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Chapter 26: Problem 3

A spaceship traveling at speed \(0.13 c\) away from Earth sends a radio transmission to Earth. (a) According to Galilean relativity, at what speed would the transmission travel relative to Earth? (b) Using Einstein's postulates, at what speed does the transmission travel relative to Earth?

Short Answer

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Question: A spaceship is traveling at a speed of 0.13c away from Earth and sending a radio transmission back to Earth. Calculate the speed of the radio transmission relative to Earth using (a) Galilean relativity, and (b) Einstein's postulates. Answer: (a) Using Galilean relativity, the radio transmission travels at a speed of 0.87c relative to Earth. (b) Using Einstein's postulates, the radio transmission travels at a speed of c relative to Earth.

Step by step solution

01

Analyze Galilean Relativity

According to Galilean relativity, the relative speed between two objects is simply the difference between their two speeds. For this problem, the speed of the spaceship is given as 0.13c, and the speed of light is represented by c.
02

Calculate speed of radio transmission using Galilean relativity

Using the Galilean rule, we can find the speed of the radio transmission relative to Earth by subtracting the speed of the spaceship from the speed of light: Relative speed = c - 0.13c Relative speed = (1 - 0.13)c Relative speed = 0.87c In Galilean relativity, the radio transmission travels at a speed of 0.87c relative to Earth.
03

Analyze Einstein's Postulates

According to Einstein's postulates, one of the main principles of special relativity is that the speed of light in a vacuum is constant and does not depend on the motion of the source or the observer. Therefore, the speed of the radio transmission relative to Earth should be equal to the speed of light in a vacuum, c.
04

Calculate speed of radio transmission using Einstein's postulates

Using Einstein's postulates of special relativity, the radio transmission travels at a constant speed of light in a vacuum, c, which is the same relative to Earth. So, according to Einstein's postulates, the radio transmission travels at a speed of c relative to Earth. To summarize the answers: (a) Using Galilean relativity, the radio transmission travels at a speed of 0.87c relative to Earth. (b) Using Einstein's postulates, the radio transmission travels at a speed of c relative to Earth.

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