A probe of mass m is initially moving in a stable circular orbit 400km above Earth’s surface. Neglect atmospheric drag. Earth’s radius is RE=6.37×106m and its standard gravitational parameter is μE=3.99×1014m3⋅s−2.
(a) Determine the orbital speed of the probe in its initial orbit.
(b) Calculate the minimum speed the probe must have at that altitude so that it can escape Earth’s gravity and reach an infinite distance with zero speed.
(c) Compute the minimum change in speed (Δv) that the probe’s engines must impart to achieve escape. Explain any assumptions you make.