# Relativity question help, my brain has shut down

1. Oct 23, 2012

### dave2001

ive been practising relativity questions and theres one i cant do, ive tried loads of ways of approaching it and i cant go any further hence asking for help

it says " the diameter of the earths orbit is 3.0 x 10^8 m. a spaceship crosses the orbit in 750s, as measured in the spaceship. what is the speed of the spaceship relative to the earth?"

any guidance would be much appreciated,

2. Oct 23, 2012

### tiny-tim

welcome to pf!

hi dave2001! welcome to pf!

(try using the X2 button just above the Reply box )
ok, so in the sun's frame x = vt = 3 108,

and in the spaceship frame t' = 750,

sooo … ?

3. Oct 23, 2012

### dave2001

oh sorry , just seen it now you have said that (x2)

4. Oct 23, 2012

### dave2001

Re: welcome to pf!

sorry, thats how mashed my head is, its not 3 108 thats the value for c,

the diameter of the orbit is given as 3.0 x 1011 m

5. Oct 23, 2012

### dave2001

the diameter of the earths orbit is 3.0 x 1011 m. a spaceship crosses the orbit in 750s, as measured in the spaceship. what is the speed of the spaceship relative to the earth? (c = 3.0 x 108 ms-1

6. Oct 23, 2012

### dave2001

Re: welcome to pf!

i got that far but v comes out at 4x108 ms-1 and it doesnt work

7. Oct 23, 2012

### dave2001

cant figure out how to get to that

8. Oct 23, 2012

### tiny-tim

hi dave2001!

you have been busy while i was out!
show us how you got that …

presumably you started by finding t = 1000 ?

9. Oct 23, 2012

### dave2001

yeah that was the first assumption i made

distance x = 3x1011 m
t'=750
t=1000

so in frame for t, v=3x108
for frame t' v=(3x1011)/750 gives 4x108ms-1

10. Oct 23, 2012

### dave2001

im getting nowere either with the f-l contraction

11. Oct 23, 2012

### tiny-tim

12. Oct 23, 2012

### dave2001

3x108 x 750 = 2.25x1011m

13. Oct 23, 2012

### tiny-tim

(it'll be a lot easier if you stick to writing c instead of 3x108 )

yes, but i mean what is the formula with ct' on the LHS and x and t on the RHS?

hint: in the sun's frame, t = x/v = 1000c/v, isn't it?

14. Oct 23, 2012

### dave2001

you mean in the earths frame, yeah i get the time is 1000c/v,
as for the equation i dont know, i cant find anything in the textbook, im sorry been working on this question since yesterday and its really getting to me, i keep getting stuck at this point :-(

15. Oct 23, 2012

### dave2001

keep coming out with 1.98x108ms-1

16. Oct 23, 2012

### tiny-tim

no, in the sun's frame
i keep telling you …

17. Oct 23, 2012

### dave2001

why the suns frame?

18. Oct 23, 2012

### tiny-tim

it's "the diameter of the earth's orbit",

which is stationary in the sun's frame,

but obviously not in the earth's frame!!

19. Oct 23, 2012

### dave2001

so ct'=γ(ct-βx) with β=v/c, and γ=1/√1-β2

20. Oct 23, 2012

### tiny-tim

ok, now write that out in terms of β and x (with no γ or t), and solve