Question 1

Stellar parallax is the:

Accepted Answer

Stellar parallax is the apparent shift in the position of a nearby star because of Earth's motion. As the Earth orbits around the Sun, nearby stars appear to move slightly relative to more distant stars. This shift in position is called stellar parallax and allows astronomers to estimate the distance to stars.

Question 2

Stellar parallax is used to determine which of the following properties of a nearby star?

Accepted Answer

Stellar parallax is the apparent shift of a nearby star's position against the background of more distant stars as the Earth orbits around the Sun. By measuring the angle of this apparent shift, astronomers can determine the distance between the star and the Earth, which is a crucial piece of information in determining a star's properties, such as its size, luminosity, and age. Therefore, the correct choice is D, its distance from the Sun.

Question 3

The most straightforward way to measure the distance to a nearby star uses:

Accepted Answer

The most straightforward way to measure the distance to a nearby star is through parallax measurement. Parallax is the apparent shift in the position of a nearby object against the background of distant objects when viewed from two different positions. By measuring the angular shift of the star against distant objects at two points in Earth's orbit six months apart, astronomers can calculate the star's distance using trigonometry.

Question 4

How many stars (other than the Sun) have a stellar parallax greater than 1 second of arc?

Accepted Answer

A stellar parallax greater than 1 second of arc means the star is within 1 parsec (3.26 light years) from Earth. Currently, only the Sun has a parallax greater than 1 second of arc as all other stars are too far away for their parallax to be measured accurately. Therefore, the answer is 0.

Question 5

If a nearby star shows a parallax of 0.5 arcsec, what is its distance from Earth in light-years?

Accepted Answer

The distance to a star in light-years is given by the reciprocal of its parallax in arcseconds. So, the distance to this star is 1/0.5 = 2 light-years.

Question 6

If a nearby star shows a parallax of 0.5 arcsec, what is its distance from Earth in parsecs?

Accepted Answer

The distance in parsecs can be calculated as the reciprocal of the parallax angle in arcseconds, so 1/0.5 = 2 parsecs.

Question 7

The triple star system α Centauri has the largest known stellar parallax angle, namely 0.75 arcsec. How far is this star system from the Sun in light-years? (Careful with units!)

Accepted Answer

The formula for calculating distance (d) in light-years based on parallax angle (p) in arcseconds is d=1/p. Using this formula with the given parallax angle of 0.75 arcsec, we get d=1/0.75=1.33 light-years. Therefore, the correct answer is C.

Question 8

The triple star system α Centauri has the largest known stellar parallax angle, namely 0.75 arcsec. How far is this star system from the Sun in parsecs? (Careful with units!)

Accepted Answer

The answer of The triple star system α Centauri has...

Question 9

Proxima Centauri is the nearest star beyond the Sun. Its distance is roughly:

Accepted Answer

Proxima Centauri is approximately 1 parsec (pc) away from Earth, which is about 3.26 light-years or roughly 30 trillion kilometers.

Question 10

The total apparent motion against the background sky as a result of Earth's motion halfway around its orbit of a star whose distance from the Sun is 40 pc is:

Accepted Answer

The total apparent motion against the background sky is equal to twice the angular value of the Earth's semi-major axis divided by the distance to the star. Earth's semi-major axis is 1 AU which is approximately 1.496 x 10^11 meters. Halfway around its orbit corresponds to a distance of 0.5 AU. Therefore, the angular motion is:

2 * (0.5 * 1.496 x 10^11 meters) / (40 x 3.086 x 10^16 meters) = 0.0125 arcseconds

Question 11

The apparent angular movement of a nearby star against the background stars as a consequence of its motion in space is known as:

Accepted Answer

Proper motion is the term used to describe the apparent shift in the position of a star relative to distant background stars due to its actual motion through space. This motion is measured in units of arcseconds per year and can be used to determine the distance, direction, and speed of a star's motion through our galaxy. Radial velocity refers to the motion of a star towards or away from an observer, while tangential velocity refers to its motion perpendicular to the line of sight. Retrograde motion is a term used to describe the apparent backwards motion of planets in the sky, as seen from Earth.

Question 12

Proper motion of a star is defined as its:

Accepted Answer

Proper motion of a star refers to its apparent motion across the sky relative to more distant background stars, observed from Earth over a period of time. This motion is due to the star's actual movement through space, not related to the Doppler shift of its spectral lines (which measures radial velocity) or Earth's orbital motion.

Question 13

If a star moves in space, its proper motion appears as an angular displacement against the background stars. Its parallax motion also appears as an angular displacement against the background stars. How can we tell the difference?

Accepted Answer

Parallax motion is a result of Earth's orbit around the Sun, causing nearby stars to appear to move back and forth against the more distant stars over a one-year period. This motion is periodic, repeating every year. Proper motion, on the other hand, is the actual motion of a star through space relative to the Sun, and it does not exhibit a periodic pattern. Therefore, by observing the motion over time, astronomers can distinguish between the two based on whether the motion repeats (parallax) or is in a consistent direction (proper motion).

Question 14

Suppose a star lying on the celestial equator has a proper motion, directed along the equator, equal to the rather large value of Barnard's star, namely 10 arcsec/yr. How long would it take this star to change its right ascension by 1 hour?

Accepted Answer

The celestial equator is 360 degrees, and 1 hour of right ascension corresponds to 15 degrees. With a proper motion of 10 arcsec/yr, it would take 5400 years to change by 15 degrees (1 hour of right ascension), since 15 degrees equals 54000 arcseconds.

Question 15

The proper motion of a star is:

Accepted Answer

The proper motion of a star is the angle per unit time at which the star moves across our sky against the background stars. This is due to the star's actual motion through space relative to the Sun. It is measured in units of arcseconds per year.

Question 16

The speed of a star in km/s, measured in a direction perpendicular to the line of sight from Earth to the star, is known as:

Accepted Answer

Tangential velocity is the speed of the star in a direction perpendicular to the line of sight from Earth to the star. Proper motion is the apparent motion of a star across the sky, and radial velocity is the speed of the star in the line of sight from Earth, towards or away from us. Retrograde motion is the apparent motion of a planet moving in the opposite direction to the other celestial bodies in its system, as seen from Earth.

Question 17

What two quantities do we need to measure to calculate the tangential velocity of a star?

Accepted Answer

To calculate the tangential velocity of a star, we need to know its distance from us and its proper motion, which is the motion of the star across the sky perpendicular to our line of sight.

Question 18

The star Procyon has a parallax of 0.287 arcsec and a proper motion of 1.25 arcsec per year. What is the tangential velocity of Procyon?

Accepted Answer

To find tangential velocity, we use the formula:
vtangential = 4.74 × proper motion × distance
where proper motion is in seconds of arc per year and distance is in parsecs.
distance = 1/parallax = 1/(0.287 arcsec) ≈ 3.48 pc
vtangential = 4.74 × 1.25 arcsec/year × 3.48 pc = 20.6 km/s ≈ 21 km/s (rounded to the nearest km/s)

Question 19

The star Ross 128 has a parallax of 0.301 arcsec, a radial velocity of 13 km/s, and a proper motion of 1.40 arcsec per year. At what total velocity does Ross 128 travel through space, relative to the Sun?

Accepted Answer

To calculate the total velocity of Ross 128, we need to add up its radial velocity and proper motion.

Total velocity = radial velocity + proper motion

Total velocity = 13 km/s + (1.40 arcsec/year * 0.301 arcsec) * (3.086*10^13 km/parsec) * (1 year/365.25 days) * (1 day/24 hours) * (1 hour/3600 seconds)

Total velocity = 26 km/s

Therefore, the best choice is D.

Question 20

Neptune is about 1.5 times as far from the Sun as is Uranus, and it is about the same size. About how much radiant energy does Neptune receive from the Sun, compared to Uranus?

Accepted Answer

The amount of radiant energy received by a planet from the Sun decreases with the square of the distance from the Sun. Since Neptune is about 1.5 times farther from the Sun than Uranus, the energy it receives is (1/1.5)^2 = 1/2.25, which is approximately 44% of the energy Uranus receives.

Quiz 17: The Nature of the Stars