825.3 consequences of Einstein's postulates Example 2: (a)Can a person, in principle, travel from Earth to the galactic center(which is about 23000 ly distant) in a normal lifetime? Explain, using either time-dilation or length-contraction arguments(b)What constant speed is needed to make the trip in 30 y(proper time)? Solution: a)Do not consider the important problem such as fuel requirements, stresses to the human body due to the accelerations, the answer is yes. 8 25.3 consequences of Einsteins postulates (b)d=23000ly=23000c(y) ∥t ∠t √1-(vc)2 C 1+(∠,c/d)2√1+(30123000 299792458 √1+0.00007013 299792203 =0.99999915c20 Example 2:(a)Can a person, in principle, travel from Earth to the galactic center (which is about 23000 ly distant) in a normal lifetime?Explain, using either time-dilation or length-contraction arguments. (b)What constant speed is needed to make the trip in 30 y (proper time)? Solution: (a) Do not consider the important problem such as fuel requirements, stresses to the human body due to the accelerations, the answer is yes. §25.3 consequences of Einstein’s postulates (b) d=23000 ly=23000c (y) c c t c d c v v d v c t t 0.99999915 299792203 1 0.000017013 299792458 1 ( ) 1 (30 23000) 1 ( ) 2 2 0 2 0 = = + = + = + = = − = ∆ ∆ ∆ §25.3 consequences of Einstein’s postulates