An Enclosed Mass Profile problem

  • Thread starter Thread starter bluejazz
  • Start date Start date
  • Tags Tags
    Mass
Click For Summary
SUMMARY

The discussion focuses on deriving the enclosed mass profile M(r) for a star based on its central density and radius. The formula used is M(r) = 4(pi)(rho_c)[r^3/3 - r^5/(5R*^2)], where rho_c represents the central density and R* is the star's radius. The user initially struggled with expressing the result in terms of the total mass M*, but later clarified their understanding of central density. This indicates a successful resolution of the problem through community engagement.

PREREQUISITES
  • Understanding of calculus, specifically integration techniques.
  • Familiarity with astrophysical concepts such as mass profiles and density functions.
  • Knowledge of spherical volume calculations, particularly the formula for the volume of a sphere.
  • Basic understanding of stellar structure and properties, including central density.
NEXT STEPS
  • Study the derivation of mass profiles in astrophysics, focusing on different density distributions.
  • Learn about the implications of central density in stellar evolution and structure.
  • Explore the concept of total mass M* and its relationship with density and volume in astrophysical contexts.
  • Investigate numerical methods for solving integrals in astrophysical applications.
USEFUL FOR

Astronomy students, astrophysicists, and anyone interested in understanding stellar mass distribution and density profiles.

bluejazz
Messages
6
Reaction score
0

Homework Statement



Find the enclosed mass profile M(r) in terms of R* and the total mass M* of the star.

Homework Equations



dMr/dr = 4(pi)r2(density)

density is given as: rho(r) = (rho_c)[1-(r/R*)2]
Where rho_c is the central density and R* is the radius of the star.

3. Attempt at a solution

I plugged the given density into the enclosed mass formula, took the integral in terms of r, and ended up with the result:

M(r) = 4(pi)(rho_c)[r3/3 - r5/(5R*2)]

My problem is, I'm not sure how to put this in terms of Mstar. What I think is I have to take the central density and the expression for volume [4/3 * (pi) * r3] and get Mstar. I guess my real question is this: what is the definition of central density?
 
Physics news on Phys.org
bump! Hope this question doesn't get lost!
 
Nevermind, I found the answer! Thanks anyways guys!
 

Similar threads

Calculating a star's density profile
  • · Replies 3 ·
Replies
3
Views
3K
Confusion on product rule for mass of differential volume element
  • · Replies 4 ·
Replies
4
Views
2K
Inverse square law of gravitation and force between two spheres
  • · Replies 8 ·
Replies
8
Views
2K
What helium mass in a balloon to make it bouyant in air?
  • · Replies 12 ·
Replies
12
Views
2K
What is density of dark matter as a function of distance from the galactic core?
  • · Replies 1 ·
Replies
1
Views
1K
Coulomb's law to find electric field for charge density function
  • · Replies 11 ·
Replies
11
Views
2K
Finding an expression for the total mass of a star
  • · Replies 1 ·
Replies
1
Views
1K
Physics puzzle about the concentration of fog droplets in the air
  • · Replies 26 ·
Replies
26
Views
2K
Hydrostatic equlibrium and Centre of pressure
  • · Replies 3 ·
Replies
3
Views
1K
The density of a proton (hydrogen nucleus)
  • · Replies 9 ·
Replies
9
Views
3K