stuck on a question (1 Viewer)

[sasquatch]

Could anybody help me on this question:

"If our galaxy, the Milky Way, is 20 kiloparasecs or 65,000 light-years in radius,how fast would a spacecraft need to travel so that its occupants can trael right across it in 45 years?"

I used length contraction and time dilation to try and find an answer.

For spaceship, t_o = 45 years

t_v = 45 / root(1 -v²/c²)

For Earth, L_o = 65,000c years

L_v = 65000 root(1 - v²/c²)

then i combined using v= /\r / t but got something like 288c.

 

[Riviet]

For a start, you need to use the diameter, not the radius of the milky way. So use 130 000 ly as the distance. If I figure it out, I'll post up my answer.

 

[sasquatch]

OHHH im a dickhead... yeah ill try it now...

 

[sasquatch]

I did something wrong before. And now i cant get any answer...

 

[zeropoint]

One approximate method is just to assume that tv = 65 000 y, since the spacecraft is obviously traveling very nigh the speed of light anyway.

Then plugging into your time dilation formula

tv = 45 / root(1 -v2/c2)

you get

v/c = 0.9999997604.

If you strive for accuracy, the corrected value of tv is actually squareroot(65000^2 + 45^2). But the values of v/c are so close (the first difference occurs at the 13th decimal place) that this correction is hardly necessary.