Universal Gravitation and neutron stars

• 1st2fall
In summary, the conversation discusses determining the minimum mass of a neutron star in order for material on its surface to remain in place during its rapid rotation, using the formula F_c{}=\frac{mv^{2}}{r} and F_g{}=\frac{GM_1{M_2{}}}{r^{2}}. The attempt at a solution involves calculating the linear velocity and using the formula m=\frac{v^2r}{G}. The final result is 7.28635682 × 10^24 kg.
1st2fall

Homework Statement

Certain neutron stars (extremely dense stars) are believed to be rotating at about 6 rev/s. If such a star has a radius of 15 km, what must be its minimum mass so that material on its surface remains in place during the rapid rotation?

G=6.67*10-11m3 kg-1 s-2

Homework Equations

$$F_c{}=\frac{mv^{2}}{r}$$
$$F_g{}=\frac{GM_1{M_2{}}}{r^{2}}$$

The Attempt at a Solution

30$$\pi$$km*6rev/s=180$$\pi$$km/s
which gives the linear velocity of something on the surface of the neutron star... but I'm clueless as to how to arrive at a mass of the star from it. I could the Centripetal acceleration but I'm not sure how that's related here. the only thing I can think of there is setting the centripetal acceleration equal to the gravitation acceleration which gives

Gm/r2=v2/r
m=v2r/G
which yields something like 7.28635682 × 10^24(kg?)

I'm just looking for advice on what I'm actually looking to do. I don't know what I should be looking for...

Your formula is correct, but check the calculation.

ehild

Thank you very much! I realized a dropped a "pi" at some point when I went back over it.

What is universal gravitation?

Universal gravitation is a theory proposed by Sir Isaac Newton that states all objects in the universe attract each other with a force that is directly proportional to their masses and inversely proportional to the square of the distance between them.

How does universal gravitation apply to neutron stars?

Neutron stars are incredibly dense objects that result from the collapse of a massive star. Universal gravitation applies to neutron stars because they have a strong gravitational pull due to their high mass and compact size.

What is the difference between universal gravitation and general relativity?

Universal gravitation is a classical theory that explains the force of gravity between objects, while general relativity is a modern theory that explains gravity as the curvature of spacetime caused by the presence of mass and energy.

Why do objects on Earth experience the same gravitational pull as objects in space?

This is because the force of gravity is dependent on the masses of the objects and the distance between them, not their location. Therefore, the gravitational pull on Earth is the same as in space because the masses and distance are constant.

How do neutron stars affect their surrounding environment?

Neutron stars have a strong gravitational pull that can distort the spacetime around them, causing nearby objects to orbit or even be pulled into the neutron star. They can also emit powerful radiation, affecting their surrounding environment.

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