#### NotEinstein

**Valued Senior Member**

And I can't figure out where that factor of 3 difference is coming from.I promised you that I would post if you cannot figure that out.

From my post #132: "Note that I never claimed yours was wrong; all I said was that our formulae were different, and that because I have a derivation showing and you haven't pointed out any mistakes in it, I suspect your derivation is different (for example, using different assumptions)."But you started with a pompous claim that you cannot trust my calculations as the same is off by a factor of 3 as compared to yours.

Please stop misrepresenting what I said.

So according to you, the factor 3 difference is coming from the fact that I used a constant density, and you did too? That's incoherent. Please show your calculations, so I can see what you actually did!Even when I pointed out that this factor of 3 is due to your using M/V, you did not get the hint.

From my post #135: "It's not the factor 3 itself that worries me: it's that there is any difference."I also stated that it does not really matter as the factor of 3 will make it > 1.5 X 10^26/r^2 kg/m3 which is even more unrealistic,

Please point out where I have committed the straw-man fallacy.but you continued with your strawman.

That's not a proper proof, it's just the starting point of one. But I guess I'll do your homework for you.Ok, here is the proof: use dm = 4*pi*r^2 d(r) dr, with a condition that r < 2Gm/c^2 for every r and mass (m) contained in that r.

$$dm=4\pi r^2 d(r) dr$$ is the mass of an infinitesimal spherical shell of thickness $$dr$$ at radius $$r$$. To get the inner mass at a radius R, we thus have to integrate this from r = 0 to r = R. Thus we get: $$M=\int_0^R {4\pi r^2 d(r) dr}$$

Since I don't know the functional form of $$d(r)$$ the integral cannot be evaluated. But let's assume a constant/uniform density, so that $$d(r) = d$$. Then the integral becomes: $$M=d \int_0^R {4\pi r^2 dr}=d [\frac{4}{3}\pi r^3]_0^R=d (\frac{4\pi R^3}{3} - \frac{4\pi 0^3}{3})=\frac{4\pi d R^3}{3}$$, which is identical to my result in post #100. From that point onwards, I can just copy-paste my post #100. In other words, I get the result I got in post #100, and not yours.

Please post your calculations, because you clearly are doing something different than what I am doing.