Answer
(a) The sun's radial acceleration is $2.0\times 10^{-10}~m/s^2$
(b) The net gravitational force exerted on the sun due to the other stars in the Milky Way is $4.0\times 10^{20}~N$
Work Step by Step
(a) We can find the sun's linear speed as it orbits around the center of the galaxy:
$v = \frac{d}{t}$
$v = \frac{2\pi~r}{t}$
$v = \frac{(2\pi)(2\times 10^{20}~m)}{(2.0\times 10^8)(365)(24)(3600~s)}$
$v = 2.0\times 10^5~m/s$
We can find the sun's radial acceleration:
$a_r = \frac{v^2}{r}$
$a_r = \frac{(2.0 \times 10^5~m/s)^2}{2\times 10^{20}~m}$
$a_r = 2.0\times 10^{-10}~m/s^2$
The sun's radial acceleration is $2.0\times 10^{-10}~m/s^2$
(b) We can find the net gravitational force exerted on the sun. We can assume that this gravitational force provides the centripetal force to keep the sun moving in a circle:
$F_g = m~a_r$
$F_g = (1.989\times 10^{30}~kg)~(2.0\times 10^{-10}~m/s^2)$
$F_g = 4.0\times 10^{20}~N$
The net gravitational force exerted on the sun due to the other stars in the Milky Way is $4.0\times 10^{20}~N$
