Question

ANSWER 3A, B, AND C!

3. The star system that is closest to the earth is Alpha Centauri. It is 4.37 light years away in Earth's reference frame. The fastest spacecraft humans have ever launched is New Horizons, which sent us sweet pictures of Pluto in 2015. It attained a speed of 45 km/s relative to the sun. That's fast, but even at this rate, interstellar travel is not practical. a) Traveling at 45 km/s, how long, in years, would it take to reach Alpha Centari? (this is slow enough that you don't need to do a relativistic calculation) b) To make the trip practical, humans would need a much faster spaceship. According to an observer on Earth, how long (in years) would a spacecraft traveling at 0.91c take to make the journey? c) How long (in years) would the same trip take for an observer on the spacecraft?

Answer 1

12 -8 12 V 45 12 2 distance of Alpha Centauri from earth S= 4.37 ly 9.46x10² km a) Speed, =45km/s 9.46810 time, t= s = 2.10X10" s 2.10x10' x 3.17x10 year » time, t= 6.66 x 10 years b) Speed of the spacecraft with respect to earth, & V=0.91 C time taken for the journey, 9.46x 10 x 10 3.46x10's t= 3.468107 year time t=1.097 years c) If i to is the time observed for an observer in the space ship to = tx/1 - v2 = 1.097* / 1 - (0.91e :) 2=0.455 years for an observer on the space coaft, to = 0.455 years t=s 0.91 X3x108 10' x 3.17810 C2