Aberration of light is the apparent displacement of stars attributable to the effect of the orbital motion of the Earth. The direction to a star in the ecliptic plane varies periodically and the star performs apparent oscillations within an angle `delta theta = 41''`. Find teh orbital velocity of the Earth.

Explanation

Althrough speed of light is the same in all inertial frames of reference according to the principles of relativity, the direction of a light ray can appear different in different frames.
This phenomenon is called aberration and to first order in `(v)/(c )`, can be calculated by the elementary law of addition of velocities applied to light waves. The angle of aberration is
`tan^(-1).(v)/(c )`.
and in the present case it equals`(1)/(2) delta theta` on either side. Thus equating `(v)/(c ) = tan.(1)/(2)delta theta = (1)/(2) delta theta (delta theta` radians)
or `v=(c )/(2)delta theta = (3 xx 10^(8))/(2) xx (41)/(3600) xx (pi)/(180)`
`= (3.41 xx pi)/(3.6 xx 3.6) xx 10^(4)m//s = 29.8 km//sec`