Relativity- stars and spacecraft.

[C.E]

1.a.) A star is 450 light years from earth.
i) what is the minimum time a spacecraft could make a return trip to this star?
ii)How fast should the spacecraft travel to make the journey in 30 astranaught years?
iii) What is the distance of eart to this star as measured by the astronauts on their 30 year journey?

my answer
1.(i). 900 years
(ii). I tried to do this by solving the following length contraction/ time dilation simultaneous equations:

(where g is gamma and L0=900, to=30)
Lg=lo
t=tog

and whatever I do I can't seem to eliminate enough variables, i.e. I always have a solution in both g and L or t and g or everything disappears and I get 0=0. Are these the right equations to start with? If so, what is going wrong?

 

[tiny-tim]

Welcome to PF!

Hi C.E! Welcome to PF!

(have a gamma: γ and try using the X₂ tag just above the Reply box )

1.(i). 900 years

Yes.

(ii). I tried to do this by solving the following length contraction/ time dilation simultaneous equations:

(where g is gamma and L0=900, to=30)
Lg=lo
t=tog

You don't need length-contraction …

do everything in the "stationary" frame, and then use time dilation (only) to convert the time to astronaut time.