An astronaut on a research mission to asteroid 1566, named Icarus, ponders whether she can escape the asteroid’s gravita

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An astronaut on a research mission to asteroid 1566, named
Icarus, ponders whether she can escape the asteroid’s gravitational
pull simply by jumping upwards from the surface. Icarus has a
diameter of 1.4 km and a mass of 1.0 × 1012 kg, and Newton’s
universal gravitational constant G = 6.67 × 10−11 N m2 /kg2 .
(a) Using conservation of mechanical energy calculate the escape
speed of Icarus. Hint: you will need the universal expression for
gravitational potential energy at a distance r, which is obtained
by integrating Newton’s universal law of gravitation force,
resulting in the following Ug(r) = − G m1 m2 r where the reference
(or zero) for Ug is at infinite distance, i.e., Ug(r = ∞) = 0. For
calculating the escape speed, you should assume that the escaping
object arrives at large distances (r → ∞) with essentially zero
kinetic energy. (
b) From the escape speed calculated in part (a), estimate
whether an average person might achieve this speed by jumping
vertically. Explicitly state any assumptions / estimations made in
your estimation.