Question

Astronaut Flo wishes to travel to a star 20 light years away and return. Her husband Malcolm, who was the same age as Flo when she departs, stays home (baking cookies). If Flo travels at a constand speed of 80% of the speed of light (except for a short time to turn around), how much younger than Malcolm will Flo be when she returns? How long does Malcolm sit around baking cookies? How far is the distance to Flo?

Answer 1

Answer:

a. about 20 years younger

b. Malcolm sits around for 49.94 years

c. 2.268x$10^{17}$ m

Explanation:

light travels 3x$10^{8}$ m in one seconds

in 20 years that will be 3x$10^{8}$ x 20 x 60 x 60 x 24 x 365 = 1.89x$10^{17}$ m

for the to and fro journey, total distance covered will be 2 x 1.89x$10^{17}$  = 3.78x$10^{17}$ m

Flo's speed = 80% of speed of light = 0.8 x 3x$10^{8}$  = 2.4x$10^{8}$  m/s

time that will pass for Malcolm will be  distance/speed = 3.78x$10^{17}$ /2.4x$10^{8}$  

= 1575000000 s = 49.94 years

the relativistic time t' will be

t' = t x $\sqrt{1 - \frac{v^{2} }{c^{2} } }$

t' = 49.94 x $\sqrt{1 - 0.8^{2} }$

t' = 49.94 x 0.6 = 29.96 years       this is the time that has passed for Flo

this means that Flo will be about 20 years younger than Malcolm when she returns

relativistic distance is

d' = d x $\sqrt{1 - \frac{v^{2} }{c^{2} } }$

d' = 3.78x$10^{17}$ x $\sqrt{1 - 0.8^{2} }$

d' = 3.78x$10^{17}$ x 0.6

d' = 2.268x$10^{17}$ m     this is how far it is to Flo