Question

Time dilation help pls

Answer 1

Alpha Centauri, which is the closest star system to us here on Earth, is about 4.37 light years away. You are the lucky astronaut chosen to visit, and fly there at a constant speed of 0.85c.
1) If I stay here on Earth and watch you fly to Alpha Centauri at a speed of 0.85c, how long would I see the trip take?
2) How long would the trip take according to your watch aboard the spacecraft?

Answer 2

\[t=T/\sqrt{1-(v/c)^2}\]

Answer 3

I'm not sure how to set up for the first question since you don't have t or T

Answer 4

you simply use the time-distance relationship of non relativistic physics. You know how far it must travel and you know the speed it is traveling. The question is asking how long you will see the trip take from your point of view.

Answer 5

I guess I just need someone to walk me through the steps unfortunately. I'm having a really hard time setting the equation up.

Answer 6

Like I don't know how to solve for t if I don't know T or vice versa

Answer 7

In Earth's frame,

distance = 4.37ly = 4.37*365*24*60*60c
speed = 0.85c

time taken = distance / speed = ?

Answer 8

If it is 4.37 light years away and you the rocket is moving at 0.85c then it is 4.37/0.85 years. You could convert the 4.37 light years into meters, then convert 0.85c into meters/second and solve the equation t=d/v where d is the distance and v is the speed. You don't need the other equation you have until part B

Answer 9

oh ok that makes sense will do it now.

Answer 10

do I have to convert 4.37 light years into meters it seems like to big of a number but i guess ill do it anyways

Answer 11

I got 2,296,872(60c) so far

Answer 12

you don't really need to, you can solve it for years since you have the distance in light years like I said before. I was only showing you that you could convert them to more familiar units and it becomes a problem you're probably familiar with already

Answer 13

For example do you know how long it would take a beam of light to get there?

Answer 14

ok how would i solve it for years then?

Answer 15

um i dont know the exact number tbh speed of light lol?

Answer 16

so I got 162,132,141.18 meters following ganeshie's steps

Answer 17

It would take4.37 years. That's what a light year means, its a distance light travels in a year. If you were traveling at half the speed of light I would see you take twice that long to get there (watching from the Earth) or: 4.37/(0.5c) = 8.74 years. Since I'm watching you travel at 0.85c I see you take 4.37/(0.85c)=5.14 years.

Answer 18

ok that makes sense :D

Answer 19

so thats the answer to number 1 :D

Answer 20

Right. Now the person on board the ship sees less time pass than the person on earth. How much less? A time that is smaller by a factor of \[\sqrt{1-(v^2/c^2)}\]
So calculate that factor and multiply it by the 5.14 years from part A

Answer 21

will do

Answer 22

i got 2.8 years

Answer 23

I have 2.7 but I used 5.14 (I rounded) Did you get 0.52678 for the dilation factor?

Answer 24

i'm sorry dilation factor?

Answer 25

so i got 0.7225 by squaring .85 then i subtracted 1 from that (i think i should have rounded it before subtracting) and got 0.2775 which i rounded to 0.3 and took the square root of that and got .5477 which i rounded to .55

Answer 26

That's what the equation
\[\sqrt{1-v^2/c^2}\]
is called. It is a measure of how much space and time are dilated (contracted) in other frames of reference. For you \[v^2/c^2 = 0.85^2 \]
So I have \[\sqrt{1-0.85^2}=0.5267\]
Then \[0.5267*5.14=2.707 years\]

Answer 27

ok makes sense

Answer 28

FYI: the person on the rocket sees the world moving past her at 0.85c also, so in order to explain how she got 4.37 light years away in such a short time, she would have to conclude that the distance between Earth and Alpha Centauri shrunk by the same factor.

Answer 29

Ok that makes sense. Thank you so much for sticking around this long and helping me :D