Astronomy
1st Edition
ISBN: 9781938168284
Author: Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher: OpenStax
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Textbook Question
Chapter 20, Problem 17E
Suppose someone told you that she had discovered H II around the star Aldebaran. Would you believe her? Why or why not?
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H5.
A star with mass 1.05 M has a luminosity of 4.49 × 1026 W and effective temperature of 5700 K. It dims to 4.42 × 1026 W every 1.39 Earth days due to a transiting exoplanet. The duration of the transit reveals that the exoplanet orbits at a distance of 0.0617 AU. Based on this information, calculate the radius of the planet (expressed in Jupiter radii) and the minimum inclination of its orbit to our line of sight.
Follow up observations of the star in part reveal that a spectral feature with a rest wavelength of 656 nm is redshifted by 1.41×10−3 nm with the same period as the observed transit. Assuming a circular orbit what can be inferred about the planet’s mass (expressed in Jupiter masses)?
Let’s say you’re looking for extrasolar planets. You observe a star that has a spectral shift in the line that is supposed to be at at 656.28011 nm – this star shows this line at 656.28005 nm. What is the radial velocity of star (in m/s) and in what direction in relation to you? a) 27.4 m/s, towards b) 27.4 km/s, away c) -27.4 m/s, toward d) -27.4 km/s, away
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?
Chapter 20 Solutions
Astronomy
Ch. 20 - Identify several dark nebulae in photographs in...Ch. 20 - Why do nebulae near hot stars look red? Why do...Ch. 20 - Describe the characteristics of the various kinds...Ch. 20 - Prepare a table listing the different ways in...Ch. 20 - Describe how the 21-cm line of hydrogen is formed....Ch. 20 - Describe the properties of the dust grains found...Ch. 20 - Why is it difficult to determine where cosmic rays...Ch. 20 - What causes reddening of starlight? Explain how...Ch. 20 - Why do molecules, including H2 and more complex...Ch. 20 - Why can’t we use visible light telescopes to study...
Ch. 20 - The mass of the interstellar medium is determined...Ch. 20 - Where does interstellar dust come from? How does...Ch. 20 - Figure 20.2 shows a reddish glow around the star...Ch. 20 - If the red glow around Antares is indeed produced...Ch. 20 - Even though neutral hydrogen is the most abundant...Ch. 20 - The terms H II and H2 are both pronounced “H two.”...Ch. 20 - Suppose someone told you that she had discovered H...Ch. 20 - Describe the spectrum of each of the following: A....Ch. 20 - According to the text, a star must be hotter than...Ch. 20 - From the comments in the text about which kinds of...Ch. 20 - One way to calculate the size and shape of the...Ch. 20 - New stars form in regions where the density of gas...Ch. 20 - Thinking about the topics in this chapter, here is...Ch. 20 - Stars form in the Milky Way at a rate of about 1...Ch. 20 - The 21-cm line can be used not just to find out...Ch. 20 - Astronomers recently detected light emitted by a...Ch. 20 - We can detect 21-cm emission from other galaxies...Ch. 20 - We have said repeatedly that blue light undergoes...Ch. 20 - Suppose that, instead of being inside the Local...Ch. 20 - Suppose that, instead of being inside the Local...Ch. 20 - A molecular cloud is about 1000 times denser than...Ch. 20 - Would you expect to be able to detect an H II...Ch. 20 - Suppose that you gathered a ball of interstellar...Ch. 20 - At the average density of the interstellar medium,...Ch. 20 - Consider a grain of sand that contains 1 mg of...Ch. 20 - H II regions can exist only if there is a nearby...Ch. 20 - In the text, we said that the five-times ionized...Ch. 20 - Dust was originally discovered because the stars...Ch. 20 - How would the density inside a cold cloud (T=10K)...Ch. 20 - The text says that the Local Fluff, which...
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- H II regions can exist only if there is a nearby star hot enough to ionize hydrogen. Hydrogen is ionized only by radiation with wavelengths shorter than 91.2 nm. What is the temperature of a star that emits its maximum energy at 91.2 nm? (Use Wien’s law from Radiation and Spectra.) Based on this result, what are the spectral types of those stars likely to provide enough energy to produce H II regions?arrow_forwardThe best parallaxes obtained with Hipparcos have an accuracy of 0.001 arcsec. If you want to measure the distance to a star with an accuracy of 10%, its parallax must be 10 times larger than the typical error. How far away can you obtain a distance that is accurate to 10% with Hipparcos data? The disk of our Galaxy is 100,000 light-years in diameter. What fraction of the diameter of the Galaxy’s disk is the distance for which we can measure accurate parallaxes?arrow_forwardIf the hottest star in the Carina Nebula has a surface temperature of 51,000 K, at what wavelength (in nm) does it radiate the most energy? Hint: Use Wien's law: ?max = 2.90 ✕ 106 nm · K T How does that compare with 91.2 nm, the wavelength of photons with just enough energy to ionize hydrogen? -The wavelength calculated above is shorter than 91.2 nm. Photons at this calculated wavelength will have more than enough energy to ionize hydrogen. -The wavelength calculated above is longer than 91.2 nm. Photons at this calculated wavelength will have more than enough energy to ionize hydrogen. -The wavelength calculated above is shorter than 91.2 nm. Photons at this calculated wavelength will not have enough energy to ionize hydrogen. -The wavelength calculated above is longer than 91.2 nm. Photons at this calculated wavelength will not have enough energy to ionize hydrogen.arrow_forward
- 1) There is a one earth mass planet orbiting an M5 star of 0.2 Mo and luminosity 1x10-2 Lo- A) How close does the planet need to be to the star in order to receive the same amount of energy as the Earth receives from the sun? B) What is the orbital period of the planet at this distance? C) What is the magnitude of the radial velocity perturbation of the star? D) If the system is edge on to us, would we be likely to detect this planet using the radial velocity method?arrow_forwardMost stars (Main sequence) generate light through the same mechanism. Because of this, there is an empirical relation between their mass, M, and their Luminosity, L. This relation could be written in the form L/Lsun = (M/Msun, This relation is shown in the log-log diagram below. Find the value of a and round it to the nearest integer. 10 104 102 10-2 10-4 0.1 1.0 2.0 0.2 0.5 5.0 10.0 20.0 Mam (solar masses) Luminosty (solar units)arrow_forwardA star is transited by a planet. From the measured period T and the transit duration t alone, show that one can obtain an upper bound on the density of the transited star : rhomax= 3T/(G(pi2)(t3)). Hint: Combine Kepler's Law [(omega2)(a3)=GMstar and the equation t=((rstarT)/(pi*a))*(1-b2)1/2 to eliminate a, and then extract the density of the spherical star. The upper bound is obtained by assuming an impact parameter b=0.arrow_forward
- a) Calculate the period of the solar system's orbit around the Milky Way. Assume that we are 8.5 kpc from the galactic center and assume that the mass of the Milky Way interior to our orbit is ~ 10¹¹ solar masses. Alpha Centauri is a multiple star system only 1.34 parsecs away. The apparent magnitudes of the two main stars are: a Cen A: my = +0.01; a Cen B: my = +1.33. b) Calculate the ratio of the flux we receive in the V filter from a Cen A to the flux we receive from a Cen B. c) Calculate the absolute magnitude My of a Cen B.arrow_forward(Astronomy) White Dwarf Size I. The density of Sirius B is 2×106 g/cm3 and its mass is 1.95×1030 kg. What is the radius of the white dwarf in km? (Hint: Density = mass/volume, and the volume of a sphere is 4/3πr3) Please round your answer to two significant digits.arrow_forwardWhite Dwarf Size II. The white dwarf, Sirius B, contains 0.98 solar mass, and its density is about 2 x 106 g/cm?. Find the radius of the white dwarf in km to three significant digits. (Hint: Density = mass/volume, and the volume of a 4 sphere is Tr.) 3 km Compare your answer with the radii of the planets listed in the Table A-10. Which planet is this white dwarf is closely equal to in size? I Table A-10 I Properties of the Planets ORBITAL PROPERTIES Semimajor Axis (a) Orbital Period (P) Average Orbital Velocity (km/s) Orbital Inclination Planet (AU) (106 km) (v) (days) Eccentricity to Ecliptic Mercury 0.387 57.9 0.241 88.0 47.9 0.206 7.0° Venus 0.723 108 0.615 224.7 35.0 0.007 3.4° Earth 1.00 150 1.00 365.3 29.8 0.017 Mars 1.52 228 1.88 687.0 24.1 0.093 1.8° Jupiter 5.20 779 11.9 4332 13.1 0.049 1.30 Saturn 9.58 1433 29.5 10,759 9.7 0.056 2.5° 30,799 60,190 Uranus 19.23 2877 84.3 6.8 0.044 0.8° Neptune * By definition. 30.10 4503 164.8 5.4 0.011 1.8° PHYSICAL PROPERTIES (Earth = e)…arrow_forward
- The Sun is moving at 220 ??/? around the Galactic Center at a more-or-less constant distance of 8.5 ???. To appreciate how remarkable this is, consider the following questions: a) How massive would the Sun have to be for the Earth to have an orbital velocity of 220 km/s at 1 AU? b) How fast would the Earth move if it was in orbit around the Sun at a distance of 8.5 kpc? Of course, you may ignore the effects of all other stars in this calculation.arrow_forwardFor a main sequence star with luminosity L, how many kilograms of hydrogen is being converted into helium per second? Use the formula that you derive to estimate the mass of hydrogen atoms that are converted into helium in the interior of the sun (LSun = 3.9 x 1026 W). (Note: the mass of a hydrogen atom is 1 mproton and the mass of a helium atom is 3.97 mproton. You need four hydrogen nuclei to form one helium nucleus.)arrow_forward(Astronomy) (Part A) White Dwarf Size II. The white dwarf, Sirius B, contains 0.98 solar mass, and its density is about 2 × 106 g/cm3. Find the radius of the white dwarf in km to three significant digits. (Hint: Density = mass⁄volume, and the volume of a sphere is 4/3πr3). (Part B) Compare your answer with the radii of the planets listed in the Table A-10. Which planet is this white dwarf is closely equal to in size?arrow_forward
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