a) The fastest possible rate of rotation of a planet is that for which the gravi

ID: 2144345 • Letter: A

Question

a) The fastest possible rate of rotation of a planet is that

for which the gravitational force on material at the equator

barely provides the centripetal force needed for the rotation.

For a planet with a uniform density of 6.6 g/cm3, typical of

many planets and asteroids, evaluate the shortest period of rotation.

Certain neutron stars (extremely dense stars) are be-

lieved to be rotating at about 1.1 rev/s. If such a star has a

radius of 18.9 km, what must be its minimum mass so that ob-

jects on its surface will be attracted to the star and not thrown

off by the rapid rotation?

a) 6.6 g/cm^3 = 6600 kg/m^3

G M m/r^2 = m w^2 r

G M/r^3 = w^2

M = d * 4/3 pi r^3

G *4/3*pi*d = w^2

w = sqrt(6.67E-11*4/3*pi*6600) =0.0013579

T = 2 pi/w = 2*pi/0.0013579=4627 s

b) then

G M/r^3 = w^2

6.67E-11*M/(18.9E3)^3 = (2*pi*1.1)^2

M=4.84E24 kg

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