What's the simplest way to determine the mass of a sphere from a plot of its density varying in r?
2 views (last 30 days)
Show older comments
Hey there,
So, within the context of a spherical body, I've got a plot of density varying in r which is generated through PDE solver. What would the neatest way of calculating the sphere's mass, based on said density plot, be?
Much appreciated.
2 Comments
David Hill
on 28 Nov 2022
Can't you just integrate your density function multiplied by 4/3*pi*r^3 with respect to r over the range of r?
Accepted Answer
Torsten
on 28 Nov 2022
If r and rho are column vectors where r is ordered as r(1) < r(2) < ... < r(n) and rho is the density at position r, an approximation for the mass m of the sphere is
m = trapz(r,4*pi*r.^2.*rho)
0 Comments
More Answers (1)
William Rose
on 28 Nov 2022
I agree with @David Hill, except you want to multiply the density at each value of r by 4*pi*r^2*dr, then add them up, i.e. integrate. Because 4*pi*r^2*dr is the volume of each shell.
0 Comments
See Also
Categories
Find more on Geometry and Mesh in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!