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(a) How long does it take the astronaut in Example 28.2 to travel 4.30 ly at 0.99944$c$ (as measured by the Earth-bound observer)? (b) How long does it take according to the astronaut? (c) Verify that these two times are related through time dilation with $\gamma=30.00$ as given.

(a) $\Delta t_{0}=4.34 \mathrm{y}$(b) $\Delta t=0.143 \mathrm{y}$(c) $\Delta t=0.145 \mathrm{y}$

Physics 103

Chapter 28

Special Relativity

Relativity

Cornell University

University of Michigan - Ann Arbor

McMaster University

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in example, 48 points to go. The distance between the elf a century, the earth, the proper distance a lot I'm not, is equal to four point trade. Zero light years and the contacted lunch contacted. Land aval is equal to 0.14 pre three light years. Uh, we know that, um, one point 00 light here is equal to, uh, 9.9 points. 461 multiply by 10 to the power 15 meters, 15 meters and therefore a lot is equal to you and Mont is equal to 4.1. Multiply by 10 to the power. Ah, 16 maters. Onda um Al is equal to Elyse. Cool do 1.36 a. Multiply by 10 to the power 15 uh, meters on the relative lost two of the astronaut ese Let it be lost You, The astronaut is is equal to zero point mine mine nine, 44 times the speed of light and the speed of light is a trade 100 multiplied by 10 to the power eat meter or second All right. And no little Park hee Our game Well, we know they had done 13 are physical to allot divided by really and this is equal to a monkey's 4.1. Multiply by 10 to the power 16. Divided by re, uh is cedar 0.99 line, uh, 44 times the speed of light and therefore we have a four point run multiply by 10 to the power 16 divided by 0.99944 Multiply vcc is three months of life a tentative over eight meters per second. And this gives us Delta t not don't dirty not is equal to 4.34 two years. So Delta t noticing go to 4.34 years. Well, no, let's sew part B uh, down Titi is equal to ah contacted land which is l divided by relative velocity. I'm free and putting the values Um l is 1.36 multiplied by 10 to the power 15 meters and relative velocity equals, uh zero point 99944 times the speed of light and the speed of light is three points. It was in a multiplied by 10 to the dollar, eat meters per second and dividing the two numbers. Uh, we get, uh, zero point z. Don't point 143 years. Yeah. Now, let's do part. See well in Parsi Uh, relax. Mystic factor is given, and it's equal to attorney point 00 on DDE. Relation between a dilated time and proper time is a delta T is equal to, uh, relax, mystic factor times uh, identity, not Delta t not. And so the core delta t uh, Delta t is equal to Delta t not divided by gamma. Now let's plug in the values. Uh, well done. 30 knot is 4.34 ah, years divided by, uh, gum. I used Turkey very born 00 and therefore Delta T is equal to Placido 0.1 for five years.

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