The radius of the earth`s orbit around the sun is ` 1 A . U. Calculate the angular velocity and linear velocity of the earth. Also calculate the angle through which the earth revove around the sun in `4 4` days. ( Given 1 AU= 1.5 xx 10 ^(11)m0`

Explanation

Here, Raduus of earth, ` R= 1 AU = 1.5 xx 10^(11) m`.
period of revolution, of earth around to sum
` T= 365 days = 365 xx 24 xx 60 xx 60 s`
Angular velocity , ` omega= (2 pi) /T = ( 2 xx 3.14)/( 365 xx 24 xx 60 xx 60)` ltbRgt `= 1.99 xx 10^(-7) ` rad/s`
Linear velcity,
` v = R omega = ( 1.5 xx 10^(11)) xx ( 1. 99 xx 10^(-7))` ltbRgt ` = 2. 99 xx 10^(-4)` ms^(-1)` ltbRgt In ` 364 days , the earth revoles through and angle of ` 2pi radians. Angle through which the earth revoles in `4` days
` = ( 2pi) / 9365) xx 4 = (2 xx 3.14 xx4)/(365) = 0 .0688 rad.