Question 1

What major contribution did the German mathematician Karl Friedrich Gauss make to astronomy? A)He discovered a regular progression of planetary distances from the Sun, so that each planet's orbit could be calculated knowing the distance of any one planet from the Sun. B)He developed a method for computing an object's temperature from measurements of the intensity of emitted light at only two wavelengths. C)He derived the Stefan-Boltzmann law, emitted flux = $\sigma$ T⁴, mathematically, from basic physical principles. D)He developed a method for computing an object's orbit from only three observations.

Accepted Answer

Karl Friedrich Gauss developed a method for computing an object's orbit from only three observations, known as the method of least squares. This significantly improved the accuracy of predicting the orbit of celestial bodies and was used extensively in astronomy. While Gauss made other important contributions to mathematics and science, such as the Gaussian distribution, they were not as directly relevant to astronomy as his method of computing orbits.

Question 2

The object found about 2.8 au from the Sun when astronomers were looking for a "missing" planet between the orbital distances of Mars and Jupiter was:
A)the asteroid Ceres.
B)Pluto.
C)Halley's Comet.
D)Mercury.

Accepted Answer

The asteroid Ceres was the first object discovered in the asteroid belt between Mars and Jupiter, which was initially thought to be a missing planet. It was found at a distance of about 2.8 astronomical units (AU) from the Sun. Pluto is located much further out in the Kuiper Belt, Halley's Comet has a highly elliptical orbit that takes it far beyond the orbit of Jupiter, and Mercury is an inner planet that orbits close to the Sun.

Question 3

Most asteroids:
A)are dark and spherical in shape, with many craters on their surfaces.
B)are spherical and ice coated, and hence light colored and shiny.
C)are irregularly shaped and covered with very light-colored dust that reflects sunlight well.
D)are dark, irregular in shape, and heavily cratered.

Accepted Answer

According to current knowledge, most asteroids are dark, irregular in shape, and heavily cratered.

Question 4

How big is the largest asteroid, Ceres, in comparison with the largest mare or impact basin on the Moon, Mare Imbrium?
A)Ceres is much larger than Mare Imbrium.
B)Ceres is much smaller, because asteroids are very small objects (1 km diameter), whereas maria are large (100-1000 km diameter).
C)The Mare Imbrium is much larger than Ceres.
D)Their size is very similar-about 1000 km across.

Accepted Answer

Both Ceres and Mare Imbrium have a diameter of approximately 1000 km, making them roughly the same size.

Question 5

How do the biggest asteroids compare in size with the Moon?
A)They are very much smaller (less than 1/10).
B)They are between 1/10 and 1/2 as large.
C)They are about the same size.
D)They are very much larger (greater than 5×).

Accepted Answer

The largest asteroid, Ceres, has a diameter of about 590 miles (940 kilometers) whereas the Moon's diameter is about 2,159 miles (3,474 kilometers). Therefore, the biggest asteroids are between 1/10 and 1/2 as large as the Moon.

Question 6

The combined matter in the asteroid belt would produce an object of what approximate size?
A)about 1500 km in diameter-significantly smaller than the Moon
B)about the size of Earth
C)only a few kilometers in diameter-similar to an average mountain on Earth
D)about the size of Mercury

Accepted Answer

The combined matter in the asteroid belt would produce an object called a dwarf planet, and the largest known dwarf planet in the asteroid belt is Ceres, which has a diameter of about 950 km. Therefore, it is reasonable to assume that the combined matter in the asteroid belt would only produce an object of about 1500 km in diameter, which is significantly smaller than the Moon.

Question 7

The asteroid belt extends from 2 to 3.5 au from the Sun. If we take the average radius to be 2.75 au, what is the average sidereal period?
A)1.99 years
B)2.8 years
C)4.56 years
D)46.8 years

Accepted Answer

Using Kepler's third law, the sidereal period (P) in years is approximately equal to the square root of the cube of the semi-major axis (a) in astronomical units: P = √(a^3). For a = 2.75 au, P = √(2.75^3) ≈ 4.56 years.

Question 8

The name 1987 FD refers to the:
A)fourth asteroid to be discovered in the month of February 1987.
B)sixth asteroid to be discovered in the month of April 1987.
C)1987th asteroid ever to be discovered, named after Frances Draibre.
D)fourth asteroid to be discovered during the second half of March 1987.

Accepted Answer

The name 1987 FD indicates it was the fourth asteroid discovered during the second half of March 1987. The year is given first (1987), followed by a letter for the half-month of discovery (F for the second half of March), and a sequential letter indicating its order of discovery (D for the fourth discovery).

Question 9

The Titus-Bode Law is derived from:
A)Newton's laws of motion.
B)the conservation of energy and angular momentum.
C)Kepler's third law.
D)None of the above is correct. The Titus-Bode "law" is more of a coincidence than a fundamental law of nature.

Accepted Answer

The Titus-Bode Law, which predicts the spacing of the planets in the Solar System, is not derived from fundamental principles like Newton's laws of motion, the conservation of energy and angular momentum, or Kepler's third law. Instead, it is considered more of a coincidence or an empirical observation rather than a fundamental law of nature.

Question 10

Astronomers have been searching for additional planets, especially since the discovery of Uranus in 1781. But why were efforts concentrated around 2 to 3 au from the Sun in the early nineteenth century?
A)Kepler's third law predicts a planet within this distance.
B)The Titus-Bode law predicts a planet within this distance.
C)The discrepancies in Uranus's orbit suggested a planet around this radius.
D)The telescope, newly invented in 1781, was not powerful enough to detect anything beyond this range.

Accepted Answer

The Titus-Bode law predicted a planet to be located at a distance of 2 to 3 au from the Sun.

Question 11

How well does Ceres fit the Titus-Bode rule?
A)Neither the Ceres/Mars ratio nor the Jupiter/Ceres ratio falls into the range suggested by the Titus-Bode rule.
B)The Ceres/Mars ratio fits the Titus-Bode rule but the Jupiter/Ceres ratio does not.
C)The Ceres/Mars ratio does not fit the Titus-Bode rule but the Jupiter/Ceres ratio does.
D)Both the Ceres/Mars ratio and the Jupiter/Ceres ratio fall into the range suggested by the Titus-Bode rule.

Accepted Answer

The answer of How well does Ceres fit the Titus-Bode...

Question 12

The orbits of asteroids have a surprisingly large variety of semimajor axes, eccentricities, and inclinations to the ecliptic compared to most of the major planets. Which of these seems to be a reasonable explanation for this?
A)Asteroids are "small" objects, and they formed with the kinds of orbits they now have.
B)The orbits were stirred up when the Sun passed within the Oort cloud of another star.
C)Jupiter's gravitational pull has stirred up the asteroid orbits.
D)One or more Mars-sized planets formed in the asteroid belt, and their gravitational influence stirred up the orbits of the rest of the asteroids.

Accepted Answer

Jupiter's large mass and gravitational pull can disturb the orbits of asteroids, causing them to have a wide range of semimajor axes, eccentricities, and inclinations. This phenomenon is known as the "Jupiter-Saturn barrier" and is believed to be the reason why there are no planets in the asteroid belt.

Question 13

The Kirkwood gaps are found in the:
A)equatorial region of the Sun.
B)rings of Saturn.
C)spectrum of hydrogen gas.
D)asteroid belt.

Accepted Answer

The Kirkwood gaps are gaps found in the asteroid belt between the orbits of Mars and Jupiter. These gaps are caused by the gravitational influence of Jupiter, which causes asteroids with certain orbital periods to have unstable orbits and be ejected from the asteroid belt.

Question 14

The Kirkwood gaps are primarily caused by:
A)the gravitational tug of Jupiter nudging asteroids into new orbits.
B)shepherd satellites controlling the orbits of ring particles.
C)orbits of material being disturbed because Jupiter's gravitational field balances the Sun at this distance, and objects can escape from the solar system.
D)large asteroids sweeping parts of the asteroid belt clear of smaller asteroids.

Accepted Answer

The Kirkwood gaps are regions in the asteroid belt where there are significantly fewer asteroids. This is due to the gravitational influence of Jupiter, which nudges asteroids into new orbits and either ejects them from the asteroid belt or sends them crashing into the Sun or other planets. These gaps occur at specific resonant orbits where Jupiter's gravity interacts with the asteroid's orbit in a predictable way.

Question 15

What is the relationship between the Kirkwood gaps in the asteroid belt and the Cassini and Enke divisions in the rings of Saturn?
A)Both are caused by large objects passing through swarms of smaller objects, sweeping out gaps in the swarms.
B)Both were discovered by observers from the same group; Kirkwood and Enke worked at the Cassini Observatory.
C)Both are caused by selective melting of material at these specific locations from the central radiating body, the Sun and Saturn respectively.
D)Both are caused by disruptions of orbits of small objects by a larger object whose orbital period is a simple ratio of that of the small objects.

Accepted Answer

Both the Kirkwood gaps in the asteroid belt and the Cassini and Enke divisions in the rings of Saturn are caused by disruptions of the orbits of small objects by larger objects whose orbital period is a simple ratio of that of the small objects. In the case of the asteroid belt, Jupiter's gravity disrupts the orbits of asteroids whose orbital periods are in a simple ratio with Jupiter's, resulting in gaps in their distribution. In the case of the rings of Saturn, gravitational interactions with Saturn's moons disrupt the orbits of ring particles whose orbital periods are in a simple ratio with the moons, resulting in gaps in the rings.

Question 16

What influence did Jupiter have on the formation of the asteroid belt, and how do we know?
A)We have watched other solar systems in their early stages of formation. They show Jupiter-size planets clearing out much of their asteroid belts.
B)Computer simulations have shown that in the absence of a Jupiter-size planet, an Earth-size planet would have formed in the asteroid belt.
C)Computer simulations have shown that a Jupiter-size planet has no influence on the formation of the asteroid belt.
D)We have watched other solar systems in their early stages of formation. They show that Jupiter-size planets have no influence on the formation of an asteroid belt.

Accepted Answer

Computer simulations suggest that Jupiter's strong gravitational influence prevented the material in the asteroid belt from coalescing into a planet, which is why an Earth-size planet did not form there.

Question 17

If objects in the asteroid belt are prevented from occupying an orbit for which their period would be one-third of that of Jupiter because of repeated gravitational disturbances, at what distance would you expect a gap in the asteroid belt?
A)1.0 au
B)7.86 au
C)3.28 au
D)2.5 au

Accepted Answer

The gap occurs at a distance where the orbital period is one-third of Jupiter's. Using Kepler's third law, the semi-major axis for this period is approximately 2.5 au.

Question 18

It is believed there were originally far more objects in the asteroid belt than there are now. What happened to the rest of them?
A)The gravitational influence of Jupiter deflected most of them out of the solar system.
B)Mars-sized objects moving through the asteroid belt disrupted the orbits and deflected most of them out of the solar system.
C)The majority of the original asteroids coalesced to form a series of Mars-sized objects, one of which struck Earth and caused the formation of the Moon.
D)A passing star pulled most of the original asteroids out of the solar system.

Accepted Answer

The gravitational influence of Jupiter has played a significant role in shaping the asteroid belt. Jupiter's massive gravity has deflected many objects out of the asteroid belt, either by ejecting them from the solar system or by sending them into the inner solar system. This process has significantly reduced the number of objects originally present in the asteroid belt.

Question 19

A technique that is proving very useful for determining the shapes of a large number of asteroids is:
A)radar signals reflected from the asteroid's surface.
B)direct photography from spacecraft.
C)optical and infrared Doppler shift measurements as the asteroid rotates.
D)CCD photography using large, Earth-based telescopes.

Accepted Answer

Radar signals reflected from the asteroid's surface can provide detailed information about its shape and surface features. This technique has been used extensively in recent years to study asteroids. Direct photography from spacecraft can also provide shape information, but it is only feasible for a few specific asteroids that have been visited by spacecraft. Optical and infrared Doppler shift measurements can provide information about rotation rate, but may not reveal shape details. CCD photography using large telescopes can also provide shape information, but is limited by the size of the telescope and atmospheric conditions.

Question 20

The general shape of most asteroids is thought to be:
A)double lobed, as though two asteroids had stuck together.
B)perfectly spherical.
C)oblong but smooth.
D)irregular.

Accepted Answer

Most asteroids are irregular in shape, with no set shape or symmetry. This is because they are too small to have enough gravity to shape themselves into a sphere.

Quiz 15: Asteroids, Comets, and Impacts

What major contribution did the German mathematician Karl Friedrich Gauss make to astronomy?

The object found about 2.8 au from the Sun when astronomers were looking for a "missing" planet between the orbital distances of Mars and Jupiter was:

Most asteroids:

How big is the largest asteroid, Ceres, in comparison with the largest mare or impact basin on the Moon, Mare Imbrium?

How do the biggest asteroids compare in size with the Moon?

The combined matter in the asteroid belt would produce an object of what approximate size?

The asteroid belt extends from 2 to 3.5 au from the Sun. If we take the average radius to be 2.75 au, what is the average sidereal period?

The name 1987 FD refers to the:

The Titus-Bode Law is derived from:

Astronomers have been searching for additional planets, especially since the discovery of Uranus in 1781. But why were efforts concentrated around 2 to 3 au from the Sun in the early nineteenth century?

How well does Ceres fit the Titus-Bode rule?

The orbits of asteroids have a surprisingly large variety of semimajor axes, eccentricities, and inclinations to the ecliptic compared to most of the major planets. Which of these seems to be a reasonable explanation for this?

The Kirkwood gaps are found in the:

The Kirkwood gaps are primarily caused by:

What is the relationship between the Kirkwood gaps in the asteroid belt and the Cassini and Enke divisions in the rings of Saturn?

What influence did Jupiter have on the formation of the asteroid belt, and how do we know?

If objects in the asteroid belt are prevented from occupying an orbit for which their period would be one-third of that of Jupiter because of repeated gravitational disturbances, at what distance would you expect a gap in the asteroid belt?

It is believed there were originally far more objects in the asteroid belt than there are now. What happened to the rest of them?

A technique that is proving very useful for determining the shapes of a large number of asteroids is:

The general shape of most asteroids is thought to be: