3/31/2021 Solved: A comet orbits the sun (mass mS) in an elliptical orbit... | Chegg.com https://www.chegg.com/homework-help/comet-orbits-sun-mass-ms-elliptical-orbit-semi-major-axis-ec-chapter-13-problem-1bp-solution-978013397588... 1/8 home / study / science / physics / calculus based physics / calculus based physics solutions manuals / university physics with modern physics / 14th edition / chapter 13 / problem 1bp University Physics with Modern Physics (14th Edition) See this solution in the app 3 Bookmarks Show all steps: Chapter 13, Problem 1BP ON Problem A comet orbits the sun (mass m S ) in an elliptical orbit of semi-major axis a and eccentricity e . (a) Find expressions for the speeds of the comet at perihelion and aphelion. (b) Evaluate these expressions for Comet Halley (see Example 13.9), and find the kinetic energy, gravitational potential energy, and total mechanical energy for this comet at perihelion and aphelion. Take the mass of Comet Halley to be 2.2 X 10 14 kg. SOLUTION GUIDE IDENTIFY and SET UP 1. Sketch the situation; show all relevant dimensions. Label the perihelion and aphelion. (See Figure 13.18.) 2. List the unknown quantities, and identify the target variables. 3. Just as for a satellite orbiting the earth, the mechanical energy is conserved for a comet orbiting the sun. (Why?) What other quantity is conserved as the comet moves in its orbit? ( Hint: See Section 13.5.) EXECUTE 4. You’ll need at least two equations that involve the two unknown speeds, and you’ll need expressions for the sun–comet distances at perihelion and aphelion. ( Hint: See Fig. 13.18.) 5. Solve the equations for your target variables. Compare your expressions: Which speed is lower? Does this make sense? 6. Use your expressions from step 5 to find the perihelion and aphelion speeds for Comet Halley. ( Hint: See Appendix F.) 7. Use your results from step 6 to find the kinetic energy K , gravitational potential energy U , and total mechanical energy E for Comet Halley at perihelion and aphelion. EVALUATE 8. Check whether your results from part (a) make sense for the special case of a circular orbit (e = 0). 9. In part (b), how do your calculated values of E at perihelion and aphelion compare? Does this make sense? What does it mean that E is negative? My Textbook Solutions University Physics with... 14th Edition Understandin g Operating... 7th Edition Java Programmi 7th Edition View all solutions Post a question Answers from our experts for your tough homework questions Enter question Continue to post 20 questions remaining Snap a photo from your phone to post a question We'll send you a one-time download link 888-888-8888 Text me By providing your phone number, you agree to rec a one-time automated text message with a link to the app. Standard messaging rates may apply. Find solutions for your homework Search Textbook Solutions Expert Q&A Practice Study Pack 3/31/2021 Solved: A comet orbits the sun (mass mS) in an elliptical orbit... | Chegg.com https://www.chegg.com/homework-help/comet-orbits-sun-mass-ms-elliptical-orbit-semi-major-axis-ec-chapter-13-problem-1bp-solution-978013397588... 2/8 Step-by-step solution The orbital speed of comet that orbits around the sun is, Here, M is the mass of the sun, r is the distance of the comet from the center of the sun, a is the semi-major axis and G is the gravitational constant. Comments (1) Step 1 of 16 Textbook Solutions Expert Q&A Practice Study Pack 3/31/2021 Solved: A comet orbits the sun (mass mS) in an elliptical orbit... | Chegg.com https://www.chegg.com/homework-help/comet-orbits-sun-mass-ms-elliptical-orbit-semi-major-axis-ec-chapter-13-problem-1bp-solution-978013397588... 3/8 The sketch of the comet that orbit around the sun is given below, Comment (a) The distance r at the perihelion is The speed of the comet at perihelion is, Substitute for r. Hence, the speed of comet at perihelion is Comment The distance r at the aphelion is The speed of the comet at aphelion is, Substitute for r. Step 2 of 16 Step 3 of 16 Step 4 of 16 Textbook Solutions Expert Q&A Practice Study Pack 3/31/2021 Solved: A comet orbits the sun (mass mS) in an elliptical orbit... | Chegg.com https://www.chegg.com/homework-help/comet-orbits-sun-mass-ms-elliptical-orbit-semi-major-axis-ec-chapter-13-problem-1bp-solution-978013397588... 4/8 Hence, the speed of comet at perihelion is Comments (1) The perihelion is the position on the orbit of comet where the distance between the comet and the sun is shortest and hence there is a maximum gravitational force on the comet here. The orbital speed of comet at perihelion is and is maximum. Aphelion is the point closest to the sun in the orbit of comet. Here, gravitational force is minimum between comet and the sun. The orbital speed of comet at aphelion is and is minimum. Because of the larger gravitational force at perihelion, the orbital speed should be more at perihelion than aphelion. From (a), the speed of comet at perihelion is greater than at aphelion. > Comment The orbital speed in circular orbit is, Comment For circular orbits, eccentricity ( e ) is zero. Substitute 0 for e in formula for orbital speed at perihelion. The speed at aphelion becomes, Similarly, substitute 0 for e in formula for orbital speed at aphelion gives, Hence, it is verified that speed at aphelion and perihelion is similar to orbital speed in circular orbit for zero eccentricity. Step 5 of 16 Step 6 of 16 Step 7 of 16 Textbook Solutions Expert Q&A Practice Study Pack 3/31/2021 Solved: A comet orbits the sun (mass mS) in an elliptical orbit... | Chegg.com https://www.chegg.com/homework-help/comet-orbits-sun-mass-ms-elliptical-orbit-semi-major-axis-ec-chapter-13-problem-1bp-solution-978013397588... 5/8 Comment (b) The distance of sun at perihelion is Hence, The distance of sun at aphelion is From above, the ratio is given as, And, Comment The orbital speed of comet at perihelion is Substitute for G , for , for M and 0.967 for e Hence, the orbital speed of comet at perihelion is Comment The orbital speed of comet at aphelion is Substitute for G , for , for M and 0.967 for e Hence, the orbital speed of comet at perihelion is It is also verified that, Step 8 of 16 Step 9 of 16 Step 10 of 16 Textbook Solutions Expert Q&A Practice Study Pack 3/31/2021 Solved: A comet orbits the sun (mass mS) in an elliptical orbit... | Chegg.com https://www.chegg.com/homework-help/comet-orbits-sun-mass-ms-elliptical-orbit-semi-major-axis-ec-chapter-13-problem-1bp-solution-978013397588... 6/8 Comment The kinetic energy of comet at perihelion is, Here, m is the mass of the comet. Substitute for m and for Comment Comments (1) The kinetic energy of comet at aphelion is, Here, m is the mass of the comet. Substitute for m and for The potential energy of comet at perihelion is, Substitute for G , for , for M and for m. Comment The potential energy of comet at aphelion is, Substitute for G , for , for M and for m. Step 11 of 16 Step 12 of 16 Step 13 of 16 Step 14 of 16 Textbook Solutions Expert Q&A Practice Study Pack 3/31/2021 Solved: A comet orbits the sun (mass mS) in an elliptical orbit... | Chegg.com https://www.chegg.com/homework-help/comet-orbits-sun-mass-ms-elliptical-orbit-semi-major-axis-ec-chapter-13-problem-1bp-solution-978013397588... 7/8 Recommended solutions for you in Chapter 13 See more problems in subjects you study Was this solution helpful? Comment Total mechanical energy at perihelion is, Substitute for and for Total mechanical energy at perihelion is Comment Total mechanical energy at aphelion is, Substitute for and for Total mechanical energy at aphelion is Hence, the total energy of the comet is almost same at perihelion and aphelion. Comment Step 15 of 16 Step 16 of 16 6 6 Chapter 13, Problem 23E Two satellites are in circular orbits around a planet that has radius 9.00 X 106 m. One satellite has mass 68.0 kg, orbital... See solution Chapter 13, Problem 7E A typical adult human has a mass of about 70 kg. (a) What force does a full moon exert on such a human when it is directly... See solution Textbook Solutions Expert Q&A Practice Study Pack 3/31/2021 Solved: A comet orbits the sun (mass mS) in an elliptical orbit... | Chegg.com https://www.chegg.com/homework-help/comet-orbits-sun-mass-ms-elliptical-orbit-semi-major-axis-ec-chapter-13-problem-1bp-solution-978013397588... 8/8 COMPANY LEGAL & POLICIES CHEGG PRODUCTS AND SERVICES CHEGG NETWORK CUSTOMER SERVICE © 2003-2021 Chegg Inc. All rights reserved. Textbook Solutions Expert Q&A Practice Study Pack