Rocket A passes Earth at a speed of 0.65c . At the same...

Rocket A passes Earth at a speed of 0.65$c .$ At the same time, rocket $B$ passes Earth moving 0.85$c$ relative to Earth in the same direction. How fast is $B$ moving relative to $A$ when it passes A?

Key Concepts

Lorentz Transformation

Lorentz transformations are the mathematical formulas that relate the space and time coordinates of events as measured in different inertial frames. They underpin the derivation of the relativistic velocity addition formula and explain how measurements of time intervals and distances change for observers in relative motion, ensuring consistency with the constant speed of light.

Special Relativity

Special relativity is the framework within which the behavior of objects moving at speeds approaching that of light is described. It rests on the principle that the laws of physics are the same in all inertial frames and that the speed of light in a vacuum is constant for all observers, regardless of their motion. This leads to non-intuitive effects such as time dilation and length contraction, which must be considered when discussing high-speed scenarios.

Inertial Frames

An inertial frame is a reference system in which objects obey Newton's first law, moving at constant velocity unless acted on by a force. When analyzing scenarios in special relativity, it is essential to distinguish between different inertial frames, such as those of observers on Earth and those in moving rockets, because measurements of time and space differ between these frames.

Relativistic Velocity Addition

Relativistic velocity addition is the method used to compute the effective speed of an object as seen from one moving frame when both the object and the frame are moving at speeds comparable to that of light. This formula takes into account the effects of time dilation and the invariance of the speed of light, ensuring that the calculated relative velocity never exceeds the speed of light, unlike in classical mechanics.

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