Twin paradox on another planet

[i-am]

Hello!

I'm new here, and already did a search. Sorry if the answer is elsewhere, I just couldn't find it!

I'm writing a sci-fi novel and have been brushing up on general and special relativity.

I'm running into a small problem with the twin paradox, and how to describe it from another planets point of view. Maybe I'm not understanding it because I have the math wrong, so please bear with me.

Disregard speeding up and slowing down, Earth math goes:

if

t=2d/v

then if the travel distance between two planets is 6 light years and we are traveling at .8c, then

t=2(6)/.8c= then t=15

So 15 years of travel time @ 80% the speed of light from Earth to Planet A.

if the Lorentz factor holds

then E=.6 as the time aged on ships clocks and and travelers age.

So the pilot of the ship would have aged 6 years, but on Earth people would have aged 15 years by the time the traveler would have reached planet A.

I'm sorry if this is incorrect. I haven't taken a physics class in a long time and I'm getting a lot of this math from wiki, and other various websites.

But if I am on Planet B, and I have 30 hours in a day, and 487 days in a year, then will all the math above still hold?

If light travels at 186282 miles per second no matter what planet one is on, and I am on Planet B trying to make sense of the twin paradox for the first time, will my traveling twin still have only aged 6 years, and I 15, planet B time?

For some reason this doesn't make sense in my head.

So I'm wondering if I'm missing something else here.

 

[i-am]

I think I figured it out.

Still would like a double check though.

All I would have to do is divide:

days in a year on Earth / days in a year on Planet B

365/487 = .7494 or .75 for easiness sakes.

So if time passed on ship is 6 years, then 6 x .75 = 4.5

So if time passed on Earth is 15 years, then 15 x .75 = 11.25.

Planet B would have aged 11.25 years, for their day/night/year cycle. And according to planet B's time cycle, age on ship would have only been 4.5 years.

Correct?

And I'm assuming if Planet B has no idea of "Earth" time cycles, then a physicist greater than I will ever be would have to figure out the other stuff?

 

[ghwellsjr]

I don't know why you have that factor of 2 in there. It seems to me that in the earth/planet rest frame it will take 7.5 years and 4.5 years on the ship's clock.

 

[i-am]

I don't know why you have that factor of 2 in there. It seems to me that in the earth/planet rest frame it will take 7.5 years and 4.5 years on the ship's clock.

Thank you!

I think what I was doing was the factor of 2 was for the round trip I had been calculating at first, then for some reason I forgot to take it out of the equation.

So, yes, you are correct.

But then I would just 7.5 x .75 and on planet B it would see 5.62 years have passed? Correct?

Thank you for that. I've been trying to figure out why it would take so long for a one way trip! And the whole time my cheat sheet was for round trips, and not for just a straight, single distance :)

 

[ghwellsjr]

Now you're asking about non-relativistic issues but I don't know why you mentioned the 30-hour day if you're not going to use it in your conversion. To avoid confusion, you should always say "earth-hour" or "planet-hour" so that your audience knows what your intention is.