Question 1

What particular and very important phenomenon frequently occurs in binary star systems where the stars are very close together?
A) The less massive star, in its elliptical orbit, repeatedly passes through the thin, extended atmosphere of the second star, producing periodic rises and falls in light output from the star system.
B) The radiation from the hotter star slowly heats and evaporates away the cooler star.
C) Mass lost from one star is deposited on its companion.
D) The less massive star spirals slowly into its more massive companion because of tidal interactions.

Accepted Answer

Mass transfer is a common phenomenon in close binary star systems, where material from one star can be pulled onto its companion, often through an accretion disk. This process can significantly affect the evolution of both stars and is a key area of study in astrophysics.

Question 2

What condition is necessary on Earth to see eclipses of stars in binary star systems?
A) The stars must have very similar surface temperatures, whatever the inclination of their orbital plane to the line of sight, to see a significant eclipse.
B) The line of sight from Earth to the star system must be very close to perpendicular to the orbital plane of the stars.
C) The line of sight from Earth to the star system must be in or very close to the orbital plane of the stars.
D) One of the stars must be much bigger than the other so that it can hide its smaller companion when the orbital plane is at a large angle to the line of sight.

Accepted Answer

To observe eclipses in binary star systems from Earth, our line of sight needs to be in or very close to the plane in which the stars orbit each other. This alignment allows one star to pass in front of the other, relative to our viewpoint, causing an eclipse.

Question 3

Which of these observations would NOT be an indication of a binary star system?
A) The "star" appears to move in a straight line against a background field of stars.
B) A "star" appears to become periodically dimmer and then brighter for a few hours at a time.
C) A "star" image periodically separates into two distinct images and then blends again.
D) The "star" appears to wiggle in its path across Earth's sky against the background stars.

Accepted Answer

Observation A, where a "star" appears to move in a straight line against a background field of stars, would not indicate a binary star system. This movement is more indicative of proper motion of a single star rather than the gravitational interactions seen in binary systems. Binary systems often show periodic dimming (due to eclipses), separation into two distinct images (when the binary nature is resolved), or a wiggle in the path (due to the gravitational influence of the companion star), as described in options B, C, and D.

Question 4

In a particular binary star system, only one star is visible because the other star is too faint to see at that distance. An astronomer measures the size (semimajor axis) and period of the orbit of the visible star. From this information, the astronomer
A) cannot calculate anything about the mass-both stars have to be visible to do so.
B) can calculate the mass of each star.
C) can calculate the sum of the masses of the two stars but not the mass of each star separately.
D) can calculate the mass of the visible star but not that of the unseen star.

Accepted Answer

The mass of each star separately cannot be determined with the given information, but the sum of the masses can be calculated using Kepler's third law, which relates the orbital period and the size of the orbit (semimajor axis) to the total mass of the system.

Question 5

An astronomer is observing a binary system with two stars of masses M₁ and M₂. She determines a, the semimajor axis (also the average distance between the stars) and P, the period of their motion. Using this information in Kepler's third law she can calculate A) M₁ or M₂ but not both. B) M₁/M₂. C) M₁ + M₂. D) both M₁ and M₂.

Accepted Answer

Kepler's third law, when applied to a binary star system, allows for the calculation of the total mass of the system (M₁ + M₂) using the semimajor axis (a) and the orbital period (P). It does not directly provide the individual masses without additional information.

Question 6

An eclipsing binary system consists of
A) a star that is periodically eclipsed by the Moon.
B) two stars that periodically eclipse each other, as seen from Earth.
C) two stars in which spectral lines move back and forth periodically due to Doppler shift, indicating mutually orbiting stars.
D) two mutually orbiting and gravitationally bound stars that are close enough to be resolved when viewed from Earth.

Accepted Answer

An eclipsing binary system is defined by two stars that periodically eclipse each other from our point of view on Earth, leading to changes in the system's observed brightness as one star moves in front of the other.

Question 7

The light intensity from a particular star remains essentially constant except for short and regular decreases, after which it increases again to its constant value. What is the MOST plausible explanation for this phenomenon?
A) One star is regularly eclipsing its companion as they move in mutual orbits when the plane of those orbits is close to Earth's line of sight.
B) A variable star is pulsating in size, temperature, and intensity.
C) The star is undergoing periodic supernova events.
D) Shells of absorbing gas and dust are being periodically ejected from the star's surface and are subsequently dispersing into space.

Accepted Answer

The most plausible explanation for the observed phenomenon of regular, short decreases in light intensity from a star, followed by a return to its constant value, is that one star is regularly eclipsing its companion star in a binary system. This occurs when their mutual orbits align in such a way that from Earth's perspective, one star passes in front of the other, temporarily blocking some of the light that reaches us.

Question 8

For a pair of stars to be classified as an optical double, which one of these conditions must be true?
A) The stars must lie in almost the same direction from Earth but must not be orbiting around each other.
B) The stars must be orbiting around each other, and one must periodically cross in front of the other (i.e., it must eclipse the other) as seen from Earth.
C) The stars must be orbiting around each other, and absorption or emission lines from both stars must be visible in the spectrum.
D) The stars must be orbiting around each other, and both stars must be visible through telescopes from Earth.

Accepted Answer

Optical doubles are pairs of stars that appear close to each other in the sky as seen from Earth but are not gravitationally bound and do not orbit each other. They merely lie in almost the same direction from our viewpoint.

Question 9

An eclipsing binary system consists of
A) two stars orbiting each other in which periodic spectral line shifts due to Doppler shift are measured.
B) two stars that are clearly resolved as separate but orbiting each other and obviously gravitationally bound to each other.
C) a star that is periodically eclipsed by the Moon.
D) two stars whose combined light output toward Earth varies regularly as one star periodically moves in front of the other.

Accepted Answer

An eclipsing binary system is characterized by two stars whose orbits cause them to pass in front of each other relative to the observer's line of sight, leading to periodic variations in the system's combined light as seen from Earth. This results in one star periodically eclipsing the other.

Question 10

What is the difference between an optical double star and a visual binary star?
A) An optical double is an illusion-the stars are at vast distances from each other and are not actually orbiting each other-whereas in a visual binary, the stars are actually orbiting each other.
B) There is no difference; they are two names for the same thing.
C) The stars in an optical double star are actually orbiting each other, whereas a visual binary is an illusion. The stars are at vast distances from each other and are not actually orbiting each other.
D) Optical double stars can be seen as separate stars only through a telescope, whereas visual binaries can be seen with the unaided eye (e.g., the star Mizar in the Big Dipper's handle).

Accepted Answer

An optical double star appears to be close together when viewed from Earth, but the stars are not gravitationally bound and are at significantly different distances from us. In contrast, a visual binary consists of two stars that are gravitationally bound and orbit each other, which can sometimes be resolved as separate stars through a telescope or, in rare cases, with the naked eye.

Question 11

Which one of these properties is NOT needed to determine individual masses in a binary star system?
A) the distance to the binary system
B) the plane of the orbit of the two stars
C) the relative sizes of the orbits of the two stars
D) the absolute magnitude of at least one star

Accepted Answer

To determine the individual masses in a binary star system, the distance to the system (A), the plane of the orbit (B), and the relative sizes of the orbits (C) are crucial for applying Kepler's laws and the mass function. The absolute magnitude of at least one star (D) is not directly needed for mass determination; it is more related to the luminosity and physical properties of the star rather than its mass.

Question 12

Which of these major perturbations can occur to a close binary system and radically alter the evolution and behavior of the two individual stars?
A) gravitational disturbance of one star's motion by its companion to force it to move in an orbit
B) transfer of matter from one star to its companion
C) heating of the localized areas of the atmosphere of one star by its companion
D) eclipsing of the light from one star by the other when viewed from Earth

Accepted Answer

Transfer of matter from one star to its companion in a close binary system can significantly alter the mass, evolutionary stage, and behavior of both stars, leading to phenomena such as mass accretion disks, novae, or even the formation of a type Ia supernova under certain conditions.

Question 13

If the Sun were orbited by a star of 1.8 solar masses at Jupiter's distance of 5.2 au (or, more precisely, the Sun and the other star were orbiting each other 5.2 au apart), what would be the orbital period of the system? (It might be useful to compare the answer with the actual orbital period of Jupiter, 11.9 years.)
A) 7.1 years
B) 9.4 years
C) 50.2 years
D) 11.3 years

Accepted Answer

The orbital period can be calculated using Kepler's third law, which states that the square of the orbital period (T) is directly proportional to the cube of the semi-major axis (a) of its orbit, with the proportionality constant being the same for all objects orbiting the same primary. However, when considering a binary system of two stars, the formula needs to account for the total mass of the system rather than just the mass of the primary. The formula becomes $T^2 = \frac{4\pi^2}{G(M_1 + M_2)}a^3$, where $M_1$ and $M_2$ are the masses of the two stars, $G$ is the gravitational constant, and $a$ is the semi-major axis (in this case, 5.2 AU). Given that the total mass is 1 + 1.8 = 2.8 solar masses, and using the fact that Jupiter's period is 11.9 years at the same distance from a single solar mass, we can infer that the period will be shorter due to the increased mass. The exact calculation would show that the period is significantly less than Jupiter's, leading to the correct answer of 7.1 years, which accounts for the increased gravitational pull from the additional mass, shortening the orbital period.

Question 14

Two stars of equal mass form a visual binary system. The separation between the two stars is 4 au and the period of the orbital motion is 8 years. What is the mass of each star relative to the mass of the Sun?
A) 1
B) 1/2
C) 1/4
D) 2

Accepted Answer

The answer of Two stars of equal mass form a...

Question 15

Which of these statements is NOT true about the center of mass of a binary star system?
A) The center of mass is always on the line joining the two stars.
B) The center of mass is simultaneously a focus of the ellipse of each star's motion.
C) The center of mass is always more distant from the more massive star.
D) The center of mass can move with respect to the more distant background stars.

Accepted Answer

The center of mass is closer to the more massive star, not more distant.

Question 16

How do two unequal-mass stars in a binary star system move around each other, in general?
A) The stars move in a single circular orbit around the same center and always on opposite sides from each other.
B) The stars move in straight lines, back and forth past each other.
C) The low-mass star moves in a circular orbit around the high-mass star, which remains stationary.
D) The stars move in elliptical orbits about a common center of mass.

Accepted Answer

In a binary star system, both stars orbit around their common center of mass. The shape of their orbits can be elliptical, and the center of mass is not fixed in either of the stars but is a point in space relative to their masses. This means that both stars, regardless of their mass difference, move in response to their mutual gravitational attraction.

Question 17

For a pair of stars to be classified as a visual binary, which one of these conditions must be true?
A) The stars must be orbiting around each other, and both stars must be visible through telescopes from Earth.
B) The stars must be orbiting around each other, and absorption or emission lines from both stars must be visible in the spectrum.
C) The stars must be orbiting around each other, and one must periodically cross in front of the other (i.e., it must eclipse the other) as seen from Earth.
D) The stars must lie in almost the same direction from Earth but must not be orbiting around each other.

Accepted Answer

For a pair of stars to be classified as a visual binary, they must be orbiting each other and both must be individually resolvable with a telescope from Earth.

Question 18

To determine the sum of the masses of a visual binary star system, what needs to be measured?
A) temperatures and periods of the stars
B) distance from Earth and the semimajor axis of the orbit of one star relative to the other
C) periods and the semimajor axes of the stars
D) temperatures and distances from Earth of the stars

Accepted Answer

The sum of the masses of a visual binary star system can be determined by measuring the periods and the semimajor axes of the stars' orbits. This is based on Kepler's third law of planetary motion, which relates these two quantities to the mass of the system.

Question 19

The star Algol in the constellation Perseus has these unusual characteristics. Every 68.75 hours its brightness dims suddenly from apparent magnitude 2.3 to apparent magnitude 3.5 and remains there for a few hours before returning just as suddenly to 2.3. In addition, halfway through this 68.75-hour period, the apparent magnitude becomes slightly dimmer than 2.3 for a few hours and then returns to 2.3. From this information alone it is possible to classify Algol as a(n)
A) optical double.
B) eclipsing binary.
C) totally eclipsing binary.
D) partially eclipsing binary.

Accepted Answer

Algol's periodic dimming and brightening is characteristic of an eclipsing binary system, where one star passes in front of the other from our viewpoint, causing the observed brightness to decrease. The brief period of dimming halfway through the cycle suggests the secondary eclipse when the dimmer star is eclipsed by the brighter one.

Question 20

A particular star in a binary star system orbits the other in an elliptical orbit with a semimajor axis of 3 au and a period of 5 years. What is the sum of the masses of the two stars in the system?
A) 0.9
B) 1.1
C) 13.9
D) 0.07

Accepted Answer

The sum of the masses of the two stars in a binary system can be calculated using Kepler's third law of planetary motion, which states that the square of the orbital period (P) of a planet (or star in this case) is directly proportional to the cube of the semimajor axis (a) of its orbit around the sun (or the other star in a binary system). The formula, when adapted for a binary star system and expressed in terms of the masses of the two stars (M1 + M2), is given by:$$ P^2 = \frac{4\pi^2}{G(M_1 + M_2)}a^3 $$Where:- $ P $ is the orbital period in years,- $ a $ is the semimajor axis in astronomical units (AU),- $ G $ is the gravitational constant, but when using AU for the semimajor axis, years for the period, and solar masses for the mass, $ G $ effectively becomes a constant that allows us to simplify the equation to $ P^2 = a^3 / (M_1 + M_2) $,- $ M_1 + M_2 $ is the sum of the masses of the two stars in solar masses.Given that $ a = 3 $ AU and $ P = 5 $ years, we can rearrange the formula to solve for $ M_1 + M_2 $:$$ 5^2 = \frac{3^3}{M_1 + M_2} $$$$ 25 = \frac{27}{M_1 + M_2} $$$$ M_1 + M_2 = \frac{27}{25} $$$$ M_1 + M_2 = 1.08 $$This value is closest to the given option B) 1.1, which is the correct answer. This calculation assumes the units are consistent with the simplified version of Kepler's third law for binary star systems, where the period is in years, the semimajor axis is in astronomical units, and the mass is in solar masses.

Quiz 12: Characterizing Stars

What particular and very important phenomenon frequently occurs in binary star systems where the stars are very close together?

What condition is necessary on Earth to see eclipses of stars in binary star systems?

Which of these observations would NOT be an indication of a binary star system?

In a particular binary star system, only one star is visible because the other star is too faint to see at that distance. An astronomer measures the size (semimajor axis) and period of the orbit of the visible star. From this information, the astronomer

An astronomer is observing a binary system with two stars of masses M1 and M2. She determines a, the semimajor axis (also the average distance between the stars) and P, the period of their motion. Using this information in Kepler's third law she can calculate

An eclipsing binary system consists of

The light intensity from a particular star remains essentially constant except for short and regular decreases, after which it increases again to its constant value. What is the MOST plausible explanation for this phenomenon?

For a pair of stars to be classified as an optical double, which one of these conditions must be true?

An eclipsing binary system consists of

What is the difference between an optical double star and a visual binary star?

Which one of these properties is NOT needed to determine individual masses in a binary star system?

Which of these major perturbations can occur to a close binary system and radically alter the evolution and behavior of the two individual stars?

Two stars of equal mass form a visual binary system. The separation between the two stars is 4 au and the period of the orbital motion is 8 years. What is the mass of each star relative to the mass of the Sun?

Which of these statements is NOT true about the center of mass of a binary star system?

How do two unequal-mass stars in a binary star system move around each other, in general?

For a pair of stars to be classified as a visual binary, which one of these conditions must be true?

To determine the sum of the masses of a visual binary star system, what needs to be measured?

A particular star in a binary star system orbits the other in an elliptical orbit with a semimajor axis of 3 au and a period of 5 years. What is the sum of the masses of the two stars in the system?

An astronomer is observing a binary system with two stars of masses M₁ and M₂. She determines a, the semimajor axis (also the average distance between the stars) and P, the period of their motion. Using this information in Kepler's third law she can calculate