What's the simplest way to determine the mass of a sphere from a plot of its density varying in r?

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island-lad 2022-11-28

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回答： Torsten 2022-11-28

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.

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David Hill 2022-11-28

Can't you just integrate your density function multiplied by 4/3*pi*r^3 with respect to r over the range of r?

island-lad 2022-11-28

And that would require curve fitting?

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Answer 1

Torsten 2022-11-28

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在 MATLAB Online 中打开

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)

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Answer 2

William Rose 2022-11-28

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@Alain Vella,

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.