Gravitational Redshift in Motion

📌 CONCEPT: Gravitational redshift in motion is the change in frequency of a photon emitted by a spacecraft due to both gravitational and special relativistic effects when it is moving at high speed relative to the observer.

📐 RULE / FORMULA: The formula for gravitational redshift in motion is given by f' = f ∗ √(1 - 2GM/r) ∗ √(1 - v^2/c^2), where f' is the observed frequency, f is the emitted frequency, G is the gravitational constant, M is the mass of the object, r is the distance from the object, v is the velocity of the spacecraft, and c is the speed of light.

💡 WORKED EXAMPLE: Suppose a spacecraft emits a photon with frequency f = 10^15 Hz while moving at v = 0.8c relative to an observer. If the spacecraft is at a distance r = 10^6 m from a massive object with mass M = 2 ∗ 10^30 kg, the observed frequency f' can be calculated using the formula above.

⚠️ COMMON MISTAKE: Students often forget to include both the gravitational and special relativistic effects in their calculations, leading to incorrect results.