Question 1

-In the light curve shown below,what is the period of the eclipsing binary?

Accepted Answer

The period of an eclipsing binary is the time it takes for the system to complete one orbit. In the light curve shown, the period is the time between the two minima. The time between the two minima is 32.5 days.

Question 2

Based on the mass-luminosity relation,approximately what luminosity would a 2 solar mass star on the main sequence have?

Accepted Answer

According to the mass-luminosity relation, L ∝ M^3.5. Therefore, a 2 solar mass star would have a luminosity of approximately 11 times that of the Sun (since 2^3.5 = 11). Thus, the correct answer is D) 11 solar luminosities.

Question 3

Which of the following kinds of stars best obey the mass-luminosity relation?

Accepted Answer

Main-sequence stars are in a state of balance between the force of gravity pulling the star inward and the energy generated by nuclear fusion pushing outward. This balance is maintained throughout the star's life, and the mass-luminosity relation holds true for main-sequence stars. This relation states that more massive stars are generally more luminous than less massive ones. Therefore, main-sequence stars best obey the mass-luminosity relation.

Question 4

If we can solve the orbital motion of a spectroscopic binary,what can we find?

Accepted Answer

The answer of If we can solve the orbital motion...

Question 5

If two stars are emitting the same amount of light,how will the star that is farther away appear?

Accepted Answer

The farther away star will appear dimmer than the closer star because the same amount of light is spreading out over a larger area. This is known as the inverse square law of light.

Question 6

What does a spectroscopic binary show periodic variations in?

Accepted Answer

A spectroscopic binary shows periodic variations in its radial velocity, as the two stars orbit around a common center of mass. This can be detected through observations of the star's spectral lines, which will shift back and forth as the stars move towards and away from us. Proper motion refers to the apparent motion of a star across the sky, and is not directly related to a binary companion. Brightness and spectral type may also vary in a binary system, but they do not show the same periodicity as radial velocity.

Question 7

The parsec is defined so that a star at a distance of 1 parsec has a parallax of one arcsecond.If a star has a parallax of 0.02 seconds of arc,what is its distance?

Accepted Answer

The distance in parsecs is the reciprocal of the parallax angle in arcseconds. Therefore, 1/0.02 = 50 parsecs.

Question 8

Which of the following kinds of stars is most dense?

Accepted Answer

White dwarfs are the most dense kind of stars, as they are remnants of stars that have exhausted their nuclear fuel and collapsed under their own gravity, squeezing the mass of the star into a very small volume. They can have a mass similar to that of the Sun, but their size is comparable to that of the Earth, making their density incredibly high.

Question 9

Consider two binary star systems,A and B,in which the distance between the stars is the same.If the total mass of the stars in system A is greater than the total mass of the stars in system B,which of following can you conclude?

Accepted Answer

The answer of Consider two binary star systems,A and B,in...

Question 10

An eclipsing binary has been analyzed and it has been determined that the ratio of the mass of star A to the mass of star B is 6 : 1,and that the total mass of the two stars is 26 solar masses.What are the masses of star A and star B?

Accepted Answer

Let the masses of star A and star B be represented by 6x and x, respectively.

The total mass of the system is:

6x + x = 26

Simplifying this equation:

7x = 26

x = 3.7

Therefore, the mass of star A is:

6x = 6(3.7) = 22.2 solar masses

And the mass of star B is:

x = 3.7 solar masses

Thus, the correct answer is C.

Question 11

-The diagram illustrates two stars in a visual binary system and the centre of mass of this system.Based on this diagram,what is the ratio of the mass of star A to the mass of star B?

Accepted Answer

In a binary system, the center of mass is closer to the more massive star. If the center of mass is closer to star B, then star B is more massive, indicating the mass ratio of star A to star B is 1 to 2.

Question 12

$$\begin{array} { | l | c | c | } 
\hline { \text { Star } } & \begin{array} { c } 
\text { Parallax } \
\text { (sec of arc) }
\end{array} & \begin{array} { c } 
\text { Spectral } \
\text { Type }
\end{array} \
\hline 5 \text { Cen } & 0.026 & \text { B2 IV } \
\hline \text { HR 4758 } & 0.05 & \text { G0 V } \
\hline \text { HD 39801 } & 0.005 & \text { M2 I } \
\hline 9 \mathrm { CMa } & 0.4 & \text { Al V } \
\hline
\end{array}$$
-Which star in the table has the highest surface temperature?

Accepted Answer

The spectral type of a star is directly related to its surface temperature. The spectral types are arranged in order of decreasing temperature as O, B, A, F, G, K, M. Among the given stars, the spectral type of 5 Cen is B2 IV, which is hotter than G0 V (HR 4758), M2 I (HD 39801), and Al V (9 CMa). Therefore, 5 Cen has the highest surface temperature among the given stars.

Question 13

If the orbital velocity of an eclipsing binary is 97 km/sec and the smaller star is completely eclipsed in 2 hours,what is the diameter of the smaller star?

Accepted Answer

The answer of If the orbital velocity of an eclipsing...

Question 14

$$\begin{array} { | l | c | c | } 
\hline { \text { Star } } & \begin{array} { c } 
\text { Parallax } \
\text { (sec of arc) }
\end{array} & \begin{array} { c } 
\text { Spectral } \
\text { Type }
\end{array} \
\hline 5 \text { Cen } & 0.026 & \text { B2 IV } \
\hline \text { HR 4758 } & 0.05 & \text { G0 V } \
\hline \text { HD 39801 } & 0.005 & \text { M2 I } \
\hline 9 \mathrm { CMa } & 0.4 & \text { Al V } \
\hline
\end{array}$$
-Which star in the table has the largest diameter?

Accepted Answer

The diameter of a star is related to its spectral type and luminosity. Generally, stars with later spectral types (such as M stars) have larger diameters than earlier spectral types (such as B or G stars). In this table, HD 39801 has the latest spectral type (M2) of all the stars listed, indicating that it is likely to have the largest diameter. Additionally, it is classified as a supergiant (I), which also suggests a large size. Therefore, the answer is C) HD 39801.

Question 15

$$\begin{array} { | l | c | c | } 
\hline { \text { Star } } & \begin{array} { c } 
\text { Parallax } \
\text { (sec of arc) }
\end{array} & \begin{array} { c } 
\text { Spectral } \
\text { Type }
\end{array} \
\hline 5 \text { Cen } & 0.026 & \text { B2 IV } \
\hline \text { HR 4758 } & 0.05 & \text { G0 V } \
\hline \text { HD 39801 } & 0.005 & \text { M2 I } \
\hline 9 \mathrm { CMa } & 0.4 & \text { Al V } \
\hline
\end{array}$$
-Which star in the table is the closest to Earth?

Accepted Answer

The star with the largest parallax angle is the closest to Earth. 9 CMa has the largest parallax of 0.4 arcseconds, indicating it is the closest.

Question 16

-At what point in the eclipsing binary light curve below is the cooler star in front of the hotter star?

Accepted Answer

The answer of 
-At what point in the eclipsing binary...

Question 17

-The diagram shows the radial velocity curve of a double-line spectroscopic binary.Based on this radial velocity curve,what is the mass of star B compared to star A?

Accepted Answer

In a double-line spectroscopic binary, the radial velocity curve shows the motion of both stars. If star B has a larger amplitude in its radial velocity curve compared to star A, it indicates that star B is less massive. Conversely, if star B has a smaller amplitude, it is more massive. The amplitude ratio is inversely proportional to the mass ratio, so if star B's amplitude is half that of star A, star B is twice as massive as star A.

Question 18

Which stars on the main sequence have the greatest mass?

Accepted Answer

The spectral type O stars are the hottest and brightest stars on the main sequence, and they have the greatest mass.

Question 19

Which of the following pieces of information are needed to calculate the total mass of a binary system?

Accepted Answer

To calculate the total mass of a binary system, we need the semi major axis and period of the orbit because this will give us the average distance between the two stars and the time it takes for them to complete one orbit around their common center of mass. Knowing this, we can use Kepler's laws to calculate the total mass of the system. The other pieces of information (A, C, and D) are important for studying binary systems but are not necessary for calculating the total mass.

Question 20

Absolute magnitude is defined as the apparent magnitude that a star would have if observed at a distance of 33 light years.Consider a star at a distance of 330 light years that has an apparent magnitude of +5.What would its absolute magnitude be?

Accepted Answer

Absolute magnitude is a measure of intrinsic brightness. Since the star is farther than 33 light years, its absolute magnitude would be less than its apparent magnitude of +5, indicating it is intrinsically brighter.

Quiz 6: The Family of Stars