# What is the Minimum Mass for a Rotating Neutron Star?

• Kyal_Sharpe
In summary: 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.
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?

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.

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

jbriggs444 said:
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

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

Kyal_Sharpe said:
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.

jbriggs444 said:
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.

Kyal_Sharpe said:
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?

## 1. How do you calculate the mass of a star?

The mass of a star can be calculated by using the mass-luminosity relation, which compares the luminosity of a star to its mass. This can be done by measuring the temperature and luminosity of the star, and then using these values in the relation to calculate its mass.

## 2. What is the mass-luminosity relation?

The mass-luminosity relation is an equation that relates the luminosity of a star to its mass. It is based on the understanding that the more massive a star is, the more energy it produces and thus the more luminous it is. This relation is important for calculating the mass of a star.

## 3. How accurate are mass calculations of stars?

The accuracy of mass calculations for stars depends on the available data and the methods used. Generally, the mass-luminosity relation provides a good estimate of a star's mass, but there can be variations and uncertainties due to factors such as binary systems or stellar evolution.

## 4. Can the mass of a star change over time?

Yes, the mass of a star can change over time through processes such as nuclear fusion and mass loss. As a star evolves, its mass may decrease due to the loss of mass through stellar winds or increase through the fusion of lighter elements into heavier ones.

## 5. Why is calculating the mass of a star important?

Calculating the mass of a star is important for understanding its life cycle and evolution, as well as its impact on its surrounding environment. The mass of a star also affects its properties, such as its temperature, luminosity, and lifespan. Mass calculations also provide valuable information for studying the formation and dynamics of galaxies and the universe as a whole.

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