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Science OlympiadAnnotated
Astronomy C Division EventSample Exam
Stellar Evolution: Star and Planet Formation
2014-2015
Team Number:
Team Name:
Example Instructions:1) Please turn in all materials at the end of the event.
2) Do not forget to put your team name and team number at the top of all answer pages.
3) Write all answers on the answer pages. Any marks elsewhere will not be scored.
4) Do not worry about significant figures. Use at least 2 or 3 in your answers, regardless of how
many are in the question.
5) Note, the answer key for a real exam would include ranges of acceptable answers. Use ±10% (give
or take a few %) when checking yours against the key.
6) Please do not access the internet during the event. If you do so, your team will be disqualified.
7) This test was downloaded from: www.aavso.org/science-olympiad-2015.
8) Good luck! And may the stars be with you!
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Guidelines:Hello, supervisor! Thank you for lending your time to put together an Astronomy
event. The entire Science Olympiad organization relies on the hard work of volunteerslike you (and I), and it is great that you are helping Science Olympiad continue tofoster extracurricular secondary education in the sciences.
Though the backbone of the Astronomy event is the same, focusing on stellarevolution using a mixture of image analysis, qualitative reasoning, and quantitativephysics, the specific topic has changed to star formation and exoplanets. Pay atten-tion to the bold lettering on the rules sheet, as this shows the new information forthis year.
To review the rules, first, the event parameters have remained the same. Teamsare allowed to bring in either 2 binders, 2 laptops/tablets, or 1 binder and one lap-top/tablet. Please check during the event that there is no internet access being usedby the teams. How specifically to do so is at your discretion, but checking that thewireless is turned o↵ (easy to do by sight on both PC and Mac) is the simplest way.Additionally, be sure to note that many teams may download webpages and openthem in a browser - this is fine, simply check the URL to see that it leads to theirhard drive.
The rules are split into 3 sections, as before: a) general topics, b) physics topics,and c) objects (and planetary systems for this year). Section (a) of the rules focuseson the impact of stellar evolution on planet formation, using traditional astronomicalmethods (spectra, blackbody radiation, Hertzsprung-Russell diagram, etc.) to diag-nose young stars, such as T Tauri stars, their formation environment (clouds in theinterstellar medium), and potential exoplanets forming around them. Section (b) isrelated to the physics of these planetary systems, where students use non-calculusKeplerian physics to understand how to obtain distances to and the orbits of exoplan-etary systems. Specifically, both the radial velocity and transit method of diagnosingexoplanet orbits will be focused on. Section (c) then looks at specific objects- youngstars (e.g. FU Origins), systems with exoplanets (CoRoT-2), exoplanets themselves(HD 209458b), brown dwarfs (Gliese 229B), star formation regions (M20). Studentsshould be able to identify and know basic information about these objects, specificallywhy they are important in the context of the event and their knowledge from Sections(a) and (b).
The test itself here is also split into 3 sections, which do not map directly onto therules themselves. Section (a) is a basic qualitative section, focusing on Sections (a)and (c) of the rules. Hence, it is about understanding the foundation of the event,specifically how stellar evolution works and knowing concepts and objects outlinedin the rules. Section (b) is the physics section, which here focuses on exoplanet de-tection. Essentially, given the same information as a real astronomer has about agiven system, students are asked to calculate properties of the exoplanetary system,e.g. the semi-major axis from the planet to the star or the radius and/or mass of theexoplanet. Section (c) combines material from Sections (a), (b), and (c) together forstudents to make inferences about the habitability of exoplanets and understand thecontext of exoplanetary systems with respect to stellar evolution and our own SolarSystem.
Resources may be found at http://soinc.org/astronomy_c, http://www.aavso.org/
science-olympiad-2015, and http://chandra.harvard.edu/edu/olympiad.html.
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Section A: Use Image/Illustration Set A to answer Questions 1-19. This section fo-cuses on qualitative understanding of stellar evolution, specifically relating to starformation and planets.This section is e↵ectively split into two parts, with Questions 1-4 covering Section(a) of the rules, and the remainder covering Section (c) using parts of Section (a)as a backbone. Note how questions on specific types of objects and those in Section(c) are split into their own question for easy referral to by students when collaborat-ing. Additionally, if there are many choices for an answer, they are delimited in thequestion itself for clarity.
1. A schematic of a T-Tauri star is shown in Image A1.
(a) Which point (A-F) marks the location of the disk surrounding the protostar?
(b) Which point (A-F) displays the bipolar outflow that may form Herbig-Haro objects?
(c) Which point (A-F) shows the strongly variable hot spots on the protostar?
2. A color-magnitude diagram for a sample of brown dwarfs is shown in Image A2. The x-axisshows the J-K color index, while the y-axis displays J-band magnitude. The di↵erent colorsrepresent di↵erent brown dwarf spectral types.
(a) Which lettered region (A-D) corresponds approximately to a spectral type L2 browndwarf?
(b) Which lettered region (A-D) corresponds approximately to a spectral type T6 browndwarf?
(c) Which lettered region (A-D) corresponds approximately to the brown dwarf L-T typetransition?
3. The spectrum of a star with a circumstellar disk is shown in Image A3.
(a) Which line (red or blue) represents the blackbody spectrum of the star itself?
(b) Which point (A-C) shows where the disk emission dominates over that of the star?
(c) This point is at much longer wavelengths than the peak emission from the star. Whyis this?
4. Light curves from a variety of objects are shown in Images A4-A8.
(a) Which light curve is from a star with a transiting exoplanet in orbit around it?
(b) Which light curve is from a T Tauri star?
(c) Which light curve is from an FU Orionis star?
(d) Which light curve is from a variable brown dwarf?
(e) Which light curve is from a Herbig Ae/Be star?
The following questions (5-19) correspond to Images A9-A24.
5. Which two images show star formation regions?
6. TW Hydrae is the closest T Tauri star to the solar system.
(a) Which image shows TW Hydrae?
(b) What surrounds TW Hydrae in the image?
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7. WISE 1049-5319 harbors the closest brown dwarf to Earth.
(a) Which image shows this system?
(b) How many brown dwarfs are in this system?
8. Which one of the following images shows an object with a debris disk?
(a) A15
(b) A20
(c) A10
(d) A17
9. Which image shows LP 944-20?
10. One of the images displays a star that is bright in X-Rays and has a planet in a close-inorbit.
(a) Which image shows this star?
(b) What is the name of this star?
11. FU Orionis is a prototype of a class of variable stars with its namesake.
(a) Which image shows FU Orionis?
(b) What distinguishes this type of object from normal T Tauri stars?
12. Beta Pictoris is a nearby star with a circumstellar disk.
(a) Which image shows this object?
(b) Beta Pictoris has a planet, Beta Pictoris b, in orbit around it. Is the distance from BetaPictoris to Beta Pictoris b greater or less than the distance from the Sun to Neptune?
13. The 2M 1207 system was discovered in 2004.
(a) Which image shows this object?
(b) What two types of objects comprise this system?
14. HR 8799 is a star with both a debris disk and planets in its system.
(a) Which image shows this object?
(b) Which method was used to detect the orbital motion of its planets?
15. Gliese 229B is a brown dwarf orbiting a star, Gliese 229.
(a) Which image shows this object?
(b) What type of variable star is Gliese 229?
16. Image A21 shows a simulated atmospheric temperature map of HD 209458b.
(a) What longitude and latitude is the substellar point located on this map?
(b) Why is the hottest point not located directly at the substellar point?
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17. Image A22 shows an observed atmospheric temperature map of an exoplanet.
(a) Which exoplanet is this?
(b) Does this object have a hotter or colder substellar point than HD 209458b?
18. Image A23 shows a transmission spectrum of an exoplanet. The black points show observa-tions, with the lines indicating models for di↵erent atmospheric compositions.
(a) Which exoplanet is this?
(b) What is indicated by the misfit between the data points and expectation?
19. Image A24 shows the brightness map of an exoplanet.
(a) Which exoplanet is this?
(b) What is a possible implication of the brightest point on this planet being on the oppositeside of the planet than expected?
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Section B: Use Image/Illustration Set B to answer Questions 20-25. This sectiondiscusses radial velocity and transit methods, working through the advantages ofeach, and concluding with calculations of planet properties using these methods.This section is also split into two parts, with Questions 20-23 covering qualitativeaspects of exoplanet detection with Questions 24 and 25 focusing on quantitativeproblem solving. Question 24 focuses on radial velocity detection of exoplanetmass (taking students step-by-step to the calculation), while Question 25 focuseson transit detection of radius, again taking students step-by-step to the finalanswer (and asking a follow-up question).
20. Which of the following planet properties is best constrained via the transit method?
(a) Mass
(b) Atmospheric Composition
(c) Density
(d) Radius
21. Which of the following planet properties is best constrained via the radial velocity method?
(a) Mass
(b) Atmospheric Composition
(c) Density
(d) Radius
22. How can an observer obtain the e↵ective temperature of a planet via the transit method?
23. When using the radial velocity method, is an observer measuring the maximum or minimummass of a planet? Why?
24. Image B1 shows the radial velocity curve of host Star A, around which Planet B orbits. StarA has the same mass, radius, and luminosity as the sun. Assume that the system has noinclination and Planet B has 0 eccentricity (a circular orbit).
(a) What is the distance from Star A to Planet B, in AU, assuming Planet B has a massmuch less than that of Star A?
(b) What is the velocity of Planet B in its orbit around Star A, in km/s?
(c) What is the mass of Planet B, in Jupiter masses?
(d) Planet B has a radius of 0.8 Jupiter radii. What is the density of Planet B, in g/cm3?
25. Image B2 shows the light curve of Star C, displaying transits due to Planet D. Star C is aK1 star with a mass of 0.80 Solar Masses and radius of 0.79 Solar Radii. The orbital periodof Planet D is 2.22 days. Assume that the system has no inclination and Planet D has 0eccentricity.
(a) Which point (A-E) shows the Primary Eclipse, when Planet D blocks light from StarC?
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(b) Which point (A-E) shows the Secondary Eclipse, when Star C blocks light from PlanetD?
(c) What is the transit depth of the Primary Eclipse, in terms of the % of normal (non-eclipse) system flux?
(d) What is the radius of Planet D, in Jupiter radii?
(e) What is the total duration of the Primary Eclipse, in seconds?
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Section C: Use Image/Illustration Set C to answer Questions 26-29. This sectionfocuses on the mathematics of stars & planetary systems.This section is for the astrophysical “jack of all trades,” and is nominally thehardest, hence why it is the last to appear on the exam. Question 26 goes step-by-step through a habitability calculation: knowing some basic information about anexoplanetary system, can the student say something about whether water mightbe present on its surface in liquid form? Question 27 is an astrophysical question,looking at stellar spectra and qualitatively explaining their di↵erences. Question28 is a combined astrophysical and planet question, including both calculatinga distance to a star and then using that distance to compare the brightness ofa planet and its host star. Question 29 is a question using a graph to comparethe properties of planets in the Kepler-11 planetary system, seeing which oneshave densities unlike and similar to our own Earth, for purposes of comparativeplanetology.
26. Image C1 shows the blackbody spectrum of Star E, which is a main-sequence star with aparallax of 0.1” and radius of 0.480 Solar Radii. Planet F orbits Star E, has the same massand radius as Earth, and lies at a distance of 0.176 AU from Star E.
(a) What is the distance to Star E, in parsecs?
(b) What is the e↵ective temperature of Star E, in Kelvin?
(c) What is the Spectral Type of Star E?
(d) What is the equilibrium temperature of Planet F, in Kelvin, assuming it has 0 albedo?
(e) Is Planet F potentially habitable? Use the phase diagram for water in Image C2 to aidyour response. Assume that habitability only requires the existence of liquid water onthe surface of a planet, and that Planet F has the same atmospheric surface pressureas Earth.
(f) Your response for Part (d) did not include the greenhouse e↵ect. Would the greenhousee↵ect be stronger or weaker for Planet F than for Earth? Why?
27. Images C3, C4, and C5 show spectra from 3 di↵erent main-sequence stars.
(a) Which image corresponds to the star with the highest luminosity?
(b) Which image corresponds to the star with the lowest e↵ective temperature?
(c) Which image corresponds to a spectral type F5 star?
28. Star G is a M2V star at a distance of 50 parsec. Planet H orbits Star G at a distance of 0.01AU, and has a radius equal to that of Jupiter.
(a) What is the apparent visual magnitude of Star G?
(b) Assuming that Planet H has 0 albedo, how many times brighter is Star G than PlanetH?
29. A plot of planet Radius (in Earth Radii) vs. Mass (in Earth Masses) for the Kepler-11 systemis shown in Image C6, with the Solar System planets over-plotted as triangles and a sampleof transiting exoplanets plotted as squares. Lines of constant density for a given compositionare also shown.
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(a) Which planet orbiting Kepler-11a has the highest density (b-f)?
(b) What is the density of Kepler-11c, in g/cm3?
(c) Kepler-11g is a recently discovered member of the system, with a yet-undetermineddensity. Its semi-major axis is 0.46 AU, and it has an orbital period around Kepler-11aof 118.4 days. What is the mass of Kepler-11a, in Solar Masses, assuming the mass ofKepler-11g is much smaller than Kepler-11a?
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Image/Illustration Set A:
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8.2 FU Orionis stars 289
1940.0mpgorB
10.0
11.0
12.0
13.0
14.0
15.0
16.0
JD 2428000 32000
pre-oulburslrange
36000 40000
1945.0 1950.0 1955.0 1960.0 1965.0 1970.0 1975.0
Figure 8.6 The photographic (small points) or B (large points) light curve of FU
Orionis through 1976. After brightening in the 1930s, the star has faded slowly.
(From Herbig, 1977.)
variables to active galactic nuclei. T Tauri discs are found among the lowest-
mass PMS stars, and even around brown dwarfs. The key properties of a T Tauri
star are therefore a result of its recent formation. The infall or accretion of
material, from the disc, powers most of the features of these stars, and their
variability.
8.2 FU Orionis stars
In the late 1930s, the star now known as FU Orionis brightened from
mpg +16 to mpg +10 --- a factor of more than a hundred. Since 1940, the star has
faded somewhat, as shown in the light curve in figure 8.6. It is an F2 I--II star
with an absolute magnitude of about −2. Thus, it appears, from its spectrum,
to lie several magnitudes above the main sequence (though the true brightness
of the star itself may still be that of a main sequence star). The nature of FU
Orionis before the brightening, and the cause of the brightening itself were not
known, but it was tempting to think that it represented some unique event in
the star’s evolution --- perhaps even the ‘birth’ of the star. This was a common
(mis)conception in the 1960s.
The situation was changed somewhat by the discovery of two more rather
similar objects: V1057 Cygni and V1515 Cygni. V1057 Cygni was a T Tauri star
which, in 1969, rose from mpg +16 to +10, then slowly faded. By mid 1982,
it was fainter than mpg +13; it faded by one magnitude in five years, whereas
FU Orionis faded by only 0.5 magnitude in 40 years. FU Orionis can no longer
be considered unique. Strangely enough, V1057 Cygni is not included under
282 Pre-main-sequence variable stars
V light curve of DK Tauri, a T Tauri star
V m
agni
tude
926592609255925092459240Julian Date - 2440000
9235923092259220921514.5
14.0
13.5
13.0
12.5
12.0
11.5
Figure 8.3 Light curve of the T Tauri star DK Tauri. The star shows very large
periodic variations as a result of the rotation of the star. The surface of the star is
highly non-uniform, as a result of magnetically channelled accretion from the disc
around it. The period is 8.0 days. (Data from W. Herbst.)
to classical T Tauri stars. These evolve into WTTS, which then evolve smoothly
into sunlike rotating variables, after their accretion disc is gone.
8.1.1 Photometric variability
Most WTTS have simple periodic variations, with occasional flares. V410
Tau is a well-studied example; it has a period of 1.871970 days, and an amplitude
that varies in a 5.4-year cycle, which might be analogous to the solar cycle. It
also flares in both light and X-rays (Stelzer et al., 2003).
The brightness variations in classical T Tauri stars can be complex and irreg-
ular, with amplitudes ranging from 0.01 to many magnitudes, and taking place
on time scales from days, through hours, to minutes. It is interesting that these
three time scales resemble the natural time scales of rotation of the star (or orbit
of circumstellar material), free fall, and flaring of the star, respectively. They are
indicative of the broad range and complexity of the mechanisms in these stars.
There may also be variations on time scales of weeks, months, or years. T Tauri
stars that undergo FU Orionis outbursts vary on time scales of decades.
Figure 8.3 shows a typical light curve of a periodic T Tauri star. It has an
unusually large amplitude, which is probably due to the rotation of a hot spot
produced by accretion.
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A6
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Note how the images are numbered by Section and number within Section. This is for easy referral to images in the test, to minimize confusion.
Image/Illustration Set A:
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Fig. 4.— Longitudinal brightness maps of Kepler-7b. Kepler-7b’s longitudinal brightness distributionsIp
I⋆as retrieved in Kepler’s
bandpass using the 1-free-band model (left) and the 3-fixed-band model (right) detailed in Sect.3.3).
match to the data. However, we exclude Rayleigh scat-tering from H2 molecules and homogeneous cloud struc-tures as possible sources of visible phase-curve signa-tures, which would both result in a symmetric phasecurve.Kepler-7b may be relatively more likely to show the
effects of cloud opacity than other hot Jupiters. Theplanet’s incident flux level is such that model profilescross silicate condensation curves in the upper, observ-able atmosphere, making these clouds a possible expla-nation. The same would not be true for warmer plan-ets (where temperatures would be too hot for daysideclouds) or for cooler planets (where silicates would onlybe present in the deep unobservable atmosphere). Fur-thermore, the planet’s very low surface gravity may playan important role in hampering sedimentation of parti-cles out the atmosphere. Finally, the planet’s large radiusimplies a relatively high specific entropy adiabatic in theinterior, and a correspondingly warm adiabat in the deepatmosphere at tens of bars. This removes the possibil-ity of silicate clouds condensing at pressures of 100-1000bars, as may happen in other hot Jupiters.Our results suggest that one broad-band visible phase
curve is probably insufficient to constrain the cloud prop-erties. The problem might remain degenerate until moreobservations (such as narrow-band optical phase curvesand polarimetry) become available. In the near futureit is likely that similar brightness maps of other Ke-pler planets will emerge, thereby providing an invaluablemeans to improve our understanding of cloud formationin exoplanet atmospheres.
We thank G.Basri and both anonymous referees forhelpful comments that improved the paper. This workis based in part on observations made with the SpitzerSpace Telescope, which is operated by the JPL, Caltechunder a contract with NASA. A.Zsom was supportedby the German Science Foundation (DFG) under grantZS107/2-1. This work was performed in part under con-tract with the California Institute of Technology fundedby NASA through the Sagan Fellowship Program exe-cuted by the NASA Exoplanet Science Institute. J.deWit acknowledges support from the Belgian AmericanEducational Foundation and Wallonie-Bruxelles Interna-tional.Facilities:Kepler,Spitzer
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578 SHOWMAN ET AL. Vol. 699
Thus, we performed several simulations of HD 209458bincluding TiO and VO opacity in chemical equilibrium. Whentemperatures are too cold for TiO and VO to exist in the gasphase, they are absent, but when temperatures are warm enough,they are included.
Our HD 209458b simulations develop vigorous circulationsthat, as expected, include a hot dayside stratosphere. This isillustrated in Figure 16, which shows the temperature andhorizontal wind patterns at pressures of 1 bar, 30 mbar, 1 mbar,and 0.1 mbar (bottom to top) for our case with solar abundances.At deep levels (1 bar and 30 mbar), the circulation qualitativelyresembles that of HD 189733b, with an eastward equatorial jet,westward high-latitude flows, and a hot region shifted east of thesubstellar point (compare the bottom two panels of Figures 4 and16). Nevertheless, even at these deep levels, localized regionsattain temperatures sufficient for TiO/VO to exist in the gasphase (∼1700–1900 K).
By pressures of 1 mbar, the picture changes drastically: a“baby” stratosphere with a radius of 50◦ in longitude and latitudehas developed, with temperatures reaching 2000 K (Figure 16,second panel). This stratosphere is approximately centered onthe substellar point, with an eastward offset of only ∼10◦
longitude. Its spatial confinement results from the fact thatonly air within ∼50◦ of the substellar point receives sufficientirradiation to achieve temperatures necessary for gas-phase TiOand VO to exist. Air >60◦ from the substellar point, althoughstill on the dayside, has temperatures too low for gas-phase TiO/VO, and without the benefit of the extra opacity supplied bythese species, this air remains substantially cooler (<1400 K).This nonlinear feedback between temperature and opacity leadsto a remarkably sharp temperature gradient, with temperaturesdropping from 1800 to 1400 K as one moves from 50◦ to 60◦
angular distance from the substellar point.At still lower pressures, an even greater fraction of the
starlight is available to cause heating, and the stratosphere be-comes horizontally larger until it covers most of the daysideat pressures !0.1 mbar (Figure 16, top panel). Although theequatorial winds at these low pressures involve a significanteastward flow at most longitudes, the mid- and high-latitudewinds involve a simpler motion that, to zeroth order, moves airaway from high-temperature regions toward low-temperatureregions. At low pressure, the temperature pattern is relativelysymmetric about the substellar and antistellar points, as sug-gested observationally for Ups And b (Harrington et al. 2006)and HD 179949 (Cowan et al. 2007).
A contributing factor to the widening of the stratosphere withaltitude is that stellar radiation is absorbed at lower pressurenear the limb than at the substellar point, which results directlyfrom the longer atmospheric path length to stellar irradiation atthe limb (µ → 0) than at the substellar point (µ = 1). Thus,near the limb the heating peaks at lower pressure, confiningthe stratosphere to low pressures. Near the substellar point, theheating peaks deeper, allowing the stratosphere to extend moredeeply in this localized region.
Our simulated stratospheres result directly from the existenceof gaseous TiO and VO on the dayside in these simulations. Sim-ulations of HD 209458b performed without gaseous TiO/VOlack stratospheres and develop temperature and wind patternsresembling a hotter version of our HD 189733b simulations.Likewise, our previous HD 209458b simulations performed withNewtonian heating/cooling (Showman et al. 2008a) developeda weak dayside temperature inversion but nothing resemblingthe extremely hot stratosphere shown in Figure 16.
Figure 16. Temperature (colorscale, in K) and winds (arrows) for nominal HD209458b simulation with solar abundances including TiO/VO. Panels showflow at 0.1 mbar (top), 1 mbar (second panel), 30 mbar (third panel), and 1 bar(bottom panel). Horizontal resolution is C32 (roughly equivalent to a resolutionof 128 × 64 on a longitude/latitude grid) with 53 vertical layers. Substellarpoint is at longitude, latitude (0◦, 0◦). Note the development of the daysidestratosphere.(A color version of this figure is available in the online journal.)
To illustrate the height-dependence of the composition (whichaffects the opacity), Figure 17 depicts the chemical-equilibrium
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Separated light curves/diagrams (last page) from DSO images (this page) to help students.
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0 1 2 3 4 5 6 7 8Time (days)
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Similarly to how I created Image B1 myself, you can use the radial velocity applet provided in the resources to create your own!
Image/Illustration Set C:C1
0 500 824100 1500 2000Wavelength (nanometers)
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Team name: KEY Team number: KEY
Answer Page: Section A
1. (a) B
(b) A
(c) F
2. (a) D
(b) A
(c) C
3. (a) Blue
(b) C
(c) Dust in disk re-radiates in Infrared
4. (a) A8
(b) A5
(c) A4
(d) A7
(e) A6
5. A15, A19
6. (a) A10
(b) Protoplanetary Disk
7. (a) A16
(b) Two
8. D, A17
9. A20
10. (a) A14
(b) CoRoT-2
11. (a) A11
(b) Strong outbursts
12. (a) A9
(b) Less
13. (a) A12
(b) Brown Dwarf, Planet
14. (a) A13
(b) Direct imaging
15. (a) A18
(b) Flare star (eruptive variable)
16. (a) 0�, 0�
(b) Winds moving hot air eastward
17. (a) HD 189733b
(b) Colder
18. (a) GJ 1214b
(b) It has clouds/haze in its atmosphere
19. (a) Kepler-7b
(b) It has clouds in the bright region
Scoring: Choose a point value for all ques-tions beforehand. At the National level,each question (in this test, sub-question)is worth 1 point, for ease of grading giventhat we have ⇠ 1 hour to get all of ourtests in after the day of competition isover. However, if you are supervising inthe morning, there is much more flexibil-ity in terms of grading. Hence, please takeinto account the time you are supervisingand how many teams there are to grade,along with how much help you have, whenchoosing a markscheme and deciding howto evaluate exams. For example, too manyshort-answer questions would be problem-atic if you were testing in the afternoon,as great care must be taken to ensure thatall questions are graded evenly and fairly.
Team name: KEY Team number: KEY
Answer Page: Section B
20. D
21. A
22. Secondary Eclipse depth
23. Minimum mass, because one needs to account of the (unknown) inclination of the system.
24. (a) 0.041 AU
(b) 149 km/s
(c) 0.495 Jupiter Masses
(d) 1.20 g/cm3
25. (a) B
(b) D
(c) 2.49 %
(d) 1.21 Jupiter Radii
(e) 7240 Seconds
Ensure that there is enough space for students with large handwriting to write responses on theanswer sheets, and make sure to taking the test yourself for any inconsistencies in numbering orerrors in the answer key. Also, it is nominally a good idea to have teams write their team numberand name on each page of the answer sheets, so that if there is a mix-up when the tests are handedin it is still possible to salvage misplaced sheets.
Be clear to indicate the units you want a quantitative answer in, both on the answer sheet and inthe question itself.
Team name: KEY Team number: KEY
Answer Page: Section C
26. (a) 10 Parsec
(b) 3520 Kelvin
(c) M2
(d) 280 Kelvin
(e) Yes, it is habitable, at 1 atm surface temperature needs to be between 273 and 373 Kelvin
(f) Weaker, more Infrared radiation incident than for Earth so more absorption of incoming radiation
27. (a) C4
(b) C5
(c) C3
28. (a) 13.9
(b) 1770
29. (a) B
(b) 2.38 g/cm3
(c) 0.926 Solar Masses
Be clear to indicate the units you want a quantitative answer in, both on the answer sheet and inthe question itself.
Team name: Team number:
Answer Page: Section A
1. (a)
(b)
(c)
2. (a)
(b)
(c)
3. (a)
(b)
(c)
4. (a)
(b)
(c)
(d)
(e)
5.
6. (a)
(b)
7. (a)
(b)
8.
9.
10. (a)
(b)
11. (a)
(b)
12. (a)
(b)
13. (a)
(b)
14. (a)
(b)
15. (a)
(b)
16. (a)
(b)
17. (a)
(b)
18. (a)
(b)
19. (a)
(b)
Ensure that there is enough space for stu-
dents with large handwriting to write re-
sponses on the answer sheets, and make
sure to taking the test yourself for any in-
consistencies in numbering or errors in the
answer key. Also, it is nominally a good
idea to have teams write their team num-
ber and name on each page of the answer
sheets, so that if there is a mix-up when
the tests are handed in it is still possible
to salvage misplaced sheets.
Team name: Team number:
Answer Page: Section B
20.
21.
22.
23.
24. (a) AU
(b) km/s
(c) Jupiter Masses
(d) g/cm
3
25. (a)
(b)
(c) %
(d) Jupiter Radii
(e) Seconds
Be clear to indicate the units you want a quantitative answer in, both on the answer sheet and in
the question itself.
Team name: Team number:
Answer Page: Section C
26. (a) Parsec
(b) Kelvin
(c)
(d) Kelvin
(e)
(f)
27. (a)
(b)
(c)
28. (a)
(b)
29. (a)
(b) g/cm
3
(c) Solar Masses
Be clear to indicate the units you want a quantitative answer in, both on the answer sheet and in
the question itself.