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Chapter 37: Q3P (page 1145)

You wish to make a round trip from Earth in a spaceship, traveling at constant speed in a straight line for exactly 6 months (as you measure the time interval) and then returning at the same constant speed. You wish further, on your return, to find Earth as it will be exactly 1000 years in the future. (a) To eight significant figures, at what speed parameter 尾must you travel? (b) Does it matter whether you travel in a straight line on your journey?

Short Answer

Expert verified

(a) The speed parameter is 0.99999950.

(b) It does not matter whether the journey is in straight line or not.

Step by step solution

01

Identification of given data

The duration of traveling in spaceship is t0=6months=0.5y

The duration passed on Earth for future is t=1000y

The Lorentz factor is used to find the speed parameter which is the ratio of the speed of particle with speed of light.

02

Determination of speed parameter  (a) 

The speed parameter for travel is given as:

尾=1-2t0t2

Substitute all the values in equation.

尾=1-20.5y0.999999502尾=0.99999950

Therefore, the speed parameter is 0.99999950 .

03

Effect of straight-line journey in travel  (b) 

The speed parameter is independent from the acceleration of spaceship so speed parameter does not change with change in path other than straight line. It does not matter that journey is in straight line or in any other path.

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Most popular questions from this chapter

Figure 37-21 shows one of four star cruisers that are in a race. As each cruiser passes the starting line, a shuttle craft leaves the cruiser and races toward the finish line. You, judging the race, are stationary relative to the starting and finish lines. The speeds vc of the cruisers relative to you and the speeds of the shuttle craft relative to their respective starships are, in that order, (1) 0.70c, 0.40c; (2) 0.40c, 0.70c; (3) 0.20c, 0.90c; (4) 0.50c, 0.60c. (a) Rank the shuttle craft according to their speeds relative to you, greatest first. (b) Rank the shuttle craft according to the distances their pilots measure from the starting line to the finish line, greatest first. (c) Each starship sends a signal to its shuttle craft at a certain frequency f0 as measured on board the starship. Rank the shuttle craft according to the frequencies they detect, greatest first.

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