Question

Two starships, the Enterprise and the Constitution,are approaching each other head-on from a great distance. The separation between them is decreasing at a rate of 750.5 km/s . The Enterprise sends a laser signal toward the Constitution.

If the Constitution observes a wavelength λ = 675.1 nm , what wavelength was emitted by the Enterprise ?

Answer 1

Actual wavelength      λ₀   =   (1   -   v/c)* λ

   here   relative speed ofspaceships   v = -750.5 km/s   

= -750.5 * 10³ m/s   ( - ve sign since spaceships are approaching)

            apparentwavelength   λ   =   675.1 nm

   =>   λ₀   =   {1- (-750.5* 10³ / 3.0 * 10⁸)} * 675.1 nm

                  = 676.78 nm