An astronaut is traveling in a space vehicle that has a...

An astronaut is traveling in a space vehicle that has a speed of $0.500 c$ relative to the Earth. The astronaut measures his pulse rate at $75.0$ beats per minute. Signals generated by the astronaut's pulse are radioed to Earth when the vehicle is moving in a direction perpendicular to a line that connects the vehicle with an observer on the Earth. What pulse rate does the Earth observer measure? What would be the pulse rate if the speed of the space vehicle were increased to $0.990 c ?$

Key Concepts

Special Relativity

Special relativity is the branch of physics that explains how time, length, and mass are perceived differently by observers in different inertial reference frames, particularly when they are moving at significant fractions of the speed of light relative to one another. It challenges the classical notions of absolute time and space, laying the foundation for understanding effects like time dilation and length contraction.

Time Dilation

Time dilation is a phenomenon predicted by special relativity wherein a clock moving relative to an observer ticks slower than a clock at rest with respect to that observer. This explains why moving processes, such as an astronaut's pulse rate, are observed to occur more slowly when viewed from a frame where the clock (or the astronaut) is in high-speed motion.

Lorentz Factor

The Lorentz factor, denoted as ? (gamma), is a critical component in calculating time dilation and other relativistic effects. Defined mathematically as ? = 1/?(1 - v²/c²), it quantifies the extent to which time, length, and relativistic mass differ from their non-relativistic values as the velocity of an object approaches the speed of light.

Transverse Doppler Effect

The transverse Doppler effect is a relativistic effect observed when the relative motion of a source is perpendicular to the line of sight of an observer. Unlike the classical Doppler effect, which depends on the component of velocity along the line of sight, the transverse Doppler effect arises purely from time dilation, resulting in a redshift of the frequency of light or signals such as radio pulses emitted by a moving source.

Transcript

Please give Ace some feedback