Answer
The centripetal acceleration is $5.96\times 10^{-3}~m/s^2$
The net force exerted on the Earth is $3.56\times 10^{22}~N$. This force comes from the gravitational force exerted on the Earth by the Sun.
Work Step by Step
We can find the speed of the Earth as it orbits the Sun;
$v = \frac{d}{t}$
$v = \frac{2\pi~r}{t}$
$v = \frac{(2\pi)(1.50\times 10^{11}~m)}{(365)(24)(3600)~s}$
$v = 2.99\times 10^4~m/s$
We then use the speed to find the centripetal acceleration;
$a_c = \frac{v^2}{r}$
$a_c = \frac{(2.99\times 10^4~m/s)^2}{1.50\times 10^{11}~m}$
$a_c = 5.96\times 10^{-3}~m/s^2$
The centripetal acceleration is $5.96\times 10^{-3}~m/s^2$.
Also, we find the net force exerted on the Earth:
$F = M~a_c$
$F = (5.98\times 10^{24}~kg)(5.96\times 10^{-3}~m/s^2)$
$F = 3.56\times 10^{22}~N$
The net force exerted on the Earth is $3.56\times 10^{22}~N$. This force comes from the gravitational force exerted on the Earth by the Sun.
