Question

The radius of the earth's very nearly circular orbit around the sun is 1.5 1011 m. find the magnitude of the earth's velocity, angular velocity, and centripetal acceleration as it travels around the sun. assume a year of 365 days. (a) the earth's velocity

Answer 1

The radius of Earth's circular trajectory is
$R=1.5*10^{11} m$
The time for the Earth to travel around the Sun is
$t=365(days)*24(hours)*3600(seconds) =3.1536*10^7 (s)$
Thus the velocity is velocity
$v=2\pi R/t =2\pi *1.5*10^{11}/(3.1536*10^{7})=2.99*10^4 (m/s)$
From this we can deduce the centripetal acceleration
$a=v^2/R =(2.99*10^4)^2/(1.5*10^{11}) =5.96*10^{-3} (m/s^2)$
Angular velocity is
$\omega =v/R =(2.99*10^4)/(1.5*10^{11})=2*10^{-7} (rad/s)$