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- Maybe something summing up infinitesimal masses or densities?

$$F=G\frac{m_1 m_2}{r^2}$$

is presumably for point masses. If the masses weren't a point masses, then wouldn't you need a version of the formula that sums up the gravity for each infinitesimal portion of the masses? And for my money, "summing up" in physics is integrals, right?

So would it be something like this?

$$F = G\int_0^r \int_0^m \frac{m_1 m_2}{r^2} dmdr\\$$

Actually no, if it's three dimensional, I imagine maybe something like this?

$$F = G\int_0^r \int_0^p \frac{p_1 p_2}{r^2} dpdr\\$$

where p is density?

I feel like this would get very complicated. You have the two masses, which are a distance r apart. But within those masses are other masses, each at a different r, and possibly with a different density that is dependent upon R, the radius of the objects. Now, I'm quite sure these two made up integrals are wrong, but can someone point me in the right direction to where I'd want to look for spatially extended objects and Newton's gravity law? Or is it simply that it doesn't matter because of Gauss' law or something?

Thanks.

is presumably for point masses. If the masses weren't a point masses, then wouldn't you need a version of the formula that sums up the gravity for each infinitesimal portion of the masses? And for my money, "summing up" in physics is integrals, right?

So would it be something like this?

$$F = G\int_0^r \int_0^m \frac{m_1 m_2}{r^2} dmdr\\$$

Actually no, if it's three dimensional, I imagine maybe something like this?

$$F = G\int_0^r \int_0^p \frac{p_1 p_2}{r^2} dpdr\\$$

where p is density?

I feel like this would get very complicated. You have the two masses, which are a distance r apart. But within those masses are other masses, each at a different r, and possibly with a different density that is dependent upon R, the radius of the objects. Now, I'm quite sure these two made up integrals are wrong, but can someone point me in the right direction to where I'd want to look for spatially extended objects and Newton's gravity law? Or is it simply that it doesn't matter because of Gauss' law or something?

Thanks.