What is the Minimum Mass for a Rotating Neutron Star?

[Kyal_Sharpe]

Homework Statement

Neutron stars are thought to rotate at about 1 revolution every second. What is the minimum mass for the neutron star so that a mass on the star’s surface is in the same situation as a satellite in orbit, that is, the strength of the gravitational field equals the centripetal acceleration at the surface?

Homework Equations

g=(GMm)/r^2
F=(mv^2)/r
a=(4pi^2r)/T^2

The Attempt at a Solution

Apologies for bad formatting, new to the forums. Basically just a question from my year 12 physics studies, pretty unsure on where to go given the openness of the question. Thankyou in advance.

 

[jbriggs444]

Would it help if you knew the density of a neutron star?

 

[Kyal_Sharpe]

Would it help if you knew the density of a neutron star?

I briefly attempted to go down that path but got lost pretty quickly

 

[andrevdh]

And if you take Kepler's 3rd law into consideration? ... not sure it is necessary though

 

[jbriggs444]

I briefly attempted to go down that path but got lost pretty quickly

Show your work -- how far did you get before you got lost?

We are here to help get you unstuck. But that only works if you show us where you are getting stuck.

 

[Kyal_Sharpe]

Show your work -- how far did you get before you got lost?

We are here to help get you unstuck. But that only works if you show us where you are getting stuck.

Well I setup the relationship in the question where (GM/r^2) = M * (4pi^2r)/T^2, which then simplified to (GM/r^2) = M * (4pi^2r) as T is equal to one. I gave some thought to the idea of density but was unsure on how to implement it as I only got the idea from some other reading.

 

[jbriggs444]

Well I setup the relationship in the question where (GM/r^2) = M * (4pi^2r)/T^2, which then simplified to (GM/r^2) = M * (4pi^2r) as T is equal to one. I gave some thought to the idea of density but was unsure on how to implement it as I only got the idea from some other reading.

Since you do not have a value for r and since, as you are discovering, there is no way to reduce your equations so that it drops out, you need to bring some additional constraints to bear. Otherwise, you have too many unknowns and too few equations relating them.

Density is one such constraint.

Suppose that you have a fixed density to work with -- what is your next step?