To solve this problem we will apply the concept of gravity as a function of density, the universal gravity constant and the radius of the Planet to be investigated. This relationship is written mathematically as
[tex]g = \frac{4}{3} \pi \rho GR[/tex]
Here
G = Universal gravitational constant
[tex]\rho[/tex] = Density
R = Radius
Given acceleration due to gravity on Venus's surface is
[tex]g = 8.9m/s^2[/tex]
and Radius of Venus is
[tex]R = 6.05*10^6m[/tex]
Using the previous equation and rearranging to find the density we have,
[tex]\rho = \frac{3g}{4\pi GR}[/tex]
[tex]\rho = \frac{3(8.9)}{(4\pi)(6.67*10^{-11})(6.05*10^6)}[/tex]
[tex]\rho = 5265.26kg/m^3[/tex]
Therefore the average density of Venus is [tex]5265.26kg/m^3[/tex]
