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Chapter 37: Q7P (page 1145)


The premise of the Planet of the Apes movies and books is that hibernating astronauts travel far into Earth鈥檚 future, to a time when human civilization has been replaced by an ape civilization. Considering only special relativity, determine how far into Earth鈥檚 future the astronauts would travel if they slept for 120 y while traveling relative to Earth with a speed of 0.9990c, first outward from Earth and then back again?

Short Answer

Expert verified

The duration for future travel by astronaut is 2.683脳103y.

Step by step solution

01

Identification of given data

The speed of astronauts relative to Earth is v=0.9990c

The duration of the sleep of an astronaut is t=120y

The time dilation is used to find the duration of particles before decaying from the detector.

02

Determination of duration for future travel by astronaut

The duration for future travel by astronaut is given as:

鈭�t=t1-vc2

Here, is the speed of light and its value is 3脳108m/s .

Substitute all the values in equation.

鈭�t=120y1-0.9990cc2鈭�t=2.683脳103y

Therefore, the duration for future travel by astronaut is 2.683脳103y.

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Most popular questions from this chapter

A spaceship of rest length 130 m races past a timing station at a speed of 0.740c. (a) What is the length of the spaceship as measured by the timing station? (b) What time interval will the station clock record between the passage of the front and back ends of the ship?

The center of our Milky Way galaxy is about 23000ly away. (a) To eight significant figures, at what constant speed parameter would you need to travel exactly (measured in the Galaxy frame) in exactly 23000ly (measured in your frame)? (b) Measured in your frame and in light-years, what length of the Galaxy would pass by you during the trip?

Question: Temporal separation between two events. Events and occur with the following spacetime coordinates in the reference frames of Fig. 37-25: according to the unprimed frame,andaccording to the primed frame, (xA,tA)and(xB,tB). In the unprimed frame 鈭�t=tB-tA=1.00渭sand 螖x=xB-xA=240m. (a) Find an expression for 螖t'in terms of the speed parameter尾and the given data. Graph 螖t' versus 尾for the following two ranges of 尾: (b) 0 to 0.01and 0.1 (c) 0.1 to 1. (d) At what value of 尾is 螖t'minimum and (e) what is that minimum? (f) Can one of these events cause the other? Explain.

In Fig. 37-9, observer S detects two flashes of light. A big flash occurs at x1=1200mand, 5.00渭蝉later, a small flash occurs at x2=480m. As detected by observer S', the two flashes occur at a single coordinate x'. (a) What is the speed parameter of S', and (b) is S' moving in the positive or negative direction of the x axis? To S', (c) which flash occurs first and (d) what is the time interval between the flashes?

As in Fig. 37-9, reference frame S'passes reference Sframe with a certain velocity. Events 1 and 2 are to have a certain temporal separation 鈭�t'according to the S'observer. However, their spatial separation 鈭�x'according to that observer has not been set yet. Figure 37-24 gives their temporal separation 鈭�x'according to the observer as a function of for a range of values. The vertical axis scale is set by 鈭�ta=6渭蝉. What is 鈭�t'?
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