Measuring Distance to a Star One Light Year Away at 0.5c Speed

[PatrickPowers]

Sorry to ask such a basic question, but I can't seem to figure it out.

On Earth a device is made that can measure the distance to a star one light year away. Now suppose the device is coincidental with the Earth and has already been accelerated to 0.5c. What distance will it measure now?

It can use radar and bounce a pulse off the star, measure the time delay and blue shift, and do a calculation to determine how far away the star was when the pulse was sent. But this is beyond me. I can't even tell whether the star would be measured as less than one light year, more, or the same.

 

[HallsofIvy]

Are you asking: If an object that can measure the distance (at distance 1ly in Earth's frame of reference) to a star measures that distance as it passses the Earth at 0.5c, what distance will it measure? I would think that would be just the Lorentz contraction:
$$\sqrt{1- .5^2}= \frac{\sqrt{3}}{2}$$
about .87 ly.

 

[ghwellsjr]

Sorry to ask such a basic question, but I can't seem to figure it out.

On Earth a device is made that can measure the distance to a star one light year away. Now suppose the device is coincidental with the Earth and has already been accelerated to 0.5c. What distance will it measure now?

It can use radar and bounce a pulse off the star, measure the time delay and blue shift, and do a calculation to determine how far away the star was when the pulse was sent. But this is beyond me. I can't even tell whether the star would be measured as less than one light year, more, or the same.

There are many ways to measure distance but if you're going to use radar, it will take two years to determine the distance of an object 1 light year away. So if you're going to do the same thing traveling at 0.5c, you have the added problem that since it is going to take a substantial length of time to make the measurement and that you will have moved during that length of time, which distance are you measuring? The distance at the start of the measurement, the end of the measurement, or somewhere in between? And if you think about traveling toward an object 1 light year away at 0.5c, that will take 2 years, the same amount of time that the measurement would take on the stationary earth. But, of course, your measurement will take less time but then your time is dilated and your distance contracted so this further complicates things.

So the safest way to answer the question of how far away is an object that was 1 light year away prior to accelerating is to determine its distance in the common rest frame and then use the Lorentz Transform to determine its distance in the moving frame. Frames of Reference provide a consistent means of defining remote distances and times.