Problem 7.10 Please. 306****Problem 7.8 Assume that the period of elliptical orbits around the sun depends onlyupon G, M (the sun's mass), and a, the semi-major axis of the orbit. Prove Kepler'sthird law using dimensional arguments alone.Problem 7.9 A spy satellite designed to peer closely at a particular house every dayat noon has a 24-h period, and a perigee of 100 km directly above the house. Whatis the altitude of the satellite at apogee? (Earth's radius is 6400 km.)Problem 7.10 Show that the kinetic energy7 Gravitationwhere M = misystem.K.E=| = {m} + {/m₂²²of a system of two particles can be written in terms of their center-of-mass velocityRem and relative velocity i as1= {MŘ²m + ½µř³²³,K.E. =m2 is the total mass andm1m2/M is the reduced mass of theProblem 7.11 Show that the shape r() for a central spring-force ellipse takes thestandard form ² = a²b²/(b² cos² y + a² sin² p) if (in Eq. (7.37)) we use the plussign in the denominator and choose 40 = π/4.Problem 7.12 Show that the period of a particle that moves in a circular orbit closeto the surface of a sphere depends only upon G and the average density p of thesphere. Find what this period would be for any sphere having an average densityequal to that of water. (The sphere consisting of the planet Jupiter nearly qualifies!)Problem 7.13 (a) Communication satellites are placed into geosynchronous orbits;that is, they typically orbit in earth's equatorial plane, with a period of 24 h. Whatis the radius of this orbit, and what is the altitude of the satellite above earth'ssurface? (b) A satellite is to be placed in a synchronous orbit around the planetJupiter to study the famous "red spot." What is the altitude of this orbit above the"surface" of Jupiter? (The rotation period of Jupiter is 9.9 h, its mass is about 320earth masses, and its radius is about 11 times that of earth.)Problem 7.14 The perihelion and aphelion of the asteroid Apollo are 0.964 x 108 kmand 3.473 x 108 km from the sun, respectively. Apollo therefore swings in and outthrough earth's orbit. Find (a) the semi-major axis, (b) the period of Apollo's orbitin years, given earth's semi-major axis aɛ= 149.6 x 106 km. (Apollo is only oneof many "Apollo asteroids" that cross earth's orbit. Some have struck the earth inthe past, and others will strike it in the future unless we find a way to prevent it.)

Answered: Image /qna-images/answer/3390e76d-0ab7-4879-9702-869531b65839.jpg

Problem 7.10 Show that the kinetic energy K.E = {m₁²+ m₂ of a system of two particles can be written in terms of their center-of-mass velocity Rem and relative velocity i as 1 K.E. „E. = — MŘ²m + µ²², where M = my + m2 is the total mass and μ = mm₂/M is the reduced mass of the system.

Problem 7.10 Show that the kinetic energy K.E = {m₁²+ m₂ of a system of two particles can be written in terms of their center-of-mass velocity Rem and relative velocity i as 1 K.E. „E. = — MŘ²m + µ²², where M = my + m2 is the total mass and μ = mm₂/M is the reduced mass of the system.

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter8: Conservation Of Energy

Section: Chapter Questions

Problem 64PQ: FIGURE 8.38 Comparison of a circular and an elliptical orbit. The semimajor axis of the ellipse is...

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