A simple astrophysics rough estimate exercise

[shanepitts]

Homework Statement

Homework Equations

(mv²)/r=(GMm)/r² --------(1)
r≈8kpc≈2.47×10²⁰m
v≈220kms^-1

The Attempt at a Solution

Using equation (1) and solving for M I got

M=(v²r)/G=(4.84×10¹⁰2.47×10²⁰)/6.67×10^-11

M=1.79×10⁴¹ kg

does this answer seem correct?

P.S. This is not a homework assignment, it's an exercise from an introductory book I'm reading.

 

[gneill]

Your result looks fine for the given estimation method.

 

[shanepitts]

Your result looks fine for the given estimation method.

Thanks for the quick response

Would the given estimation method be appropriate?
Moreover, would you have any other Newtonian estimation methods to suggest?

 

[gneill]

Thanks for the quick response

Would the given estimation method be appropriate?
Moreover, would you have any other Newtonian estimation methods to suggest?

The method is a reasonable first approximation. It'll fall short by at least an order of magnitude though; Consider the actual shape of the galaxy as opposed to the assumed shape for the method. Also consider that the Sun does not orbit outside the entire galaxy, but rather within it: The galaxy is about 30 kpc across.

Other methods of estimation would involve much more effort and more complicated math. For example, the actual shape is more disk-like than spherical, and does not have a uniform density, making estimating the mass of the outlying portions tricky.

A better estimate might had by using the globular clusters which orbit outside the Milky Way as the "test particles", rather than the Sun.

 

[shanepitts]

The method is a reasonable first approximation. It'll fall short by at least an order of magnitude though; Consider the actual shape of the galaxy as opposed to the assumed shape for the method. Also consider that the Sun does not orbit outside the entire galaxy, but rather within it: The galaxy is about 30 kpc across.

Other methods of estimation would involve much more effort and more complicated math. For example, the actual shape is more disk-like than spherical, and does not have a uniform density, making estimating the mass of the outlying portions tricky.

A better estimate might had by using the globular clusters which orbit outside the Milky Way as the "test particles", rather than the Sun.

The method is a reasonable first approximation. It'll fall short by at least an order of magnitude though; Consider the actual shape of the galaxy as opposed to the assumed shape for the method. Also consider that the Sun does not orbit outside the entire galaxy, but rather within it: The galaxy is about 30 kpc across.

Other methods of estimation would involve much more effort and more complicated math. For example, the actual shape is more disk-like than spherical, and does not have a uniform density, making estimating the mass of the outlying portions tricky.

A better estimate might had by using the globular clusters which orbit outside the Milky Way as the "test particles", rather than the Sun.

Thank you