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Use Kepler’s first law to derive explicit expressions for the perihelion and aphelion distances for a...

Use Kepler’s first law to derive explicit expressions for the perihelion and aphelion distances for a planet in terms of the semi-major axis a, and the eccentricity e, for an elliptical orbit. r=a(1-e^2)/1+ecos(theta) Calculate these distances for Mercury. What are the perihelion and aphelion speeds of Mercury? V^2=GM(2/r-1/a)

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Solution attached.Solution the Orbital period of fleecury is 87.97 days. the planets Semi major anu à ai pe=a3 the gemi masor anie in a(AU) =Closet at perikelion, 0-0 r =all-e) = 1 AU*(1-0.017). = 0.983 AU IC te) = 1 AU*(1+0.017) Sant = 1.017 AU va - amrage speed aThe total eneegy, E = 1 mv-amom E= - Grom za a encegy values divide to get the vz-AMO --CM for speed. Some v- samole valoda)

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