Question

N12R.3Imagine you are the orbital engineer for the first NASA space shot to Ceres, the largest known asteroid. Ceres’s nearly circular orbit around the sun has a radius of R = 2.77 AU. After being launched from the earth, the probe will initially be in a circular orbit around the sun with the same radius (rc = 1.0 AU) and the same orbital speed Inline_Formula as the earth’s orbit. The probe’s rocket engines will then fire briefly to increase the probe’s speed to that speed Inline_Formula needed to put the probe into an elliptical orbit whose initial (and minimum) distance from the sun is rc = 1.0 AU and whose final (and largest) distance from the sun is R = 2.77 AU (this is a Hohmann transfer orbit). (a) How long will it take the probe to get from the earth to Ceres in such an orbit? (b) What is the speed Inline_Formulathat the probe has to have just after firing its engines to be inserted into this orbit? (Assume the duration of the boost is short enough that its distance from the sun is still nearly rc just after the engines have been fired.)

Answer 1