The in-person version of this activity is attached below. The following is the version used in ASTR150 online. We run it as a Canvas quiz but I envision running this in a variety of ways (group discussion, short answer, essay, etc). I recommend running this online with a accompanying discussion so students can interact with their peers as they would in an in-person lab. You or your TAs can help moderate and jump in in the students need help.
Please be aware that due to the timing of the final exam this assignment will not have the usual 24hr grace period after the due date. The assignment will be unavailable and the answers will be revealed at 12:01am Monday.
Introduction
Planets that orbit stars other than our Sun are called exoplanets. As you have seen, detecting planets orbiting distant stars is no simple task and it’s taken us over 20 years to really become proficient at it. The discovery rate has increased tremendously since the discovery of the very first exoplanet, 51 Pegasi b in 1995 and has increased to nearly 3-4000 confirmed exoplanets and well over 3000 potential candidates that are currently being vetted. The plot below shows the number of exoplanet discoveries each year through April 2018. The different colors indicate the detection technique. The green coloring are exoplanets discovered using the Radial Velocity Method and the purple coloring are exoplanets discovered using the Transit Method.
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The large increase in the discovery rate in 2014 and 2016 corresponds to the release of data from the Kepler space telescope mission. The Kepler mission, launched in 2009, continually monitored the brightness of over 145,000 stars in a single field of view a bit over 10 square degrees on the sky. The brightness of some of these monitored stars dimmed periodically as planets passed in front of the star, blocking out or eclipsing some of the starlight. We call these eclipses transit events. This is how the majority of exoplanets have been discovered to date. The image below shows how a transit looks in our own Solar System. Here, a series of images added together shows Venus transiting or passing between the Earth and the Sun, blocking some of the Sun’s light.
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The amount of light that a planet blocks out, known as the transit depth, is related to how big the planets is. If the planet were the same size (had the same radius) as the star it would block out the star light completely when it passed precisely in front (between us and the star), and if the planet were the size of a piece of dust it wouldn’t block out much light at all as demonstrated in the figure below.
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Goals
In this experiment you will use the light curves of two different exoplanets orbiting a Sun-like star. The light curves will allow you to determine the radius of the planet. This radius when combined with the mass from another method can be used to determine the density of the exoplanets. To obtain the radius of a planet we use the following formula (Equation 1):
Δ A B = ( R p l a n e t R s t a r ) 2
where Δ AB is the change in the apparent brightness of the parent star, Rplanet is the radius of the exoplanet and Rstar is the radius of the parent star. To simplify our calculations, we will assume the parent star is Sun-like. In other words, we’ll assume the star has the same mass and radius as the Sun so all of the dynamics in this system are the same as in our own Solar System..
Our goal is to determine the radius of each planet from the change in brightness of the parent star. Using the fact that the Sun has a radius that is 109 times larger than the radius of Earth, we can rearrange Equation 1 to yield the radius of the planet in units of Earth radii (REarth) like so (Equation 2):
R p l a n e t = 109 R E a r t h × Δ A B
Keep in mind that the units are REarth so your final equation should look like Rplanet = #REarth.
Procedure
Assume we measured the brightness of a star about which two planets orbit. We found the following transit events for the two planets, which we will call Exoplanet A and Exoplanet B.
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The values in the data table were determined for each Exoplanet in the above light curve. Use the values given in the data table as well as the rest of the information given here to find the missing values and answer the following questions. Keep in mind that there is an associated activity forum, Lesson 10 Activity Forum, for you to work with your classmates on these questions. As usual, do not give out the exact answers, but feel free to help your fellow students. You have only one attempt at this activity so take your time and work carefully.
Exoplanet
A
B
Period
(days)
10
300
Mass
(MEarth)
6.0
1.3
Rplanet
(REarth)
?
?
Composition
?
?
Δ A B
( % Δ 100 )
7 x 10-4
1.5 x 10-4
Credits:
Image 01 - Transit of Venus. Slovak Union of Amateur Astronomers VT-2004 Team, Jun 8, 2004.
Question 1
Use Equation 2 and the data given in the table to find the radius of Exoplanet A in terms of Earth's radius. Your answer should be given to two decimal places (e.g. 1.11).
Question 2
Use Equation 2 and the data given in the table to find the radius of Exoplanet B in terms of Earth's radius. Your answer should be given to two decimal places (e.g. 1.11).
Question 3
There is good reason to believe that planets with radii 1.5 times larger than the Earth’s are likely to be gaseous, and smaller planets are likely to be rocky. By comparing the radii of these exoplanets with the radii of planets in our Solar System (Earth’s radius = 1 R⊕ and Jupiter’s radius = 11 R⊕), what is the composition of Exoplanet A?
Group of answer choices
1 pts
1 pts
1 pts
Rocky
Gaseous
Need more information to determine the composition.
Question 4
There is good reason to believe that planets with radii 1.5 times larger than the Earth’s are likely to be gaseous, and smaller planets are likely to be rocky. By comparing the radii of these exoplanets with the radii of planets in our Solar System (Earth’s radius = 1 R⊕ and Jupiter’s radius = 11 R⊕), what is the composition of Exoplanet B?
Group of answer choices
1 pts
Rocky
Gaseous
Need more information to determine the composition.
Question 5
At least one of your exoplanets should be a rocky planet. Let’s assume that the exoplanets you are looking at formed at the same time as our Solar System 4.5 Byrs ago. What do you expect its level of geologic activity to be most like?
Group of answer choices
1 pts
Slightly more active than the Earth.
Slightly less active than the Earth.
Not active at all. It's entered the "Big Chill" phase of its evolution.
Several times more active than the Earth.
Question 6
The period for each exoplanet given in the Data Table was determined by observing multiple transits of each planet. Use the period as well as the radius of each planet, and determine which planet you’d be most likely to find life (like Earth's) on.
Group of answer choices
1 pts
Exoplanet A
Exoplanet B
Both Exoplanets could have life.
Neither Exoplanet would have life.
Question 7
Pretend these planets orbit our Sun. Where in our Solar System would you expect to find Exoplanet B in orbit?
Group of answer choices
1 pts
Closer to the Sun than Mercury.
Between Mercury and Venus.
Between Venus and Earth.
Beyond the Snow Line
Question 8
The mass of each exoplanet given in the data table was determined using the Radial Velocity method, of which you are now familiar with. With the mass and the radius, we have enough information to calculate the density. The density of a world can be calculated using the following equation to yield the density in units of g/cm3:
ρ = 5.5 × M ( R ) 3
Calculate the density of Exoplanet A. You answer should be give to two decimal places (e.g. 1.01)
Question 9
The mass of each exoplanet given in the data table was determined using the Radial Velocity method, of which you are now familiar with. With the mass and the radius, we have enough information to calculate the density. The density of a world can be calculated using the following equation to yield the density in units of g/cm3:
ρ = 5.5 × M ( R ) 3
Calculate the density of Exoplanet B. You answer should be give to two decimal places (e.g. 1.01)
Question 10
Based on all of the data you have now calculated for these exoplanets, how would you best describe Exoplanet A?
Group of answer choices
1 pts
1 pts
1 pts
It's a big, "hot Jupiter".
It's a "hot Neptune".
It's a small, hot rocky world like Mercury.
It's probably very much like Venus.