Special Relativity and Space Travel (1 Viewer)

[TeaYarn]

Alpha Centauri is 4.5 light years away from Earth.

a) travelling at 0.1c, calculate how long it would take to get there as measured on earth.
b) calculate the time this would represent for the astronauts
c) use the length contraction formula to calculate the distance the astronauts travel
d) if the spacecraft is travelling at 0.1c, calculate the time from the astronauts perspective

For a, i got my answer as being 4.48 light years, but in the answers it has 45 years? Is there some way of converting the light years into earth years or..?

 

[Zeref]

a) light year is a measure of distance/length, not time. So you might want to drill that idea in your head before you make careless mistakes. time= distance/speed which is 4.5/0.1 which is what the answer says: 45 years

b) isn't that the same as d? idk LOL

c) cbf but find the distance of a light year and then multiply it by 4.5. Substitute into the formula.

d) im confusing myself with this question. i think the answer should be 44.77 because time passes more slowly for the astronauts opposed to the people on earth.

 

[hit patel]

hi tea,
Bit late for the reply but might still help.
a) So basically its about whether the length is seen by the person on earth or the person on spaceship. The Principle of relativity says that laws of mechanics hold true in all relativistic frames. The frame of reference of the length provided is the person on earth. Therefore we can use s=d/t to find this. And yes you need to consider what Zeref denotes.
b) Now it is asking you to find the relativistic time. So you need to use the time dilation formula and since time dilates when seen by an external observer you can use the time dilation formula and set the person on spacecraft as t_v and the person on earth as t_0. I get 45.2267 years.
c) In the astronauts frame of reference, the length using the length contraction formula , where l_v is always smaller and since the spacecraft is travelling at 0.1 c, the astronaut must be seeing length he travels contract. Note here it doesn't refer to length of spacecraft in ratio to the distance travelled. If it was to talk about that then the astronaut would see on difference, however the person outside would see the spacecraft contract. Its talking about length covered in astronauts frame of reference at his relativistic speed. So l_v is astronaut and l_o is earth man. I get 4.47744 LIGHT Years. This is the answer you got for a) hehe.

Hope that helps. PLease clarify If my calculations are right.