One of the early attempts to measure the speed of light was to measure the position of a star located at right angles to the path of the Earth in its orbit (Fig). (a) If the measured angle 8 is found to be between 89°59'39.3/1 and 89°59'39.4\", then what would be the range of values for the speed of light? (b) Describe a reasonable method for measuring this angle tothe above accuracy. The answer to this question. might not be as straightforward as you think!

(a)
The angle in degrees is:

The angle in degrees is:

It is important to note that this method is quite inaccurate because the final answer depends on the accurate measurement of angle, which varies with the significant digits and approximation method.
(b)
To measure the angle θ of the star accurately, let your right hand point in the direction of the motion of the Earth in its orbit while the left hand must point in the direction of the star. However, this will not be the true angle that the star subtends relative to velocity vector of Earth. To measure the angle correctly, take into account the effect and magnitude of the latitude of your location.
It is important to note that in locating the star using your hands, you must take the error that may creep in due to stellar parallax.