A starship blasts past the earth at 2.0 ×10^8 m / s. Just...

A starship blasts past the earth at $2.0 \times 10^{8} \mathrm{m} / \mathrm{s}$. Just after passing the earth, the starship fires a laser beam out its back. With what speed does the laser beam approach the earth?

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Key Concepts

Relativistic Velocity Addition

Relativistic velocity addition is the process used to combine velocities in such a way that the resulting speed never exceeds the speed of light. Unlike classical (Newtonian) mechanics where velocities simply add up, the relativistic formula ensures that, even when combining high speeds close to the speed of light, the outcome respects the invariant nature of light speed.

Special Relativity

Special Relativity is a fundamental theory in physics that describes the behavior of objects moving at significant fractions of the speed of light. It introduces the notion that the laws of physics, including the speed of light, are the same in all inertial frames, fundamentally changing the classical ideas of absolute time and space.

Invariant Speed of Light

The invariant speed of light is a core principle of Special Relativity stating that the speed of light in a vacuum (approximately 3.0 x 10^8 m/s) is constant for all observers, regardless of their relative motion. This means that even if a light source is moving relative to an observer, the measured speed of the emitted light remains the same.

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