21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 13, Problem 24QP
To determine
The reason for the Kepler mission finding eclipsing binary stars
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The NASA Kepler mission detected a transiting planet that blocks 1.3% of the stars light and the host star has a radius 82% of the Sun's radius (the Sun has a radius of 700,000 km) what is the radius of the exosolar planet in km?
Consider the attached light curve for a transiting planet observed by the Kepler mission. If the host star is identical to the sun, what is the radius of
this planet? Give your answer in terms of the radius of Jupiter.
Brightness of Star
Residual Flux
0.99
0.98
0.97
0.006
0.002
0.000
-8-881
-0.06
-0.04
-0.02
0.00
Time (days) →
0.02
0.04
0.06
One way that astronomers detect planets outside of our solar system (called exoplanets) is commonly referred to as the radial velocity method. This relies on the __________ ___________ to cause shifts in the spectral lines of stars as the stars perform tiny orbits around the center of mass of the host star and its orbiting planets. Those tiny orbits cause the stars to periodically (and therefore predictably) move closer to and further away from our solar system. Luckily, this method only relies on the motion of the star; its physical distance from us does not impact the resulting shifts.
Chapter 13 Solutions
21st Century Astronomy
Ch. 13.1 - Prob. 13.1CYUCh. 13.2 - Prob. 13.2CYUCh. 13.3 - Prob. 13.3CYUCh. 13.4 - Prob. 13.4CYUCh. 13 - Prob. 1QPCh. 13 - Prob. 2QPCh. 13 - Prob. 3QPCh. 13 - Prob. 4QPCh. 13 - Prob. 5QPCh. 13 - Prob. 6QP
Ch. 13 - Prob. 7QPCh. 13 - Prob. 8QPCh. 13 - Prob. 9QPCh. 13 - Prob. 10QPCh. 13 - Prob. 11QPCh. 13 - Prob. 12QPCh. 13 - Prob. 13QPCh. 13 - Prob. 14QPCh. 13 - Prob. 15QPCh. 13 - Prob. 16QPCh. 13 - Prob. 17QPCh. 13 - Prob. 18QPCh. 13 - Prob. 19QPCh. 13 - Prob. 20QPCh. 13 - Prob. 21QPCh. 13 - Prob. 22QPCh. 13 - Prob. 23QPCh. 13 - Prob. 24QPCh. 13 - Prob. 25QPCh. 13 - Prob. 26QPCh. 13 - Prob. 27QPCh. 13 - Prob. 28QPCh. 13 - Prob. 29QPCh. 13 - Prob. 30QPCh. 13 - Prob. 31QPCh. 13 - Prob. 32QPCh. 13 - Prob. 33QPCh. 13 - Prob. 34QPCh. 13 - Prob. 35QPCh. 13 - Prob. 36QPCh. 13 - Prob. 37QPCh. 13 - Prob. 38QPCh. 13 - Prob. 39QPCh. 13 - Prob. 40QPCh. 13 - Prob. 41QPCh. 13 - Prob. 42QPCh. 13 - Prob. 43QPCh. 13 - Prob. 44QPCh. 13 - Prob. 45QP
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- Describe three methods to find extrasolar planets.arrow_forward(Astronomy) Binary Pulsar. Part A: Use the orbital period 27 min for the binary pulsar (two neutron stars orbit each other) to find the orbital separation of the pair in AU and solar radii. Assume a neutron star's mass is 3 solar masses. (Hints: Use the version of Kepler's third law for binary stars.) Part B: Is this system orbiting closer or further than Mercury is to the Sun?arrow_forwardTime From this light curve, we can deduce that... O the star has a high mass exoplanet orbiting it O the star has an exoplanet orbiting it that has an eccentric orbit O the star has an exoplanet orbiting it that has an eccentric orbit O the star has an exoplanet that is not on the same orbital plane as the star L Brightnessarrow_forward
- A certain binary system consists of two stars that have equal masses and revolve in circular orbits around a fixed point half-way between them. If the orbital velocity of each star is v=186 km/s and the orbital period of each is 11.3 days, calculate the mass M of each star. Give your answer in units of the solar mass, 1.99×1030 kg (e.g. if each planet's mass is 3.98×1030 kg, you would answer "2.00").arrow_forwardWhich of these views cannot be used when trying to detect exoplanets using the radial velocity method? XYZ all of these can be observed using the radial velocity method none of these can be observed using the radial velocity method? X Y Z all of these can be observed using the radial velocity method none of these can be observed using the radial velocity method Figure X to Earth Figure Y to Earth Figure Z to Earth Which of the systems above could not be detected using the transit method?arrow_forwardIf a transit depth of 0.001 (or 0.1% decrease in brightness) is detected for a star with a radius of 0.3 RSun, what would the radius of the exoplanet be in units of RSun?arrow_forward
- the co te on Pictor. The 270 TOI System TOI 270 c Earth 365-day orbit $1 AU from Sun Habitable 5.7-day orbit 0.05 AU $2.4 Earth radii Largest in system 59 F, 15 C 300 F, 150 C TOI 270 TOI 270 d M3-type dwarf star TOI 270 b $11.4-day orbit 0.07 AU 3.4-day orbit 2.1 Earth radii 0.03 AU Temperate 1.25 Earth radii Likely rocky 150 F. 67 C 490 F. 254 C Figure taken from https://exoplanets.nasa.gov/news/1593/tess-scores-hat-trick-with-3-new-worlds/ What makes the TOI-270 system particularly interesting is that the three exoplanets detected this far (there may be more) have sizes comparable to the Earth. Compare the orbital period of TOI 270 c and TOI 270 d. For every revolution that TOI 270 d makes around the host star TOI 270, how many revolutions does TOI 270 c make?arrow_forwardUsing high resolution adaptive optical techniques, observations of a nearby (9.5 pc) cool star of mass 0.2 solar masses indicate the presence of a small rocky exoplanet in a circular orbit with a radius of 0.01 arcseconds. Using Kepler's Laws, estimate the period of the exoplanet's orbit in days. select units Aarrow_forwardPluto is considered a binary dwarf planet system with its companion Charon. Pluto has a mass of 1.303 x 1022 kg and mean radius of 1188.3 km. Charon has a mass of 1.586 x 1021 kg and mean radius of 606 km. The binary 5. system has a semi-major axis with the sun of 39.482 AU and there is an average distance of 19,591.4 km between the two dwarf planets. What is the system's center of mass with respect to Pluto, and why does this mean that Charon is a binary system and not a moon?arrow_forward
- If the mass of a star is 9.94 10^30 kg then what is Kepler's constant for that star?Reminder k = ( T^2 / R^3 )arrow_forward1. Planet A has an orbital period of 12 years and radius that is 0.033 times the radius of the star. Calculate the fractional dip of the star brightness in the case that planet A is transiting. Give the answer as a number. Quote the formula you use and explain any assumptions you have to make. 2. Planet B has an orbital period of 1 year and is located closer to its star than planet A. You succeed in detecting planet B with the radial velocity technique as well! From this measurement you calculate a minimum mass of planet B to be 75% that of the Earth. (a) Since you detect the planet with both transit method and radial velocity method, what do you know about the inclination of the planetary system? (b) Given this inclination, estimate the true mass of planet B (in units of Earth mass). You do not need to do a detailed calculation, just explain the argument. 3. You also measure the radius of planet B to be the same as Earth, one Earth radius. (a) How does the density of planet B compare…arrow_forward2. Over several months an astronomer observes an exoplanet orbiting a distant star at a distance of 5.934 AU. Its orbit period was projected to be 3.875 years. Convert the orbit radius to meters and period to seconds. Use this information to calculate the mass M of the star in kg and solar mass units (Mo). Star Exoplanet Orbit radius (m) Orbit period (s) Star mass (kg) Star mass (Mo)arrow_forward
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