homework

Question 1

Grass (that is healthy) looks green because:

Answer 1

it reflects green light and absorbs other colors.

Question 2

The frequency of a wave is

Answer 2

the number of peaks passing by any point each second.
measured in cycles per second.
measured in hertz (Hz).
equal to the speed of the wave divided by the wavelength of the wave.

Question 3

From lowest energy to highest energy, which of the following correctly orders the different categories of electromagnetic radiation?

Answer 3

radio, infrared, visible light, ultraviolet, X rays, gamma rays

Question 4

Astronomers sometimes joke: “If Mars is blue, you’re landing too fast!” The joke references the fact that Mars is red and the Doppler effect. But seriously, how fast would you have to travel towards Mars in order to make it appear blue? Let’s assume red light is 600 nanometers, and blue light is 400 nm. Answer in km/s (do not include the units in your answer), and answer as a positive number.

Answer 4

100,000

Question 5

Nightvision goggles work by imaging the thermal emission from people. Assuming people are 98.6 degrees Fahrenheit, what wavelength should night vision goggles operate to receive the most radiation from a person? Answer in microns (one millionth of a meter).

Answer 5

9.5

Question 6

Which of the following could not be determined by an observation that uses only spectroscopy?

Answer 6

the size of a distant galaxy

Question 7

Suppose you see two stars: a blue star and a red star. Which of the following can you conclude about the two stars? Assume that no Doppler shifts are involved.

Answer 7

The blue star has a hotter surface temperature than the red star.

Question 8

If we observe one edge of a planet to be redshifted and the opposite edge to be blueshifted, what can we conclude about the planet?

Answer 8

The planet is rotating.

Question 9

If one object has a large redshift and another object has a small redshift, what can we conclude about these two objects?

Answer 9

The one with the large redshift is moving away from us faster than the one with the small redshift.

Question 10

Suppose you watch a leaf bobbing up and down as ripples pass it by in a pond. You notice that it does two full up and down bobs each second. Which statement is true of the ripples on the pond?

Answer 10

They have a frequency of 2 hertz.

Question 11

Saturn’s moon Titan orbits Saturn with a semi-major axis of 1,221,870 km. What is the angular size of the Saturn-Titan separation when seen from Earth, when Saturn and Titan at 9 AU away? Express you answer in degrees. Do not include the units in your answer.

Answer 11

0.051

Question 12

Suppose the angular separation of two stars is smaller than the angular resolution of your eyes. How will the stars appear to your eyes?

Answer 12

The two stars will look like a single point of light.

Question 13

What do we mean by the diffraction limit of a telescope?

Answer 13

It is the best angular resolution the telescope could achieve with perfect optical quality and in the absence of atmospheric distortion.

Question 14

What does angular resolution measure?

Answer 14

the angular size of the smallest features that the telescope can see

Question 15

Turbulence in the Earth’s atmosphere blurs images of stars in the night sky. This effect is called “seeing.” The seeing at Lowell Observatory in Northern Arizona is roughly 0.5 arcseconds, meaning the image of a star will be blurred to an angular size of 0.5 arcseconds. The Discovery Channel Telescope (DCT) at Lowell is 4.3 meters in diameter. When viewing stars at visible wavelengths (~550 nm), is the DCT seeing-limited, or diffraction-limited? That is to say, which blurring effect is larger, that from seeing or that from diffraction?

Answer 15

Seeing-limited

Question 16

Suppose you tried to view an exoplanet orbiting a star with a separation of 1.0 AU, with the star and planet a distance of 1 parsecs away, using the Discovery Channel Telescope (see Question 6). Ignoring the brightness difference between the star and the exoplanet, and considering only the blurring introduced by seeing and diffraction, could you resolve the planet from the star?

Answer 16

Yes

Question 17

Which of the following is not an advantage of the Hubble Space Telescope over ground-based telescopes?

Answer 17

It is closer to the stars.

Question 18

How large would an ultraviolet telescope operating at 100 nm have to be to achieve the same resolution as the Hubble Space Telescope (2.4-meter diameter) observing in visible light (550 nm)? Answer in meters, and do no include the units in your submission.

Answer 18

0.436

Question 19

What is the angular resolution of the Five hundred meter Aperture Spherical Telescope (FAST), when operated at 400 MHz? FAST has a diameter of 500 meters. Answer in degrees, and do not include the units in your submission.

Answer 19

0.104

Question 20

Which of the following is not a reason why telescopes tend to be built on mountaintops that are relatively far from cities and are in regions with dry climates?

Answer 20

The thin air on mountaintops makes the glass in telescope mirrors less susceptible to warping.

Question 21

What do we mean when we say that the Sun is in gravitational equilibrium?

Answer 21

There is a balance within the Sun between the outward push of pressure and the inward pull of gravity.

Question 22

Suppose that, for some unknown reason, the core of the Sun suddenly became hotter. Which of the following best describes what would happen?

Answer 22

Higher temperature would cause the rate of nuclear fusion to rise, which would increase the internal pressure, causing the core to expand and cool until the fusion rate returned to norma

Question 23

In discussion, you derived the formula for the peak radial velocity introduced on a star from an orbiting exoplanet. Here is one version of this relationship:

Where v is in meters/second (m/s), MP is in Earth masses, MS is in Solar masses and P is in Earth years.

Answer 23

0.09

Question 24

Now, calculate the peak radial velocity introduced on a Sun-like star by a planet identical to Jupiter, again assuming an edge-on orbit. You will need to look up the mass of Jupiter and covert it to earth masses, and look up the orbital period of Jupiter. Answer in m/s without the units.

Answer 24

12.5

Question 25

Based on the equation in Question 3, which of the following scenarios would result in the largest peak radial velocity? Assume all are in an edge-on orbit.

Answer 25

Small star, massive planet, short orbital period.

Question 26

Now let's consider the effect of eccentricity on the peak radial velocity, which was assumed to be zero in the equation in Question 3. Draw a highly eccentric orbit of a planet, and consider the resulting motion of the star. Where in the planet's orbit would the velocity of the star be the largest?

Answer 26

The velocity would be largest when the planet is closest to the star ("periastron", similar to "aphelion" for planets orbiting the sun).

Question 27

Let's think about the concept of "insolation": That is, the amount of energy a planet receives from a star. What are the most appropriate units to describe the energy received at a given distance from a star?

Answer 27

Watts / (meter squared)

Question 28

Which of the following planet properties will change its resulting equilibrium temperature?

Answer 28

Albedo

Question 29

Near the end of its life, our Sun’s radius will increase significantly. When the sun has a radius of 0.5 AU, it will have a surface temperature of about 4000 K. What will happen to its luminosity? By what factor will it increase or decrease?

Answer 29

2,658

Question 30

The entire world consumes about 4 × 1020 joules of energy per year (primarily from fossil-fuel sources). Suppose we want to use solar panels to replace fossil fuels. The best solar panels can covert about 10% of incident energy into usable energy. What area of solar panels would be needed to match our current energy usage, assuming only 10% of the incident energy is converted into usable energy? Answer as a decimal fraction of the Earth's surface area. In other words, answer in units of Earth's surface area. You may need to look up the surface area of a sphere.

Answer 30

0.000181924184

Question 31

Exoplanets.org is a website that catalogs all of the known extrasolar planets found to date. For this assignment, we are going to use this website. Go to exoplanets.org and select "plots". Make a plot of exoplanet orbital period (x-axis) versus exoplanet minimum mass (M x sini, y-axis), which will select for planets found using the radial velocity method. Click "advanced" and make the y-axis of the plot a log scale.

Answer 31

alpha Cen B b

Question 32

You should notice 2 clusters of planets in your plot. Where are the located? Select 2 answers, and think about why this might be.

Answer 32

High mass planets with small orbital periods High mass planets with large orbital periods High mass planets with small orbital periods

Question 33

Now make a histogram plot. You can do this by selecting "histogram" on the website. Make a histogram of the masses of exoplanets found to date. You can either use the minimum mass (msini) or the true planet mass. Check the box next to "logarithmic bins." You should notice a dip in the number of planets at a specific mass. What solar system planet is the "dip" closest to?

Answer 33

Neptune

Question 34

Which of the following is a reasonable explanation for the dip in the previous plot? You may answer more than one.

Answer 34

There exists a "bias" against detecting those types of planets in our methods. There are fewer of those types of planets in the Universe. There exists a "bias" against detecting those types of planets in our methods.

Question 35

Now let's play with the table database. Reload exoplanets.org and select "Table." Sort the planets by semi-major axis. Find the planet with the largest semi-major axis (ignore planets with values of 0, since these are mistakes). How as this planet discovered

Answer 35

Imaging

Question 36

Go back to the plots. Now make a plot of planet orbital period on the x-axis and planet radius on the y-axis. Find the exoplanet with the smallest size. Which solar system planet is that planet most similar to?

Answer 36

Mercury

Question 37

You will notice that the distribution of planets is different for radius vs. orbital period than for Msini vs orbital period. Think about why that might be. For now, choose the populations that you see when you plot radius versus orbital period.

Answer 37

Large radius planets with short orbital periods Small radius planets with short orbital periods

Question 38

Why would the distribution of planets for periods vs. Msini look so different from the distribution of planets for period vs. radius? You can answer this question by experimentation with the website.

Answer 38

They are different planets in the two plots: Some planets have a radius measurement but no mass measurement, and some planets have an Msini measurement with no radius measurement.

Question 39

Finally, for fun, make a histogram plot of planet separation (be sure to use "separation" and not semi-major axis, you will learn why this is important soon). Use the "Add a Filter" button and only show the separations for planets discovered via the microlensing technique. What do you notice about their separations?

Answer 39

They are between 1.0 and 10 AU.

Question 40

Consider a transiting exoplanet. Mark all of the planet and star characteristics than would alter the duration of a transit event.

Answer 40

Planet radius. Planet orbital period Stellar radius Orbital inclination

Question 41

Assuming the star in the last problem is the size of the Sun, how large is the planet? Rather, which planet in the solar system is it most similar to?

Answer 41

Jupiter

Question 42

Now assume the star in the last problem has a radius one-tenth the radius of the Sun. Now which planet in the solar system is it most similar to?

Answer 42

Earth

Question 43

Now suppose you have radial velocity observations of a transiting exoplanet. Check everything that you can measure about the exoplanet system (assuming you know the star's mass and radius).

Answer 43

Exoplanet orbital period Exoplanet radius Exoplanet mass Exoplanet eccentricity

Question 44

The transit method of planet detection works best for

Answer 44

big planets in edge-on orbits around small stars.

Question 45

The composition of a planet's atmosphere can be measured during a transit by analyzing:

Answer 45

the excess absorption of starlight at specific wavelengths.

Question 46

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

Answer 46

They formed as gas giants beyond the ice line and then migrated inwards.

Question 47

Which of the following is a consequence of the discovery of hot Jupiters for the nebular theory of solar system formation?

Answer 47

It has been modified to allow for planets to migrate inwards or outwards after they form.

Question 48

Suppose a transiting exoplanet had a spin-orbit misalignment of 90 degrees and an impact parameter of 0. What would the Rossiter-Mclaughlin effect look like? You might draw yourself a diagram to help.

Answer 48

There would be no measurable Rossiter-Mclaughlin effect.

Question 49

What is the primary evidence supporting eccentricity migration instead of disk migration for the origin of hot Jupiters?

Answer 49

Disk migration predicts that hot Jupiters will orbit in the same direction as their host star's rotation, and some hot Jupiters do not.

Question 50

What is the primary evidence supporting disk migration instead of eccentricity migration for the origin of hot Jupiters?

Answer 50

Eccentricity migration requires a 3rd massive object, either a long-period planet or nearby star, and not all hot Jupiters have a 3rd object nearby.

Question 51

Which of the following exoplanet attributes can microlensing measure. Select all correct answers.

Answer 51

Exoplanet mass | Exoplanet-star separation at the time time of the microlensing

Question 52

In class, we talked about how the Doppler and transit methods are both sensitive to hot Jupiters. What type of planet is microlensing sensitive to?

Answer 52

Distant, massive planets.

Question 53

According to general relativity, why does Earth orbit the Sun?

Answer 53

Earth is following the straightest path possible, but spacetime is curved in such a way that this path goes around the Sun.

Question 54

Which of the following statements is not a prediction of the general theory of relativity?

Answer 54

Different observers can disagree about the fundamental structure of spacetime

Question 55

How many exoplanets have been discovered via the microlensing technique, according to exoplanets.org?

Answer 55

16

Question 56

Dig around the website for NASA's upcoming WFIRST Mission (https://wfirst.gsfc.nasa.gov/index.html). How many exoplanets is WFIRST expected to discovery via microlensing?

Answer 56

4,000

Question 57

Think about rogue planets, or planets that are not hosted by stars. Microlensing is currently the best technique for discovering rogue planets. Why is that?

Answer 57

Other techniques rely on how the planet affects the host star, and rogue planets are too faint to be seen in images.

Question 58

What is the primary reason why it is challenging to directly image exoplanets?

Answer 58

The contrast between the host star and planet is too great.

Question 59

The nearest star to the sun, Proxima Centauri, is 1.296 parsecs away. It hosts an exoplanet orbiting at a distance of 0.0485 AU from the star (discovered by the Doppler method). What is the corresponding angular separation between the star and the planet, as seen from earth? Answer in arc seconds, and do not include the units in your answer.

Answer 59

0.0374

Question 60

Could the Hubble Space Telescope (diameter = 2.4 meters) resolve Proxima Centauri b from Proxima Centauri if observing at a wavelength of 500 nm? Consider only the diffraction limit of the telescope and the angular separation between the planet and star, as observed from Earth.

Answer 60

No

Question 61

Could the upcoming James Webb Space Telescope (diameter = 6.5 meters) resolve Proxima Centauri b from Proxima Centauri if observing at a wavelength of 500 nm? Consider only the diffraction limit of the telescope and the angular separation between the planet and star, as observed from Earth.

Answer 61

Yes

Question 62

Which of the following combinations make for the easiest planets to find via direct imaging?

Answer 62

Massive, young, long-period exoplanets orbiting low-luminosity stars.

Question 63

All of the directly imaged planets found to date have been detected in which wavelengths of the electromagnetic spectrum?

Answer 63

Infrared

Question 64

What does the term "coronagraphy" refer to?

Answer 64

The study of objects or phenomena close to stars

Question 65

Check all that you can learn about an exoplanet from direct imaging (you can assume you have multiple observations):

Answer 65

Exoplanet mass. Exoplanet orbital period. Exoplanet temperature. Exoplanet eccentricity.

Question 66

Why is a "starshade" necessary to directly image Earth-like exoplanets?

Answer 66

A starshade blocks the light from the host star and reduces scattered light.

Question 67

Now consider their habitable zones. Which star would have a habitable zone furthest from it?

Answer 67

O type star.

Question 68

Which star would have a habitable zone closet to it?

Answer 68

M type star.

Question 69

Assuming the Earth's radius is exactly 1/100 times the radius of the Sun, what is the transit depth of an Earth-like planet transiting a Sun-like star? Answer as a decimal, not as a percentage.

Answer 69

0.0001

Question 70

Again, supposing the Earth's radius were 1/100 times the radius of the sun, what is the transit depth of an Earth-like planet transiting an M dwarf star? Use the diagram for the M dwarf radius. Again, answer as a decimal and not as a percentage.

Answer 70

0.0009

Question 71

Calculate the transit probability of an Earth-like planet transiting a sun-like star at a distance of 1 AU. Answer as a decimal not as a percentage.

Answer 71

0.00465

Question 72

Now consider the transit probability of an Earth-like planet orbiting within the habitable zone of an M dwarf star. Would the transit probability be higher, lower, or stay the same?

Answer 72

Higher

Question 73

Which of the following is a disadvantage when searching for exoplanets orbiting within the habitable zones of M dwarf stars?

Answer 73

The stars are intrinsically faint, meaning it is harder to survey a large number of them.

Question 74

The habitable zone changes throughout a star's life. The sun was significantly fainter 3.5 billion years ago, when evidence suggests life started on Earth. Why do scientists believe the Earth was still habitable then?

Answer 74

There was a stronger greenhouse effect on Earth 3.5 billion years ago

Question 75

Which of the following reasons might make it hard for life to form on M dwarf stars? Note that M dwarfs and "red dwarfs" are the same stars.

Answer 75

The stars emit significant ultraviolet radiation. Planets orbiting in the habitable zones of M dwarfs would likely be tidally locked.

Question 76

What is meant by the term "super-Earth"?

Answer 76

A planet with a size in between that of Earth and Neptune.

Question 77

Suppose you detected oxygen in the atmosphere of an exoplanet. What additional molecule would provide the strongest evidence for life on that planet?

Answer 77

Methane

Question 78

Which of the following Earth-generated radio waves are the strongest when viewed by an alien civilization?

Answer 78

ICBM detection radar.

Question 79

What can secondary eclipse observations tell you about a planet?

Answer 79

The albedo of the planet. The reflected spectrum of the planet. The temperature of the planet.

Question 80

Which of the following techniques would be best for detecting the "red-edge" signature of chlorophyll on an exoplanet?

Answer 80

Secondary eclipse spectroscopy.

Question 81

Why did Carl Sagan's team write that "Life is the hypothesis of last resort"?

Answer 81

Given the societal impact of discovering life on other planets, all abiotic scenarios must be ruled out before a detection is claimed.

Question 82

Why might you not expect a "red edge" for planets orbiting M dwarf stars with vast plant life?

Answer 82

They would absorb as much visible light as possible and would appear black.

Question 83

NASA's upcoming James Webb Space Telescope is capable of detecting biosignatures on what type of habitable zone planet?

Answer 83

A Super-Earth transiting an M dwarf star.

Question 84

During a new or half moon, you can often perceive the full circle of the moon in the sky despite only part of the moon being lit. Why is that?

Answer 84

Sunlight reflected off of the Earth lights up the dark portion of the moon.

Question 85

What happened to the canals observed on Mars in the early 20th century?

Answer 85

They were optical illusions.

Question 86

What causes ozone in the Earth's upper atmosphere?

Answer 86

Ultraviolet radiation in the upper atmosphere.