The gravitational redshift of light leaving the surface of Sirius B is Δλ /λ = 3.0 × 10^-4. What velocity of Sirius B (relative to Earth) would be needed to produce an equivalent Doppler shift?

Question

Quizplus · Accepted Answer

The gravitational redshift is equivalent to a Doppler shift caused by a velocity away from the observer. The formula for Doppler shift for velocities much less than the speed of light is Δλ/λ = v/c, where v is the velocity and c is the speed of light (approximately 3.0 × 10^8 m/s). Substituting the given redshift Δλ/λ = 3.0 × 10^-4, we find v = 3.0 × 10^-4 * 3.0 × 10^8 m/s = 90,000 m/s or 90 km/s. Therefore, the equivalent Doppler shift would be caused by moving away from Earth at 90 km/s.

The Gravitational Redshift of Light Leaving the Surface of Sirius