Puny Earth doomed?

$dV=4\pi r dr$

$dm=\rho(r)dV=\frac { 0.5-r }{ 10^{ 3 } }4\pi r dr=\frac { 0.5r-r^2 }{ 10^{ 3 } }4\pi dr$

$\displaystyle m=\int_{0}^{m}{dm}=\int_{0}^{\frac{1}{2}}{\frac { 0.5r-r^2 }{ 10^{ 3 } }4\pi dr}\approx 261\cdot10^{-6}$

$Computational speed of alien=1.359\cdot10^{50}\cdot261\cdot10^{-6}=3.547\cdot10^{46}$

$Ratio=\frac{3.547\cdot10^{46}}{400\cdot10^9}=8.895\cdot10^{34}$

Average density of the alien brain is given by:

$\int_0^{0.5} \frac{0.5-r}{10^{3}}\,\mathrm{d}r = 1.25{\times}10^{-4}kgm^{-3}$

Since the alien's head is a sphere, and assuming that the brain takes up all of its head volume:

$Mass = \frac{4\pi}{3}(0.5^{3}) \times 1.25{\times}10^{-4} = 6.545{\times}10^{-5}kg$

The total computational power of the alien brain is therefore:

$6.545{\times}10^{-5} \times 1.359{\times}10^{50} = 8.895{\times}10^{45} bits/second$

$Ratio = \frac{8.895{\times}10^{45}}{400{\times}10^{9}} = \boxed{2.224{\times}10^{34}}$

mass of alien's head = integral(rho .dr)[from 0 --->0.5] * v(volume of his head)= 0.125 10^-3 * (0.5)^3 pi (4/3) computational speed of alien=m (c^2/h)=8.8946 10^45 bets/s ratio between alien and human minds c.p =2.223658 10^34 (approx.)