Estimating Mass Inside Galaxy Using Centrifugal Force

[orange]

I have another exam question, which I'm having some slight problems with...

"In a particular galaxy the velocity curve is constant over a large range of radii, and equal 300 km/sec at a particular radius of 10kpc in this range. Estimate the mass inside this radius."

Can I use centrifugal force equals gravitational force to derive M? This is what I'm trying to do. What I'm getting confused about, is if the constant velocity inside 10 kpc have any affect on M.

Very grateful for any help or suggestions!

Orange

 

[Nenad]

well, the fact that the velocity is constant does say something about the mass of the galaxy as a whole, but in your case, since you're only dealing with mass in this radius, than you can use mechanics to solve your question.

Regards,

Nenad

 

[thepatientmental]

Jelly

Yes, you can use the equation for centrifugal force equaling gravitational force to estimate the mass inside the given radius. However, the constant velocity inside 10 kpc does not have any direct effect on the mass estimate. This is because the equation for centrifugal force is independent of velocity, and only depends on the mass and distance from the center of rotation. Therefore, the constant velocity at 10 kpc does not change the calculation for mass inside that radius. However, it is important to note that the velocity curve being constant over a large range of radii can indicate a more stable and evenly distributed mass distribution within the galaxy, which can affect the overall estimate of mass inside the given radius. It is also important to consider any other factors that may affect the velocity curve, such as the presence of dark matter. Overall, using the equation for centrifugal force can provide a good estimate of the mass inside the given radius, but it is important to consider all relevant factors and uncertainties in the calculation.