Mathematics

Problem

Mercury has an eccentricity

e = 0.206

. Its distance from the Sun at aphelion is

r_{\mathrm a} = 69.8\times10^{9}\,\text{m}

and its speed there is

38\,\text{km}\,\text{s}^{-1}

. The solar gravitational parameter may be taken as

GM_{\odot} = 1.327\times10^{20}\,\text{m}^3\,\text{s}^{-2}

. a. (a) Determine Mercury’s semi-major axis

a

and its perihelion distance

r_{\mathrm p}

. b. (b) Calculate Mercury’s speed at perihelion. c. (c) If Mercury were to move in a circular orbit of radius equal to the semi-major axis found in part (a), compute the speed it would have. d. (d) Compare the circular speed with the actual perihelion and aphelion speeds and briefly comment on the differences.

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