Gaussian Gravity

Density is described by the given $ρ(r)=p_0(R-r)$ The mass contained within a sphere of radius $r$ is found by integrating concentric shells with area $4πr^2$ , density $ρ(r)$ and thickness $dr$ :

$m(r^*)=\int_0^{r^*}4πr^2 ρ(r) dr = \int_0^{r^*}4πr^2 p_0(R-r)\ dr = 4πp_0\int_0^{r^*}r^2R-r^3\ dr=  4πp_0(\frac13 {r^*}^3R-\frac14 {r^*}^4)$ , or $m(r)= 4πp_0(\frac13 r^3R-\frac14 r4)$ The gravitational acceleration is determined by this mass, and can be expressed as : $a=\frac{mG}{r^2}$ , or $a(r)= 4πp_0G(\frac13 rR-\frac14 r^2)$ To find the radius at which acceleration is at maximum, set the derivative to 0: $\frac{da}{dr}= 4πp_0G(\frac13 R-\frac24 r)=0 \Rightarrow r=\frac23R$ .

The answer to the question is requested in the form $a+b=2+3=\boxed{5}$