Question 1

Light from fires that were lit at the time of the Battle of Hastings in England in a.d.1066 has traveled out into space at the speed of light.How far out into space has this light now reached,compared with the distances to the 20 brightest stars (see Appendix,Table C-6,Comins,Discovering the Essential Universe,6th ed.)?

Accepted Answer

The Battle of Hastings occurred in 1066, which is approximately 957 years ago. Light travels at about 5.88 trillion miles per year, so the light has traveled approximately 5,628 trillion miles. This distance is beyond Sirius, Betelgeuse, and Rigel, but not beyond Deneb, which is about 1,400 light-years away.

Question 2

If Halley's Comet has an elliptical orbit with a semimajor axis of 17.5 AU,approximately how far out into the planetary system does it reach at its farthest point (aphelion)? (Assume that perihelion distance from the Sun is negligible.Be careful-the question needs some thought.)

Accepted Answer

The aphelion distance can be calculated using the formula: aphelion = 2 * semimajor axis - perihelion. Given the semimajor axis is 17.5 AU and assuming the perihelion is negligible, the aphelion is approximately 35 AU, which places it between the orbits of Neptune and Pluto.

Question 3

An inhabitant of a planet orbiting the star Betelgeuse observes the flash from the first nuclear weapon on Earth,exploded in July 1945.If this extraterrestrial being were to send a signal to Earth immediately to confirm this sighting by exploding a bomb of equivalent brightness,and astronomers on Earth were watching his planet,when would they expect to see the flash?

Accepted Answer

Betelgeuse is located approximately 640 light-years away from Earth. This means that the flash from the first nuclear weapon on Earth would take 640 years to reach Betelgeuse. Therefore, if the extraterrestrial being were to explode a bomb of equivalent brightness immediately after observing the flash from Earth, the light from that explosion would take an additional 640 years to reach Earth.

The first nuclear weapon was detonated in July 1945, so if the extraterrestrial being were to immediately send a signal to Earth, we would receive it in 1985 (1945 + 640 years = 1985). If the astronomers on Earth were watching the planet at that time, they would see the flash from the explosion.

Therefore, the year we would expect to see the flash from the extraterrestrial explosion would be 1985 + 814 (which is half of the time it takes for light to travel from Betelgeuse to Earth) = 2799. Thus, the correct answer is C) a.d. 2799.

Question 4

If light takes about 8.3 minutes to travel from the Sun to Earth,approximately how much longer would light take to travel from Jupiter to Earth when Jupiter is at conjunction (appearing closest to the Sun in our sky)than when it is at opposition (on the opposite side of Earth from the Sun)? (Assume that light from Jupiter is not blocked by the Sun at conjunction.A diagram might help.)

Accepted Answer

At conjunction, light travels from Jupiter to the Sun and then to Earth, taking about 43.2 minutes. At opposition, light travels directly from Jupiter to Earth, taking about 35.6 minutes. The difference is approximately 7.6 minutes, which rounds to 8.3 minutes.

Question 5

Suppose an asteroid is discovered with an elliptical orbit,a period of exactly one year,and perihelion 0.5 AU from the Sun.Using Kepler's third law,how far from the Sun is this asteroid at aphelion? (Drawing a diagram of the orbit,including the Sun,will help.)

Accepted Answer

Kepler's third law states that the square of the orbital period is proportional to the cube of the semi-major axis. Since the period is one year, the semi-major axis is 1 AU. The perihelion is 0.5 AU, so the aphelion must be 1.5 AU to maintain the semi-major axis of 1 AU.

Question 6

Halley's Comet returns to the Sun's vicinity approximately every 76 years in an elliptical orbit.According to Kepler's third law,what is the semimajor axis of this orbit?

Accepted Answer

Kepler's Third Law states that the square of the period of a planet (or comet) orbiting the Sun is proportional to the cube of the semimajor axis of its orbit. Halley's Comet has a period of approximately 76 years, so we can determine its semimajor axis as follows:

T^2 = a^3
76^2 = a^3
a = (76^2)^(1/3)
a = 17.904 AU (rounded to three significant figures)

Therefore, the semimajor axis of Halley's Comet's elliptical orbit is approximately 17.9 AU. Therefore, the correct choice is B.

Question 7

Why do astronomers need special units,in addition to the metric system of units such as meters and kilograms,to describe the universe?

Accepted Answer

The distances and masses involved in astronomical objects are extremely large, making it cumbersome to represent them in metric units. Therefore, astronomers use specialized units such as astronomical units, light-years, and solar masses to describe the universe.

Question 8

If we sent a radio message toward the star nearest to the Sun,and intelligent beings from a planet near the star sent back a reply immediately on receipt of the message,how long after our transmission would we have to wait for a reply?

Accepted Answer

The nearest star to the Sun is Proxima Centauri, which is 4.22 light-years away from us. This means that it would take 4.22 years for our radio message to reach the star. And if the intelligent beings respond immediately upon receiving the message, it would take another 4.22 years for their reply to reach us. Therefore, we would have to wait a total of 8.6 years for a reply.

Question 9

One light-year is the:

Accepted Answer

A light-year is defined as the distance that light travels in one year. It is equal to approximately 9.46 trillion kilometers or 5.88 trillion miles.

Question 10

An asteroid-like object (or a cometary nucleus)is seen to be orbiting the Sun in a circular path with a period of 120 years.What is its distance of closest approach to Earth (the separation distance when the object is at opposition)? (Be careful with your answer; a diagram might be helpful.)

Accepted Answer

The answer of An asteroid-like object (or a cometary nucleus)is...

Question 11

A light-year is a measure of:

Accepted Answer

A light-year is the distance that light travels in a vacuum in one year. Therefore, it is a measure of distance.

Question 12

If a supernova was first seen in the year of Christ's birth (the Star of Bethlehem?)and its distance from Earth was 3 kpc,approximately when did the supernova actually explode?

Accepted Answer

The answer of If a supernova was first seen in...

Question 13

Suppose that,at the same time on the same night,we see two supernovas (exploding stars)explode in the night sky.If one is in the Andromeda Galaxy,2 million light-years away from us,and the other is in the galaxy M82,6 million light-years away from us,which of the following statements concerning the actual explosion times of these supernovas is CORRECT?

Accepted Answer

The answer of Suppose that,at the same time on the...

Question 14

A comet is observed to return to the vicinity of the Sun on a long elliptical orbit with a period of 31.7 years.What is the semimajor axis of the orbit?

Accepted Answer

The semimajor axis (a) of a comet's orbit can be found using Kepler's Third Law, which states that the square of the orbital period (P) is proportional to the cube of the semimajor axis (a): P^2 = a^3. For a period of 31.7 years, solving for a gives approximately 10 AU.

Question 15

One light-year is a distance of approximately:

Accepted Answer

A light-year is defined as the distance that light travels in one year, which is approximately 9.5 × 10¹² km. Therefore, option C is the correct answer. Options A and B are much smaller distances, whereas option D is about 1/60th the actual value of a light-year.

Question 16

Suppose we were to observe two supernovas (exploding stars)exploding in the night sky on a particular night.If one was in the nearby arm of the Milky Way Galaxy while the other was in the Andromeda Galaxy,M31,2 million light-years away from us,which of the following statements concerning the actual explosion times of these supernovas is CORRECT?

Accepted Answer

The light from the supernova in the Andromeda Galaxy took 2 million years to reach us, while the light from the supernova in the Milky Way took much less time. Therefore, the Andromeda supernova actually occurred long before the one in our Galaxy.

Question 17

In a.d.2012,an inhabitant of a planet orbiting a distant star observed the flash of the first nuclear explosion on Earth,which occurred in July 1945.Approximately how far away is his solar system from Earth?

Accepted Answer

To solve this problem, we need to use the fact that the speed of light is constant and equals approximately 299,792,458 m/s.

The time between the first nuclear explosion on Earth in July 1945 and the observation of the flash in a.d.2012 is:

t = 2012 - 1945 = 67 years

To find the distance traveled by the light emitted by the explosion, we can use the formula:

d = c*t

where d is the distance traveled by the light, c is the speed of light, and t is the time.

Plugging in the values, we get:

d = 299,792,458 m/s * (67 years * 365.25 days/year * 24 hours/day * 3600 s/hour)

Simplifying, we get:

d = 20.6 parsecs

Therefore, the best choice is B) 20.6 pc.

Question 18

The time taken for light to travel from a galaxy that is 10 Mpc away is:

Accepted Answer

The speed of light is approximately 3 × 10⁸ m/s. 
1 Mpc is equivalent to 3.086 × 10¹⁹ meters. 
So, the distance to the galaxy in meters is:

10 Mpc × 3.086 × 10¹⁹ m/Mpc = 3.086 × 10²⁰ m.

The time for light to travel this distance is:

time = distance / speed 
time = (3.086 × 10²⁰ m) / (3 × 10⁸ m/s)

time = 1.029 × 10¹² s

Converting this to years:

time = 1.029 × 10¹² s × (1 year / 3.154 × 10⁷ s)

time = 3.26 × 10⁷ years

Therefore, the answer is D: 3.26 × 10⁷ years.

Question 19

An astronomical unit (AU)is a unit of:

Accepted Answer

An astronomical unit is defined as the average distance between the Sun and Earth, which is approximately 149.6 million kilometers or 93 million miles.

Question 20

1 AU,or 1 astronomical unit,is defined as the:

Accepted Answer

An astronomical unit (AU) is defined as the mean distance between the Earth and the Sun. It is used as a standard unit of measurement for distances within the solar system.

Quiz 2: Gravitation and the Waltz of the Planets

If Halley's Comet has an elliptical orbit with a semimajor axis of 17.5 AU,approximately how far out into the planetary system does it reach at its farthest point (aphelion) ? (Assume that perihelion distance from the Sun is negligible.Be careful-the question needs some thought.)