21ST CENT.AST.W/WKBK+SMARTWORK >BI<
6th Edition
ISBN: 9780309341523
Author: Kay
Publisher: NORTON
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Chapter 13, Problem 22QP
To determine
How the astronomers measure the mass of the stars
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"51 Pegasi" is the name of the first normal star (besides the Sun) around which a planet was discovered. It is in the constellation Pegasus the horse. Its parallax is measured to be 0.064 arcsec.
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The Algol binary system consists of a 3.7 Msun star and a 0.8 Msun star with an orbital period of 2.87 days. Using Newton’s version of Kepler’s Third Law, calculate the distance, a, between the two stars. Compare that to the size of Betelgeuse (you’ll need to look that up).
Newton’s Version of Kepler’s Law: (M1 + M2) P2 = (4p2 /G) a3
Rearrange the equation to solve for a. Pi, p, is equal to 3.14. IMPORTANT NOTE: Google the value of G (the Universal Gravitational Constant) or look it up in your text. NOTICE THE UNITS. You must convert every distance and time in your equation to the same units, otherwise, you’ll get an incorrect answer. That means you must convert distances to meters, solar masses to kilograms, and time to seconds. When you compare your value to the size of Betelgeuse, it will also help that they are in the same units.
Which of the following is a true statement?
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Chapter 13 Solutions
21ST CENT.AST.W/WKBK+SMARTWORK >BI<
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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- 15: A star has a parallax angle of 0.0270 arcseconds and an apparent magnitude of 4.641. What is the distance to this star? Answer: 37 16: What is the absolute magnitude of this star? Answer:1.8 17: Is this star more or less luminous than the Sun? Answer "M" for More luminous or "L" for Less luminous. (HINT: the absolute magnitude of the Sun is 4.8) Answer: M 18: What is the luminosity of this star? (HINT: The luminosity of the Sun is 3.85×1026 W.) Please answer question #18, #15-17 are correct, the photos provide the work for them.arrow_forwardIn a binary star system, the average separation between the stars is 4.0 AU, and their orbital period is 5.0 years. What is the sum of their two masses? The average distance of Star A from the center of mass is four times that of Star B. What are their individual masses?arrow_forwardWhich star in the table below has the greatest diameter? Star Name d (parsecs) Parallax (seconds of arc) Spectral Type 65 Tau 0.025 A7 IV HR 4621 B2 IV $$ \alpha $$ Pic 20 A7 V 58 Ori 0.005 M2 I HR 2491 2.5 A1 V a. 65 Tau b. HR 4621 c. $$ \alpha $$ Pic d. 58 Ori e. HR 2491arrow_forward
- If two stars are in a binary system with a combined mass of 5.5 solar masses and an orbital period of 12 years, what is the average distance between the two stars?arrow_forwardWhy do you think astronomers have suggested three different spectral types (L, T, and Y) for the brown dwarfs instead of M? Why was one not enough?arrow_forwardLook elsewhere in this book for necessary data, and indicate what the final stage of evolution-white dwarf, neutron star, or black hole-will be for each of these kinds of stars. A. Spectral type-O main-sequence star B. Spectral type-B main-sequence star C. Spectral type-A main-sequence star D. Spectral type-G main-sequence star E. Spectral type-M main-sequence stararrow_forward
- Which of the following can you determine about a star without knowing its distance, and which can you not determine: radial velocity, temperature, apparent brightness, or luminosity? Explain.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_forwardReview this spectral data for five stars. Which is the hottest? Coolest? Most luminous? Least luminous? In each case, give your reasoning.arrow_forward
- Which of the following is least reasonable regarding the mass of stars? Group of answer choices The vast majority of stars fall into the range of 0.08 to 100 solar mass. Stars which are too small cannot sustain nuclear fusion. Stars which are excessively big are too sluggish to sustain nuclear fusion. There are more stars on the low end than on the high end of the mass spectrum. A brown dwarf has a mass just below the least massive star.arrow_forwardWhich star in the table below has the least surface temperature? Star Name d (parsecs) Parallax (seconds of arc) Spectral Type $$ \delta $$ Cen 0.026 B2 IV HR 4607 0.039 G8 III HR 4758 20 G0 V HR 39801 0.005 M2 I 9 CMa 2.5 A1 V a. $$ \delta $$ Cen b. HR 4607 c. HR 4758 d. HD 39801 e. 9 CMaarrow_forwardStar A and Star B are a bound binary at a distance of 20 pc from the Earth. Their separation is 30 AU. Star A has a mass twice that of Star B. The orbital period of the binary is 100 years. Assume the stars orbit in circular orbits. a. What is the parallax of Star A, in units of arcsec? Assume parallax is measured from the Earth. For part a, ignore the presence of the binary companion. b. What is the angular separation we would observe between Star A and Star B, in units of arcsec? If we compare multiple images of this star system taken across different months and years, which source of motion will be the dominant effect? What is the total mass of the binary system (combined mass of Star A and Star B)? Provide your answer in both kg and solar masses. c. d. What is the distance from Star A to the center of mass of the binary system?arrow_forward
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