As a first approximation to the analysis of a space flight

Chapter 13, Problem 13.104

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As a first approximation to the analysis of a space flight from the earth to Mars, it is assumed that the orbits of the earth and Mars are circular and coplanar. The mean distances from the sun to the earth and to Mars are \(149.6 \times 10^{6} \ \mathrm{km}\) and \(227.8 \times 10^{6} \ \mathrm{km}\), respectively. To place the spacecraft into an elliptical transfer orbit at point A, its speed is increased over a short interval of time to \(v_{A}\) which is faster than the earth’s orbital speed. When the spacecraft reaches point B on the elliptical transfer orbit, its speed \(v_{B}\) is increased to the orbital speed of Mars. Knowing that the mass of the sun is \(332.8 \times 10^{3}\) times the mass of the earth, determine the increase in velocity required (a) at A, (b) at B.