In the following problems, except where otherwise indicated, assume that the radius of the earth is 6378 km, the earth's mass is 5.976(1024) kg, the mass of the sun is 1.99(1030) kg, and the gravitational constant is G = 66.73(10−12)m3/(kg • s2).
A satellite is launched with an initial velocity v0 = 2500 mi/h parallel to the surface of the earth. Determine the required altitude (or range of altitudes) above the earth’s surface for launching if the free-flight trajectory is to be (a) circular, (b) parabolic, (c) elliptical, and (d) hyperbolic. Take G = 34.4(10−9)(lb • ft2)/slug2, Me = 409(1021) slug, the earth’s radius re = 3960 mi, and 1 mi = 5280 ft.
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