Question: Pined With [7] (5 Points) Using Table E-1 In Appendix E (A-6) Verify Kepler’s Third Law For Three Planets Of Your Choosing. The Letter “P” Is Defined As The Planet’s Period (the Time Required To Orbit The Sun Once). The Letter “a” Is Defined As The Length Of The Planet’s Semi-major Axis Of Orbit (the Average Distance Of The Planet To The Sun) Kepler’s …

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Pined with [7] (5 points) Using Table E-1 in Appendix E (A-6) verify Kepler’s third law for three planets of your choosing. The letter “P” is defined as the planet’s period (the time required to orbit the sun once). The letter “a” is defined as the length of the planet’s semi-major axis of orbit (the average distance of the planet to the Sun) Kepler’s third taw: – M = constant of the change ciated with es and the k summer wit h fewer. This are the connd f”p” is measured in Earth years, and “a” is measured in astronomical units (au) (1 au is the average Earth-Sun distance), then the “M” in Kepler’s third law is the mass of the system (in this case the mass of the dominant central Sun in solar units). Therefore, M is approximately equal to 1. So, in this version of Kepler’s third law relevant for the planets of our solar system is: p? = a Show that this equality is approximately true for three planets selected from table E-1 (show work). I’ve seen, the circles tilted lestial sphere tilted 23% ptic Figure internet at ach other on fore 1-8a). E from the when the su arth’s equato ours of night Imagine how amazed Kepler was to discover this mysterious harmony in Tycho Brahe’s planetary data. Newton used this harmony of Kepler’s third law to invent his universal theory of gravity and his three laws of dynamics. APPENDIX E: DATA TABLES APPENDICES A-7 TABLE E-1 THE PLANETS: ORBITAL DATA Semimajor axis (AU) (10 km) Sidereal period Mean orbital speed (km/s) Synodic period (day) Inclination of orbit to ediptic Planet (year) (day) Orbital cocentricity 115.88 583.92 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune 0.3871 0.7233 1.0000 1.5237 5.2034 9.5371 19.1913 57.9 108.2 149.6 227.9 778.6 1433.5 2872.5 0.2408 0.6152 1.0000 1.8808 11.862 7,00 3.39 0.00 1.85 87.97 224.70 365.26 686.98 4,332.6 10,759 30,685 60.189 47.9 35.0 29.8 24.1 13.1 9.7 6.8 779.94 398.9 378.1 0.206 0.007 0.017 0.093 0.048 0.054 0.047 0.009 1.31 29.457 2.48 0.77 1.77 369.7 367.5 84.01 164.79 54 30.0690 4495.1 TABLE E-2 THE PLANETS: PHYSICAL DATA Inclination dator Surface Escape Speed