One more Universal Gravitation

In summary, the problem presented is determining the greatest possible angular speed of a neutron star with twice the mass of the Sun and a radius of 5.0 km, in order for matter on its equator to be held in orbit by the gravitational force. The escape velocity at the surface of the star is calculated to be about 2.2469 x 10^9, and this is related to the angular speed of the star through the centripetal force of gravity.
  • #1
Antepolleo
40
0
Ok, here's the problem:

Neutron stars are extremely dense objects that are formed from the remnants of supernova explosions. Many rotate very rapidly. Suppose that the mass of a certain spherical neutron star is twice the mass of the Sun and its radius is 5.0 km. Determine the greatest possible angular speed it can have so that the matter at the surface of the star on its equator is just held in orbit by the gravitational force.

I will be honest, I'm not even sure where to start... any hints on where to begin would be appreciated.
 
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  • #2
What is the escape velocity at the surface of such a star?
 
  • #3
Originally posted by StephenPrivitera
What is the escape velocity at the surface of such a star?

That would be

[tex]
v_{esc} = \sqrt_{\frac{2GM}{R}}
[/tex]

which I believe is about 2.2469 x 109.

How would I relate this to the answer? I'm afraid I can't see the connection.
 
  • #4
I'll take you through it.
How is angular speed of the star related to the linear speed of an object on the equator of the star?
 
Last edited:
  • #5
Originally posted by Antepolleo
I will be honest, I'm not even sure where to start... any hints on where to begin would be appreciated.
Consider that the rotating surface is centripetally accelerated and that gravity is the centripetal force.
 

1. What is the Universal Gravitation equation?

The Universal Gravitation equation, also known as Newton's Law of Universal Gravitation, is F = G(m1m2)/r², where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of two objects, and r is the distance between them.

2. How does Universal Gravitation explain the motion of planets?

Universal Gravitation states that all objects with mass are attracted to each other with a force proportional to their masses and inversely proportional to the square of the distance between them. This force of gravity is what keeps planets in orbit around the sun and governs the motion of all celestial bodies in the universe.

3. What is the difference between Universal Gravitation and the Law of Gravity?

The terms Universal Gravitation and Law of Gravity are often used interchangeably, but technically the Law of Gravity refers to Newton's theory of gravity, while Universal Gravitation includes other theories and equations that describe the force of gravity in the universe.

4. What is the significance of the gravitational constant in Universal Gravitation?

The gravitational constant, denoted as G, is a fundamental physical constant that determines the strength of the gravitational force between two objects. It is an important factor in the Universal Gravitation equation and its precise value has been determined through various experiments and observations.

5. How does Universal Gravitation relate to other fundamental forces?

Universal Gravitation is one of the four fundamental forces in the universe, along with electromagnetism, strong nuclear force, and weak nuclear force. It is the force responsible for the attraction between objects with mass, while the other forces govern interactions at the atomic level. However, efforts are being made to unify these forces into a single theory, known as the theory of everything.

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