Question 1

You are measuring how velocity changes with time of two stars like the Sun in order to detect their planets. Both stars have a velocity curve with a period of 2 years, but the maximum size (peak- to- peak amplitude)of the velocity curve of star A is 100 km/s, and for star B it is 200 km/s. What causes this difference? Assume the planets are named after their stars.

Accepted Answer

The maximum size of the velocity curve depends on the mass of the planet causing the gravitational pull on the star. Therefore, the larger amplitude of the velocity curve for star B indicates that the planet causing the pull is more massive than the planet causing the pull on star A. Thus, planet B is less massive than planet A.

Question 2

According to Kepler results in mid- 2013, what fraction of stars host an Earth- size planet?

Accepted Answer

This was the fraction of stars that Kepler had observed to have an Earth-size planet in the habitable zone as of mid-2013. However, later studies using data from Kepler and other telescopes suggest that the actual fraction of stars with Earth-like planets could be much higher, possibly as high as 40%.

Question 3

Which of the following methods has led to the most confirmed discoveries of massive planets orbiting near their parent stars?

Accepted Answer

The most confirmed discoveries of massive planets orbiting near their parent stars have been made by detecting the gravitational effect of an orbiting planet by looking for the Doppler shifts in the star's spectrum. This technique, known as the radial velocity or wobble method, involves measuring tiny changes in the star's spectrum caused by its motion around the center of mass of the star-planet system.

Question 4

A star is seen to have two transiting planets. Planet 1 transits every 3 months, and Planet 2 transits every 15 months. What can we infer about their orbits? (Hint: Review the use of Newton's version of Kepler's Third law from Ch. 4)

Accepted Answer

According to Kepler's Third Law, the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit. This means that if Planet 2 takes 5 times longer to orbit the star than Planet 1 (15 months vs. 3 months), then the semi-major axis of Planet 2's orbit is larger. The relationship between the periods (T) and the semi-major axes (a) can be expressed as $T_2^2/T_1^2 = a_2^3/a_1^3$. Solving for the ratio of the semi-major axes gives $a_2/a_1 = (T_2/T_1)^{2/3}$, and substituting $T_2/T_1 = 5$ yields $a_2/a_1 = 5^{2/3}$, which is approximately equal to 2.92, or about 3 times larger.

Question 5

As of the time of the publication of the textbook, how many planet candidates have been discovered using the transit method?

Accepted Answer

The transit method, which detects planets by observing the dimming of a star as a planet passes in front of it, has been highly successful, leading to the discovery of a few thousand planet candidates.

Question 6

How do we think the "hot Jupiters" around other stars were formed?

Accepted Answer

"Hot Jupiters" are gas giants that orbit very close to their star, which is unexpected given current models of planetary formation. However, it is believed that they formed further out from their star, beyond the frost line where ices could condense, and then migrated inwards due to planetary interactions or tidal forces. This theory is supported by observations of some hot Jupiters having highly elliptical orbits or being in retrograde orbits, which could be the result of gravitational interactions with other planets or the star itself during their migration.

Question 7

How does the theory of planetary migration in disks possibly account for the highly eccentric orbits discovered for some extrasolar planets?

Accepted Answer

According to the theory of planetary migration in disks, planets form closer to their parent stars and then slowly migrate outward or inward due to interactions with the protoplanetary disk. When two migrating planets pass close enough to each other, a gravitational encounter may occur, which could fling one planet from the system while the other is shifted to a highly eccentric orbit. This could account for the highly eccentric orbits discovered for some extrasolar planets.

Question 8

The first planets around other Sun- like stars were discovered

Accepted Answer

The first planets around other Sun-like stars were discovered about two decades ago, in the 1990s. This was done through the use of advanced technologies such as the radial velocity method, which detects the gravitational effects of planets on their stars.

Question 9

How can astronomers measure the composition of an extrasolar planet's atmosphere?

Accepted Answer

By comparing spectra for when the planet is in transit or eclipse with spectra taken at other times, astronomers can look for the chemical signatures of the planet's atmosphere. The planet blocks some of the starlight during transit, allowing astronomers to see the light that passes through the planet's atmosphere. By comparing this spectrum to the spectrum of the star alone, astronomers can detect the chemical composition of the planet's atmosphere.

Question 10

What is astrometry?

Accepted Answer

Astrometry is the branch of astronomy concerned with measuring the positions of celestial objects on the celestial sphere. This includes measuring the positions of stars in the sky, as well as motion and distances of celestial objects.

Question 11

What are the two primary methods by which planets have been found around other stars in our galaxy? I)Direct images in visible and infrared light
II)Indirectly by detecting the motion of the host star
III)Indirectly by measuring the drop in brightness of the host star when the planet crosses our line of sight

Accepted Answer

The two primary methods by which planets have been found around other stars in our galaxy are indirectly by detecting the motion of the host star (method II) and indirectly by measuring the drop in brightness of the host star when the planet crosses our line of sight (method III). Direct images in visible and infrared light (method I) are also used but are less common and have only been successful for larger planets that are far from their host star.

Question 12

Which of the following statements about the accelerations and gravitational forces between a planet and a star is true?

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that the gravitational forces between two bodies, such as a planet and a star, are equal in magnitude and opposite in direction. However, according to Newton's second law, F=ma, the acceleration of an object is directly proportional to the force acting upon it and inversely proportional to its mass. Since the star has a much greater mass than the planet, the same force will result in a smaller acceleration for the star compared to the planet. Therefore, while the forces are equal and opposite, the planet is accelerated more than the star due to its smaller mass.

Question 13

The transit method of planet detection works best for

Accepted Answer

The transit method of planet detection is most effective for large planets that pass directly in front of their host stars from our point of view, which is described as an edge-on orbit. The larger the planet and the smaller the star, the more significant the dip in brightness, making the transit easier to detect. This is why option E is correct.

Question 14

What is a so- called "hot Jupiter"?

Accepted Answer

"Hot Jupiter" refers to a gas giant planet with a mass similar to Jupiter but orbiting very close to their host star, which causes the planet's atmosphere to be very hot.

Question 15

What type of observation can astronomers use to measure the composition of extrasolar planet atmospheres?

Accepted Answer

Comparing the spectra of a planet when it passes in front of or is eclipsed by its host star can reveal the absorption lines caused by the planet's atmosphere. By comparing these absorption lines to known spectra of different chemical compounds, astronomers can determine the composition of the planet's atmosphere.

Question 16

The Doppler technique can be used to measure the eccentricity of a planet's orbit by

Accepted Answer

The Doppler technique measures the eccentricity of a planet's orbit by observing the asymmetries in the velocity curve of the star as the planet orbits it. This method relies on detecting variations in the star's radial velocity, which are influenced by the gravitational pull of an orbiting planet. The shape of the velocity curve, including its asymmetries, can reveal information about the orbit's eccentricity.

Question 17

How can astronomers measure the period of a planet's orbit?

Accepted Answer

Astronomers can measure the period of a planet's orbit by using all of these methods.

A) The time between peaks in the star's velocity curve can be used to determine the planet's orbital period through the radial velocity method. As the planet orbits the star, it causes the star to move slightly towards and away from us, causing a Doppler shift in the star's spectrum. By measuring the time between peaks in the star's velocity curve, astronomers can determine the planet's orbital period.

B) The time between repeated transits can be used to determine the planet's orbital period through the transit method. As the planet passes in front of its star, it causes a slight dip in the star's brightness. By measuring the time between repeated transits, astronomers can determine the planet's orbital period.

C) Timing the cycle of small changes in a star's position on the sky can be used to determine the planet's orbital period through the astrometry method. As the planet orbits the star, it causes the star to move slightly back and forth in its position on the sky. By measuring the time it takes for the star to complete a full cycle of these small changes in position, astronomers can determine the planet's orbital period.

Question 18

Consider two main sequence K- stars of equal mass. Each star has been measured for a periodic wobble in its velocity curve, with one having a period of 1 month and the other having a period of 2 months. Which star has the closest planet (the planet with the smallest orbit)?

Accepted Answer

The period of the wobble in the velocity curve is directly related to the period of the planet's orbit around the star. Therefore, the star with a period of 1 month has a planet with a smaller orbit than the star with a period of 2 months.

Question 19

In order to be able to directly see the Sun's motion due to Jupiter's gravity, an observer at a distance of 30 light- years would need to be able to measure changes in its position of _.

Accepted Answer

Changes in position due to Jupiter's gravity on the Sun are extremely small, on the order of a few milliarcseconds. At a distance of 30 light-years, this corresponds to a change in position of about 0.0005 arcseconds. Choice A and B are too large, while choice D is too small.

Question 20

What could happen in planetary systems where the nebular gas is quickly disbursed?

Accepted Answer

Without the presence of nebular gas, ice-rich planetesimals would not be able to gather hydrogen and helium to become gas giants. This would likely result in the absence of gas giants in the planetary system, or they would be much smaller than those found in systems where the gas is not quickly disbursed. The other choices are not necessarily true outcomes of a quickly disbursing nebular gas cloud.

Quiz 10: Other Planetary Systems: the New Science of Distant Worlds