the spin axis of Earth.
The precessional motion of the north celestial pole of Earth over a period of 26,000 years is a circle of 47° diameter in the northern sky. The equivalent motion of the south celestial pole is
a circle of 47° diameter, covered in 26,000 years.
Which of the following is the correct sequence of appearances of Moon phases in the sky?
waxing crescent, first quarter, waxing gibbous, full moon
Why do we see different phases of the Moon?
The motion of the Moon in its orbit around Earth causes us to see different amounts of the sunlit side of the Moon
A full moon is always at its highest in our sky at
In its orbit around Earth, the Moon
always keeps the same side toward Earth.
Earth’s shadow falling on the Moon is the reason we see
What is the one major difference between the Sun and the Moon in our sky?
The Sun emits light while the Moon merely reflects it.
At what approximate time does a full moon rise?
A full moon always occurs
when the Moon is farther from the Sun than is Earth.
The phase of the Moon when the Sun and Moon are separated by 6 hours of right ascension is always
either first or third quarter.
When the Sun and Moon are separated by 12 hours of right ascension, the phase of the Moon is always
The correct order of “appearance” of the following “actors” on the “stage” of scientific discovery is
Ptolemy, Copernicus, Kepler, Newton, Einstein.
The word planet is derived from a Greek term meaning
When observing planetary motions from Earth, the phrase “retrograde motion” refers to
a slow westward motion of the planet from night to night against the background stars.
Retrograde motion of a planet against the background stars is always
movement from east to west.
The epicycle in the Greek planetary model is
a small circle through which the planet moves as the center of this circle orbits Earth.
In the geocentric model for the solar system developed by Ptolemy, to what does the word “deferent” refer?
the large circle around Earth through which the center of a smaller circle moves while the planet moves around the smaller circle
When Venus is at inferior conjunction,
it is at its smallest distance from Earth.
When Venus is at superior conjunction,
it is at its greatest distance from Earth.
n which direction is Venus moving when it is at greatest elongation?
directly toward or away from Earth
When Saturn is at its farthest distance from Earth, it is at
Galileo’s early observations of the sky with his newly made telescope included the
fact that Venus showed phases similar to those of the Moon.
How many moons of Jupiter were seen by Galileo?
Which of the following statements correctly states the significance of Galileo’s observation that Jupiter has satellites (moons)?
It showed that bodies can orbit an object other than Earth.
As Venus orbits the Sun, by what factor, as viewed from Earth, does its angular size change from smallest to largest?
Which of the following statements correctly states the significance of Galileo’s observation that Venus shows phases?
The phases were correlated with angular size in a way that supported the heliocentric theory.
In the geocentric model of the solar system, which one of the following phases of Venus should be visible from Earth?
A body whose velocity is constant
has zero acceleration.
Which path would a planet (like Earth) take if the force of gravity from the Sun were to be suddenly removed?
The planet would move in a straight line tangential to its present orbit.
Newton’s law of universal gravitation is so named because it
holds for all objects in the universe.
Suppose that an object is discovered moving around the Sun once every 120 years. Which of the following paths is a possible orbit for this object?
Spring tides occur
twice a month, at full and new moon.
The highest of all tides on Earth’s oceans occur at
full or new moon, at times when Moon and Sun are closest to Earth.
Neap tides occur
twice a month, at first and third quarter moon.
Does the Sun or the Moon have a greater effect in causing the tides on Earth?
The Moon, because it has a larger difference between pulling on the near side and pulling on the far side of Earth
How many “tidal bulges” are there on Earth, due to the Moon’s gravitational pull?
two, one facing (almost) directly toward the Moon and one facing (almost) directly away from the Moon
What are spring tides?
High tides that are significantly higher than the average high tide
The reason the Moon always keeps one face toward Earth is that
gravitational forces from Earth act on the tidal bulge of the Moon.
In 1675, Rømer measured the speed of light by
timing eclipses of Jupiter’s satellites, which appeared to occur later when Earth was farther from Jupiter.
The average distance of Pluto from the Sun is 40 AU. How long does it take for light to travel across the solar system from one side of Pluto’s orbit to the other?
Radio waves travel through space at what speed?
at the speed of light, 3 × 108 m/s
When light passes through a prism of glass, the
different colors or wavelengths of light are separated in angle by the prism.
Around 1670, Isaac Newton performed a crucial experiment on the nature of light when he
demonstrated that the colors that make up white light are intrinsic, not produced by the glass through which the light passes.
Visible light occupies which position in the whole electromagnetic spectrum?
between infrared and ultraviolet
In terms of wavelengths, gamma rays are
the shortest-wavelength electromagnetic waves.
What is the wavelength of electromagnetic radiation whose frequency is 106 cycles per second (106 Hz or 1000 kHz, the frequency of ordinary AM radio)?
On the absolute scale of temperature (in kelvins), the zero of the scale corresponds to the
temperature at which motions of atoms and molecules essentially cease.
A typical but very cool star might have a temperature of 3100°C. On the Kelvin scale, this is about
Wien’s law, relating the peak wavelength λmax of light emitted by a dense object to its temperature T , can be represented by
λmax T = constant.
We plot the intensity of the radiation emitted from a solid object at a certain temperature versus its wavelength. As we increase the temperature, the wavelength at which the spectrum peaks becomes shorter and shorter. This is an illustration of
Wien’s Displacement Law.
We plot the intensity of the radiation emitted from a solid object at a certain temperature versus its wavelength. As we increase the temperature, the total amount of energy emitted all across the spectrum increases as the fourth power of the temperature. This is an illustration of
the Stefan-Boltzmann Law.
Cepheid-variable stars pulsate regularly in size. During the contraction part of the cycle, when the star’s temperature is increasing, the peak wavelength of the emitted radiation
shifts from the visible to the UV part of the spectrum.
The total energy flux F of radiation emitted per unit area by a blackbody (e.g., star) is related to its temperature T and a constant σ by which equation?
F = σT 4
A piece of iron is heated from 400 to 800 K (127 to 527°C). By what factor will the total energy per second emitted by this iron increase?
Pieces of metal are heated by varying amounts in a flame. The hottest of these is the one that shows which color most prominently?
What changes would you expect to see in the resulting spectrum of emitted light from a piece of metal when it is heated slowly in an intense flame from 500 K to 1500 K?
The intensity of radiation would increase and its color would change from red through white to blue.
The spectrum of sunlight, when spread out by a spectrograph, has what characteristic appearance?
continuous band of color, crossed by innumerable dark absorption lines
The dark absorption lines in the solar spectrum are caused by absorption
of sunlight in a cooler layer of gas overlying the hot solar surface.
The star Betelgeuse has a lower surface temperature than the Sun; therefore (with IR = infrared and UV = ultraviolet)
Betelgeuse emits less IR and less UV flux than the Sun.
When a rod of metal is heated intensely, its predominant color
changes from red, through orange to white, and then to blue.
The Sun’s surface has a temperature of 5800 K. What will be the peak wavelength of the spectrum of a star that emits twice the Sun’s flux of energy?
2.5 × 10^-7 m
Atoms in a hot, low-density gas (e.g., in a laboratory-type spectral source) emit a spectrum that is
a series of specific colors, unique to the type of atom in the tube, but fixed in position even when the gas temperature changes.
Why is the sky blue?
The air molecules scatter blue light better than red light, so more blue light reaches our eyes.
The setting Sun appears red because
its light is scattered by a thicker layer of air than during the day.
The physical structure of an atom is
negatively charged electrons moving around a very small but massive, positively charged core.
In a simple atom the electrons making transitions between the outermost energy levels and the innermost energy levels give rise to photons with
the highest energies.
Electrons in atoms
occupy levels whose energies are fixed.
The spectrum of a star shows an equivalent set of dark absorption lines to those of the Sun, but with one exception: Every line appears at a slightly longer wavelength, shifted toward the red end of the spectrum. What conclusion can be drawn from this observation?
The star is moving rapidly away from Earth.
When electromagnetic radiation (e.g., light) is Doppler-shifted by motion of the source away from the detector the
detected wavelength is longer than the emitted wavelength.
When an object is moving toward you the visible radiation which it emits is Doppler shifted toward the
An astronomer photographs the spectrum of an object and finds a spectral line at 499 nm wavelength. In the laboratory, this spectral line occurs at 500 nm. According to the Doppler effect, this object is moving
toward Earth at 1/500 the speed of light.
Compared to its speed in a vacuum (or in space), the speed of light in glass is
As light passes from air into a dense but transparent material it
Lenses are used in applications like microscopes and telescopes. What does a lens do in these applications?
Light which would not otherwise form an image enters a lens and has its direction changed so that it focuses to form an image.
When light passes from air into glass it is refracted. This means that
the wave slows down.
Refraction is the
bending of light as it enters a transparent material.
Which type of telescope uses a lens as the main optical element?
The main reason for building large optical telescopes on Earth’s surface is
to collect more light from faint objects.
A refracting telescope has an objective lens of focal length 80 cm, a diameter of 10 cm, and an eyepiece of focal length 5 cm and diameter 1 cm. What is the magnifying power of this telescope?
A particular reflecting telescope has an objective mirror with a focal length of 1.2 m and an eyepiece lens of focal length 6 mm. What is the magnifying power of this telescope?
Chromatic aberration occurs in a refracting telescope when
all colors of light do not come to the same focal point.
How can you increase the magnification of a refracting telescope without decreasing the light gathering power?
decrease the focal length of the eyepiece
At the mirror of a reflecting telescope, the light reflects from a coated surface rather than refracting through a lens. This eliminates
It is difficult to improve the angular resolution of optical telescopes located on the surface of Earth beyond a certain limit because
air turbulence distorts the star images more than does the telescope optics.
One major difference between radio waves and light is that
radio waves have lower frequencies.
A radio telescope
is very similar to a reflecting optical telescope.
The correct sequence of planets in our solar system from the Sun outward is
Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.
In our solar system, which of the following planets is not a member of the terrestrial group?
In our solar system, which of the following planets is not a member of the Jovian group?
Orbital eccentricity is a number that describes the
shape of the orbital ellipse.
The planet whose orbit is inclined at the greatest angle to the plane of the ecliptic is
A perfect circle is an ellipse with an eccentricity of
The best way to measure the mass of a planet is to measure the
gravitational pull of the planet on an orbiting satellite or a nearby spacecraft.
A curious fact about the structure of the planet Jupiter, compared to that of Earth, is that it has
much greater mass but much lower average density.
Viewed from a position above the north pole of the Sun, the directions of the motions of the planets in their orbits are
Determination of the chemical composition of the atmospheres of the planets is carried out most effectively by what type of study?
spectroscopy—the measurement of absorption features in their spectra
Comets are typically
chunks of ice that begin to vaporize if they pass close to the Sun.
In general, large bodies in the solar system show less evidence of cratering than do small bodies. Why should we expect this correlation?
Large bodies cool more slowly and are more likely to retain internal heat and be geologically active, capable of resurfacing the planet and obliterating craters.
In general, small bodies in the solar system are less likely than large bodies to possess a planet-wide magnetic field. Why should we expect size and magnetism to be correlated?
A small body cools more rapidly and is less likely to possess a molten, liquid interior — one requirement for planet-wide magnetism.
One distinct difference between Earth and its neighboring planets, Venus and Mars, is the presence of
liquid water on its surface and water molecules chemically locked into rocks.
The albedo of a planet is the fraction of energy that is
reflected by the whole planet, including atmosphere and surface.
The greenhouse effect is the
absorption by atmospheric gases of infrared radiation emitted by a planet that has been heated by solar visible and ultraviolet radiation.
Earth has an average density of
5.5 times that of water.
“Chemical differentiation” in planetary sciences refers to
the sinking of heavier elements toward the center of a planet and the floating of lighter elements toward the surface.
The mantle of Earth is composed of
What is the basic structure of Earth’s interior?
solid iron inner core, molten iron outer core, rocky mantle, lighter rocky crust
Earth’s magnetic field is caused by
electric currents flowing in the molten core.
The auroral display of northern and southern lights in the atmosphere is caused by
solar wind electrons hitting the high atmosphere after being accelerated by the magnetosphere.
Photosynthesis is a chemical process which takes place in green plants. What is its effect on our atmosphere?
Photosynthesis consumes carbon dioxide from our atmosphere and produces oxygen.
Which is the most abundant gas in Earth’s atmosphere?
Why did Earth’s earliest atmosphere, composed primarily of hydrogen, not last long?
Hydrogen is a very light gas, and it soon escaped into space.
The major layers of Earth’s atmosphere from the surface upward in correct order are
troposphere, stratosphere, mesosphere, thermosphere.
In which layer of Earth’s atmosphere does all weather occur?
In which layer of Earth’s atmosphere is the ozone layer located?
In its orbit around Earth, the Moon
always keeps the same side toward Earth.
How long is a “lunar day,” or the time between two successive sunrises or sunsets on the Moon?
about 1 month
Astronauts at a Moon base visible from Earth will NOT see
Earthrise or Earthset.
The Moon has
no measurable atmosphere or liquid water.
Maria on the Moon exist
only on Earth-facing side of the Moon.
Why are the lunar maria concentrated almost entirely on the near side of the Moon?
The crust is thicker on the far side of the Moon, restricting massive lava flows after asteroid impact.
The mountains on the Moon were mostly caused by
impacts from meteoroids from outer space.
One effect of the ocean water’s tidal drag on Earth is to
slow down Earth’s spin rate.
Because of the tides on Earth’s oceans, the Moon is
spiraling outward away from Earth.
Which of the following is believed to be the correct explanation for the origin of the Moon?
Earth was struck by a large planetesima, which caused material to be ejected. This material coalesced to form the Moon.
The existence of stars composed almost entirely of neutrons was first predicted by
Fritz Zwicky and Walter Baade, in 1933.
A pulsar is
a rapidly rotating neutron star, emitting beams of radio radiation and in some cases X-rays and visible light
The pulsation periods of most pulsars are in the range
of 1/1000 second and a few seconds.
The very strong magnetic field of a neutron star is created by
the collapse of a star, which significantly intensifies the original weak magnetic field of the star.
The strength of the magnetic field around a typical neutron star is
about a trillion (1012) gauss, or about a million times stronger than the strongest magnetic fields ever produced in laboratories on Earth.
The periods of most pulsars
increase with time.
Synchrotron radiation is emitted whenever
charged particles are forced to move along curved paths within a magnetic field.
Glitches are occasionally observed by astronomers studying pulsars. What are these glitches?
sudden increases in rotation rate
Astronomers believe neutron stars may have atmospheres. What form of evidence do we have for this?
dips in the X-ray spectrum emitted by the neutron star suggesting that these wavelength ranges are absorbed by an atmosphere
The Black Widow pulsar is unusual because it appears to
be eating away at its companion star.
The age of the solar system has been dated rather precisely to 4.56 billion years. What method was used to determine this number?
determining the age of meteorites by radioactive dating
The most common elements in the universe are
hydrogen, smaller quantities of helium, and very small quantities of heavier elements.
Together, hydrogen and helium account for what percentage of the total mass of all matter in the universe?
What fraction of the mass of the universe is in the form of atoms other than hydrogen and helium?
Where in the universe are heavy elements with masses greater than that of helium being produced at this time?
central cores of stars
What was the form of the material from which the solar system formed?
a nebula made mostly of hydrogen and helium gas, but enriched in heavier elements from supernova explosions
The temperature began to rise at the center of the solar nebula because
the nebula was contracting, increasing the speed of motion of the atoms.
Which of the following statements is an example of Kelvin-Helmholtz contraction?
A contraction of a dense cloud of gas slowly gets hotter due to the release of gravitational energy.
Which one of the following is not an example of the conservation of angular momentum?
The Moon always keeps one face pointed toward Earth.
The most probable time sequence for the solar system’s formation was that the
Sun contracted first as a gas ball, and the planets and moons formed shortly afterward by accretion and condensation.
The process of accretion in planetary formation is the
slow accumulation of solid particles by gravity and collision into larger, solid objects.
The formation of terrestrial-type planets around a star is most likely to have occurred by what process?
accretion, or slow accumulation of smaller particles by mutual gravitational attraction
What is the process of chemical differentiation?
the sinking of heavy material to the center of a planet or other object and the rising of lighter material toward the surface
The reason most of the terrestrial planets have dense, iron cores is because
terrestrial planets were initially molten or partially molten, and the iron sank to the center.
A Tauri wind is
a rapid expulsion of the tenuous outer layers of a young star.
The Oort cloud is
a spherical solar system halo of icy objects far beyond the orbit of Pluto.
Astrometry is the very precise measurement of
a star’s position in the sky (e.g., to measure its motion).
So far, what is the typical mass of the majority of extrasolar planets discovered?
between the the mass of Saturn and a few times the mass of Jupiter
What is “special” about the special theory of relativity?
It deals only with objects moving in a straight line at constant speed.
In order to use the theory of special relativity to describe an object’s motion, the object must be moving
at a constant speed in a straight line; how fast it is moving is not important.
Einstein’s theory of special relativity contains some very strange ideas such as time dilation (moving clocks run slow), length contraction (moving lengths are shorter), and lack of absolute simultaneity. What are these ideas based upon?
The speed of light is the same for all observers in all reference frames.
Suppose you are in a jet airliner traveling at a constant speed of 400 km/h in a constant direction. All windows are blocked so you cannot see outside, and there are no vibrations from the engines. What experiment can you do to determine that you are in fact moving?
None. All experiments will give the same results as when you are at rest on the ground.
You are flying your spacecraft on a parallel course with another spacecraft and at the same speed. You are both moving past Earth at an appreciable fraction of the speed of light. Which one of the following statements correctly describes the relationship between your clock and the clock in the other spacecraft?
You will see the clock in the other spacecraft running at the same rate as yours.
Two rocket ships are traveling past Earth at 90% of the speed of light in opposite directions (i.e., they are approaching each other). One turns on a searchlight beam, which is seen by scientists aboard the second spaceship. What speed do the scientists measure for this light? (c = speed of light in a vacuum)
If you see an object moving past you at 90% of the speed of light, you will measure the length of this object to be
shorter than if it were at rest.
Einstein’s principle of equivalence in his general theory of relativity asserts that
being at rest in a gravitational field is equivalent to being in an upwardly accelerated frame of reference in a gravity-free environment.
According to general relativity, why does Earth orbit the Sun?
Space around the Sun is curved and Earth follows this curved space.
Black holes are so named because
no light or any other electromagnetic radiation can escape from inside them.