In the following cases,identify the source providing the centripetal force:
$(i)$ Motion of the Earth around the Sun.
$(ii)$ Motion of an electron around the nucleus.
$(iii)$ Motion of a vehicle on a horizontal curved road.

(N/A) $(i)$ The gravitational force exerted by the Sun on the Earth provides the necessary centripetal force:
$\frac{G M_e M_s}{r^2} = \frac{M_e v^2}{r}$
$(ii)$ The electrostatic force of attraction between the nucleus and the electron provides the centripetal force:
$\frac{1}{4 \pi \epsilon_0} \frac{(Ze)(e)}{r^2} = \frac{m_e v^2}{r}$
$(iii)$ The static frictional force between the road surface and the tires of the vehicle provides the centripetal force:
$\mu_s N = \frac{m v^2}{r}$