Question

Calculate the centripetal acceleration of the earth in its orbit around the sun and the net force exerted on the earth. What exerts this force on the earth? Assume the earth’s orbit is a circle of radius 1.49 × 1011 m. 

Answer 1

The centripetal acceleration of the Earth

$a_n=v^2/r=\omega^2r^2/r=\omega^2r=(\frac{2\pi}{T})^2r=(\frac{2\cdot3.14}{31557600})^2\cdot 1.49\cdot10^{11}=$

$=0.0059\ (m/s^2)$

The net force exerted on the earth

$F=G\frac{Mm}{r^2}=6.67\cdot10^{-11}\cdot\frac{1.988\cdot10^{30}\cdot5.97\cdot10^{24}}{(1.49\cdot10^{11})^2}=35.66\cdot10^{21}\ (N)$