there are two identical brothers one is named A the other one is named B both exactly 20 years of age. twin A goes in a rocket ship at a speed of .95C (C=speed of light) to a planet 37million light years away while brother B stays on earth. upon reaching the planet brother A immediatly turns around and heads back at the same speed, he traveled back to earth. now that he has arrived how much older is brother B than brother A ? how old is each brother ?
2006-11-25 16:04:40 · 8 answers · asked by tachyon excelerator 1 in Science & Mathematics ➔ Physics
by the way if you can give some actual number. hint use the formula for time dilation
2006-11-25 16:32:55 · update #1
sorry it actually 37 light years. MY BAD
2006-11-25 17:15:14 · update #2
At a speed of 0.95C, twin A's clock is:
t1=1/sqrt(1-V^2/C^2)
T=1/sqrt176,700,000^2/186,000,000^2)
or a ratio of 3.2:1 time dilation.
Total trip time:
2*(37,000,000+{2*37,000,000*0.95})
Twin B, (although long dead) will be 77,700,020 years old. Twin A, (also long dead) will ONLY be 24,281,256 years old (earth time)
This does not take into account the acceleration factor on the time dilation effects - which, obviously, are moot in this example.
Bottom line - to travel to a planet that is 37,000,000 light years away, you'd better go a hell of a lot faster or find a short cut.
Added: OK, let's look at 37 light years.
Total travel time = 77.7 years
The ratio is the same 3.2:1 time dilation
The earth twin will be 97.7 years old.
The traveler twin will be 44.3 years old
2006-11-25 17:30:01 · answer #1 · answered by LeAnne 7 · 1⤊ 4⤋
If the planet is 37 million light years away, the total trip is 74 million light years. 1 light year is the distance light travels in 1 year - it would take 74 million years to travel it at the speed of light. Are you sure you don't mean 37 light years?
If so,
Brother B is 95.7796 years old,
Brother A is 21.0526 years old.
2006-11-26 01:08:15 · answer #2 · answered by Anonymous · 0⤊ 1⤋
Using relativistic equations of motion:
t' = γ(t - vx/c^2), where γ = 1/sqrt(1-(v/c)^2)
For v = 0.95c, γ = 3.2
Time it takes for twin brother A to reach the planet 37 light years away is t':
t' = (3.2)(37)(1-0.05) = 5.92 years
So it will take twice that much time or 11.85 years for the twin brother A to return to Earth.
Brother A will be of age 32 when he returns to Earth, but brother B will be a ripe old age of 94 years old (since he had to wait 37 years for the rocketship to reach the planet and then another 37 years for it to return).
2006-11-26 02:09:52 · answer #3 · answered by PhysicsDude 7 · 4⤊ 0⤋
Although the process has been rapidly slowed down, brother A will most likely be dead as well as brother B. And since years are measured in rotations of EARTH around the sun, they will both be the same amount of years old.
2006-11-26 00:16:43 · answer #4 · answered by Rictuar 2 · 0⤊ 1⤋
brother a is traveling at the .95speed of light so time is almoast stoped. brother b is going to be 37million year* 2 years old.
2006-11-26 00:16:36 · answer #5 · answered by tony200423man 2 · 0⤊ 0⤋
High Speeds accelerates time from the passenger's point of view, i remember reading that somewhere... so the one staying on earth will be older but as for the exact speed/time thing, I can't tell...
2006-11-26 00:16:48 · answer #6 · answered by That Guy 2 · 0⤊ 1⤋
brother b has been dead and buried for a very long time
2006-11-26 00:07:37 · answer #7 · answered by Biker 6 · 0⤊ 0⤋
They are the same age.
2006-11-26 00:07:07 · answer #8 · answered by M 3 · 0⤊ 2⤋