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## Homework Statement

Plans are made to send a spacecraft from earth to a nearby start 10 light years away. The system support will last one year and one day. The trip is one way trip.

a) What speed must the craft travel to arrive at the star with battery power for one day to make the measurement? (aka, you have one year.)

b) For the reference frame with the spacecraft, what is the distance between the earth and the star? (so how far does it go that it measures?)

## Homework Equations

As far as I know only

[tex]t'=(t-vx/c^2)\gamma[/tex]

[tex]x'=(x-vc)\gamma[/tex]

[tex]\gamma=(1-v^2/c^2)^{-1/2}[/tex]

## The Attempt at a Solution

Well, from what I can gather the earth is in the x' frame and the spacecraft is in the x frame.

So t=1, and x' = 10ly

solving the t' equation for t , then pushing it into the x' equation I get (assuming I didn't make any silly mistakes)

[tex]x'=(x(1+v^2/c^2))\gamma-vt'[/tex]

which won't work because I have two unknowns, (x and v). solving the other way around (first x' for x, then putting it into the t' eqn) I get

[tex]t'=(t(1+xv^2/c^2))\gamma-x'v^2/c^2[/tex]

which predictably arrives at the same conclusion.

So my approach is wrong, but I can't figure out how else to approach it.