(M = mathematical content; I = integrative-builds on information from more than
ID: 1572023 • Letter: #
Question
(M = mathematical content; I = integrative-builds on information from more than one chapter; P = project idea; R = reflection; D = suitable for class discussion) (M) On Star Trek, the starship Enterprise travels at "warp speed, " a futuristic faster-than-light technology. Warp speed scales with powers of two; for example, "warp 3" means "2^3 = (2)(2)(2) = 8 times the speed of light." The speed of light is 300,000 km/sec, or 1 light-year/year. On the show, the Enterprise appears to be capable of warp 9-point-something, but not warp 10. So, how long would it take to reach each of the following locations, starting from Earth, at warp 9? (a) The Sun (b) Proxima Centauri (c) The center of the Milky Way (d) The Andromeda GalaxyExplanation / Answer
Speed will be = (2)9(300000000) = 153600000000 m/s = 1536*108 m/s
a) Time taken to reach sun from earth = (149.6*109m)/ (1536*108 m/s) = 0.97 s
b) Time taken to reach proxima from earth = (40.14*1015m)/(1536*108 m/s) = 2.6*105 s = 2.6*105/3.15*107 =8.3*10-3 year
c) Time taken to reach centre of Milky Way from earth = (28000 light year)/(1 light year/year) = 28000 year [The Galactic Center is the rotational center of the Milky way. The estimates for its location range from about 25,000 to 28,000 lightyear from Earth]
d) Time taken to reach The Andromeda glaxy from earth = (2.401*1022 m)/(1536*108 m/s) = 1.6*1011 s = 1.6*1011 /3.15*107 = 5.1*103 year
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