(a) What is the escape speed on a spherical asteroid whose radius is 540 km and

Question

(a) What is the escape speed on a spherical asteroid whose radius is 540 km and whose gravitational acceleration at the surface is 3.4 m/s2?

(b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?

(c) With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface?

m/s

What is the escape speed on a spherical asteroid whose radius is 540 km and whose gravitational acceleration at the surface is 3.4 m/s2? How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s? With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface? m/s

Explanation / Answer

a) ag = GM/R^2 = 3.4

M = agR^2/G

v = sqrt(2GM/R) = sqrt(2agR) = 1916.2

b) mechanical energy convension : 1/2mvi^2 -G(mM/Ri) = -G(mM/Rf)

Rf = 2GM/[(2GM/Ri)-vi^2] = 1.47 x 10^5

c) Mechanical energy conservation : -GmM/Ri = -GmM/Rf + 1/2 mvf^2

1/2vf^2 = GM(1/Rf-1/Ri)

vf = sqrt(2GM(1/Rf-1/Ri))

vf = 3132.93 m/s

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