Calculate the centripetal acceleration of the Earth which orbits around the Sun. The Sun to Earth distance is approximately 150 million km. (Assume the orbit of Earth to be circular)

Explanation

The centripetal acceleration `a_c = (v^2)/(r )`
V - velocity of Earth around the orbit
r - radius of orbit or distance of Earth to Sun Velocity of Earth is written in terms of angular velocity (`omega` ) as
By substituting in the centripetal acceleration formula, `a_c = (omega^2 r^2)/(r ) =omega^2 r`
But` omega = (2pi)/(T )` where T is time for the Earth to orbit around the Sun, which is one year.
T = 365 days =` 365 xx 24 xx 60 xx 60s`
` T = 31 xx 10^7`s
`omega = 2.02 xx 10^(-7 )` rad per sec
`a_c = (2.02 xx 10^(-7))^2 xx (150 xx10^8) `
` a_c =6.12 xx 10^(-3) ms^(-2)`