A distant quasar is found to be moving away from the earth...

A distant quasar is found to be moving away from the earth at $0.80 c .$ A galaxy closer to the earth and along the same line of sight is moving away from us at $0.20 \mathrm{c} .$ What is the recessional speed of the quasar as measured by astronomers in the other galaxy?

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Key Concepts

Relativistic Velocity Addition

Relativistic velocity addition is the formula used to combine velocities in the context of Special Relativity. Unlike the simple arithmetic addition used in classical mechanics, this method accounts for the finite speed of light and ensures that the resulting speed never exceeds the speed of light, thus providing a more accurate description of relative motion for objects moving at relativistic speeds.

Special Relativity

Special Relativity is the theory formulated by Einstein that describes how time, space, and motion are interrelated, especially at velocities close to the speed of light. It modifies classical mechanics by introducing effects such as time dilation and length contraction, which are essential for accurately describing the physics of objects moving at high speeds.

Reference Frames

Reference frames are coordinate systems used to measure and observe physical phenomena, such as position and velocity. In problems involving high-speed objects, choosing the appropriate reference frame is crucial for understanding how different observers perceive motion, since measurements can vary significantly between frames moving relative to each other.

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