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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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Most popular questions from this chapter

Show that each of these statements implies that \(v<c\) which means that \(v\) can be considered a nonrelativistic speed: (a) $\gamma-1<<1 \text { [Eq. }(26-14)] ;\( (b) \)K<<m c^{2}\( [Eq. \)(26-15)] ;(\text { c }) p<m c[\text { Eq. }(26-16)] ;\( (d) \)K \approx p^{2} /(2 m)$.
An astronaut has spent a long time in the Space Shuttle traveling at $7.860 \mathrm{km} / \mathrm{s} .$ When he returns to Earth, he is 1.0 s younger than his twin brother. How long was he on the shuttle? [Hint: Use an approximation from Appendix A.5 and beware of calculator round off errors.]
Refer to Example \(26.2 .\) One million muons are moving toward the ground at speed \(0.9950 c\) from an altitude of \(4500 \mathrm{m} .\) In the frame of reference of an observer on the ground, what are (a) the distance traveled by the muons; (b) the time of flight of the muons; (c) the time interval during which half of the muons decay; and (d) the number of muons that survive to reach sea level. [Hint: The answers to (a) to (c) are not the same as the corresponding quantities in the muons' reference frame. Is the answer to (d) the same?]
A man on the Moon observes two spaceships coming toward him from opposite directions at speeds of \(0.60 c\) and \(0.80 c .\) What is the relative speed of the two ships as measured by a passenger on either one of the spaceships?
The light-second is a unit of distance; 1 light-second is the distance that light travels in 1 second. (a) Find the conversion between light-seconds and meters: 1 lightsecond \(=? \mathrm{m} .\) (b) What is the speed of light in units of light-seconds per second?
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