The Doppler wavelength shift equation varies depending on whether the emitter or receiver is moving, with a combined equation available for both. For light emitted from the sun, the relativistic Doppler shift equation is λ = λ₀ √((1+v)/(1-v)), which accounts for high speeds. However, for corrections involving only the Earth's speed relative to the sun, the classical formula suffices. The discussion emphasizes the importance of selecting the appropriate equation based on the context of the motion involved. Understanding these equations is crucial for accurately calculating wavelength shifts in light.