What is the escape speed on a spherical asteroid whose radius is 580 km and whos

Question

What is the escape speed on a spherical asteroid whose radius is 580 km and whose gravitational acceleration at the surface is 3.0 m/s^2? (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? (a) A 4.9 kg particle and a 2.1 kg particle have a gravitational attraction with a magnitude of 2.3 times 10^-12 N. What is the gravitational potential energy of the two-particle system? J (b) If you triple the separation between the particles, how much work is done by the gravitational force between the particles? J (c) How much work is done by you? J

Explanation / Answer

part b )

using energy conservation

Ui + Ki = Uf + Kf

Ui = -GMn/R

Ki = mv^2/2

Uf = -GMm/(R+h)

Kf = 0

-GMm/R + 1/2mv^2 = -GMm/R+h

GM = a*R^2

-aR + v^2/2 = -aR^2/(R+h)

h = (2aR^2/2aR-v^2) - R

h = 1.05 x 10^5 m

part c )

Ki = 0

Ui = -GMm/(R+h)

Uf = -GMm/R

-GMm/(R+h) = - GMm/R + mv^2/2

GM = aR^2

-aR^2/(R+h) = -aR + v^2/2

v = sqrt[ ( 2aR) - (2aR^2/(R+h)]

v = 1312.45 m/s

part 18 )

F = Gm1m2/d^2

2.3 x 10^-12 = 6.67 x 10^-11 * 4.9 * 2.1/d^2

d = 17.2745 m

U = Gm1m2/d

U = 3.973 x 10^-11 J

part b )

W = -U

W = if distance triple = -1.32 x 10^-11 J

part c )

1.32 x 10^-11 J

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