Which of these is the best method to measure the distance of a star
calculate the variations in the position of the star due to movement of earth in its orbit
measure the red shift of emitted light and use it in calculations
use doppler effect to calculate the shift in light traveling from star to earth in summer
use doppler effect to calculate the shift in light traveling from star to earth in winter

I think the correct answer would be the first option. The best method to use in order to measure the distance of  star would be to calculate the variations in the position of the star due to movement of Earth in its orbit. The doppler shift which is what is being described in the last three options does not calculate the distance rather it calculates the relative velocity. The method used in measuring the distance was introduced by Edwin Hubble where he found that relative velocity of a body in space is directly proportional to the distance of that body from Earth.

The last option water because it is slow