Physics homework help....?

Question

A neutron star has radius 10 km and mass 2.5 x 10^29 kg. A meteorite is drawn into its gravitational field. Calculate the speed with which it will strike the surface of the star. Neglect the initial speed of the meteorite.

-- do i just use the formula for escpae speed which is
V= sqrt(2GM/r)

Answer 1

Here you need to use the gravitational force :

the gravitational force will be equal to the centripetal force of the meteor, because, we can take the neutron star as an sphere, and you know by circular motion and dynamics, that the centripetal force takes to the center of the circle.

G*M*m / r^2 = m*v^2 / r

r = radius

G = constant

M = mass of the star

m = mass of the meteor

G = 6.67*10^-11 (N*m^2 / kg^2)

then :

6.67*10^-11*2.5*10^29*m / (10*1000)^2 = m*v^2 / 10*1000

16.7*10^18 / 10000 = v^2

v = 4.08*10^7 m/s

This is a lot of speed, but hope that's the answer.

Check it step by step.

Answer 2

♠ V= sqrt(2GM/r) = 57768 km/s; and (v/c)^2 =3.7% << 100% (c=300000 km/s);
♣ thus you may do without caring much about relativistic phenomena and write v=57000 km/s; click me if you are not game;