Question 1

If the two stars in a binary system were moved farther apart, what would happen to the period of their motion?

Accepted Answer

According to Kepler's third law, the period of the binary system is dependent on the distance between the two stars (semi-major axis) and their masses. As the stars are moved farther apart, the distance between them increases, resulting in a longer semi-major axis. Therefore, according to Kepler's third law, the period would increase.

Question 2

Observations of binary stars have helped astronomers to determine which important scientific parameter?

Accepted Answer

Binary stars orbit around their common center of mass, and the period and separation of their orbits can be measured. By applying Kepler's laws of motion and using the observed period and separation, the masses of the stars can be calculated. This is an important parameter for understanding the properties and evolution of stars.

Question 3

What is the mass of a main-sequence star that has a luminosity 1000 times greater than that of the Sun? (See Figure 17-22.(in the text))

Accepted Answer

The mass-luminosity relationship for main-sequence stars indicates that a star with a luminosity 1000 times greater than the Sun's would have a mass approximately 5 solar masses. This relationship shows that luminosity increases much more rapidly than mass.

Question 4

On the basis of the Hertzsprung-Russell diagram (Figure 17-15a) and the mass-luminosity relationship for main-sequence stars (Figure 17-22), which of the following main-sequence stars have the greatest mass?

Accepted Answer

On the Hertzsprung-Russell diagram, O-type stars are located in the upper left corner, indicating they are very hot and very luminous. The mass-luminosity relationship for main-sequence stars shows that more massive stars have higher luminosities. Therefore, O-type stars have the greatest mass among the main-sequence stars.

Question 5

Vega is an A0 V star with a surface temperature of about 10,000 K. Use Figures 17-15a and 17-22 to estimate the mass of Vega.

Accepted Answer

According to Figure 17-15a, A0 V stars have masses between 2.5 and 3.5 solar masses. Additionally, Figure 17-22 shows that stars with a surface temperature of 10,000 K have a mass between 2 and 4 solar masses. Therefore, based on these two figures, the best estimate for Vega's mass is between 2.0 and 3.0 solar masses, which is option D.

Question 6

Using the Hertzsprung-Russell diagram in Figure 17-15a and the mass-luminosity relationship for main-sequence stars shown in Figure 17-22, which of the following is the correct sequence of stars in increasing order of mass?

Accepted Answer

The Hertzsprung-Russell diagram and the mass-luminosity relationship for main-sequence stars indicate that stars with lower luminosity and cooler temperatures (like Barnard's Star) have lower masses, while stars with higher luminosity and hotter temperatures (like Regulus) have higher masses. Therefore, the sequence from lowest to highest mass is Barnard's Star (a low-mass, low-luminosity red dwarf), the Sun (a yellow dwarf with intermediate mass and luminosity), Altair (a white, hotter, and more luminous star than the Sun), and Regulus (a blue star with high luminosity and mass).

Question 7

By studying the radial velocity curves of two visible stars in an edge-on binary system, we determine that the mass of Star A is 3 times the mass of Star B. We also observe their period to be 8 years and the semimajor axis of their relative orbit to be 4 au. What are the masses of these stars?

Accepted Answer

Using Kepler's third law and the given information, we can find the total mass of the system. The formula for Kepler's third law in this context is $P^2 = \frac{4\pi^2}{G(M_A + M_B)}a^3$, where $P$ is the period, $a$ is the semimajor axis, $M_A$ and $M_B$ are the masses of the stars, and $G$ is the gravitational constant. Given that $P = 8$ years and $a = 4$ AU, and knowing that $M_A = 3M_B$, we can solve for the total mass of the system in solar masses. The total mass comes out to be $1 M_{\odot}$, with Star A being $0.75 M_{\odot}$ and Star B being $0.25 M_{\odot}$.

Question 8

Radial velocity curves are plotted for a binary star system. The two curves cross when one star begins approaching and the other star begins receding, then cross again when they reverse, and then cross a third time when the first star again begins approaching. Which statement is TRUE about this set of curves?

Accepted Answer

At the crossing points, the radial velocity is not necessarily zero because it depends on the orientation of the orbit and the angle of inclination with respect to Earth. The other statements are not necessarily true, as the times between the crossings can vary depending on the period of the orbit and the magnitudes of the maximum radial velocities can differ depending on the masses of the stars. Additionally, the radial velocities of the two stars do not have to be equal and opposite at any given point.

Question 9

What is the physical reason for the appearance of periodic splitting and recombining of spectral lines in the spectra of binary stars?

Accepted Answer

The periodic splitting and recombining of spectral lines in the spectra of binary stars is due to the Doppler shift of light from stars that are orbiting each other. As the stars move towards Earth, the spectral lines are shifted towards the blue end of the spectrum, and as they move away from Earth, the spectral lines are shifted towards the red end of the spectrum. This results in periodic splitting and recombining of the spectral lines, providing information about the orbital motion of the stars.

Question 10

An eclipsing binary system is:

Accepted Answer

An eclipsing binary system is a type of binary star system in which two stars orbit around a common center of mass and periodically eclipse each other as seen from Earth. This is observed through the periodic dimming of the star's brightness. Option A refers to spectroscopic binary systems, option C refers to visual binary systems, and option D refers to lunar eclipses.

Question 11

Suppose we observe the light curve of a totally eclipsing binary like that in Figure 17-24b. The brightness falls gradually from magnitude 5 to magnitude 9 and remains there for 12 hours before increasing gradually to magnitude 5. Then, after a while, it drops gradually to magnitude 6, remains there for 8 hours, and returns to magnitude 5. What conclusion can be drawn from this light curve?

Accepted Answer

The answer of Suppose we observe the light curve of...

Question 12

Light intensity variations are detected from a star in which the intensity remains essentially constant, except for the periodic, short, and regular increases and decreases by a fixed amount. What is the most likely explanation for this observation?

Accepted Answer

The most likely explanation for the observed light intensity variations, where the intensity remains essentially constant except for periodic, short, and regular increases and decreases, is the eclipsing of one star by its companion in a binary star system. This causes the observed brightness of the system to decrease when one star passes in front of the other and then increase back to normal as the eclipse ends.

Question 13

How do two stars in a binary system orbit each other? (See Figure 17-21.(in the text))

Accepted Answer

In a binary system, both stars follow elliptical orbits around a common center of mass between the two stars. This is because each star feels the gravitational pull of the other star, causing them to both move in a complex orbital dance. The center of mass is also not necessarily at the center of either star, but rather at a point between them where their combined mass is balanced.

Quiz 17: The Nature of the Stars