As a first approximation to the analysis of a space flight from the earth to Mars, assume the orbits of the earth and Mars are circular and coplanar. The mean distances from the sun to the earth and to Mars are 92.96 × 106 mi and 141.5 × 106 mi, respectively. To place the spacecraft into an elliptical transfer orbit at point A, its speed is increased over a short interval of time to vA which is 1.83 mi/s faster than the earth??s orbital speed. When the spacecraft reaches point B on the elliptical transfer orbit, its speed vB is increased to the orbital speed of Mars. Knowing that the mass of the sun is 332.8 ×103 times the mass of the earth, determine the increase in speed required atB.

Orbit of earth Sun Transfer orbit Orbit of Mars