# How long would it take a matter-antimatter GeV gamma ray laser photon rocket to get to Ross128b (11 light years away)?

I'm writing a colony story, and I want my ship to colonise Ross128b, which is 11 light years away from Earth. I need the characters to be alive when they get there, but it's okay if they've aged twenty years or so. I've been using G.G. Zel'Kin's 'A Photon Rocket', translated by Z. Jakubski for my research.

So apparently the speed of light is c = 299792 km/sec, and this type of rocket would travel at a third of it, 99 930 819.3 m / s, is this correct? Assuming the rocket is able to travel at this speed, how long would it take them to get to Ross128b? I'm aware of the s=d/t triangle but I'm awful at maths.

If they're travelling very fast, does that not mean that time will act differently for them than for the people back on earth? If they've been travelling for a week on the colony ship, how much time will have passed on earth? Will everyone they knew on earth be dead?

I just found a relativistic time dilatation calculator

Filling in the data you provided it gave back the following values

At 0.33c, to cover 11 light years it would take 33 years for an Earth observer, while for a passenger of the ship it would feel like 31 years.

The above calculation does not take into account the time to accelerate and to decelerate, but they are still useful to give a lower bound.

With just a couple of years difference the passengers will still have most of the people they knew to be alive when they reach their destination.

• If we assume they accelerate at 1g (a reasonable maximum for comfort and safety), the acceleration time would be about 117 days, plus another 117 days to decelerate at the end. So it would add less than a year to your estimate. – plasticinsect Jan 9 at 19:47
• so, to clarify - the spaceship journey would last around 32.13 years (31.46 add 234 days)? – Iona Jan 9 at 21:23
• @Iona Yes, that's correct. The time dilation factor at one-third lightspeed is small, but not insignificant., It's a 33 year journey for Earth-based people, but 31 years for those on the spaceship. There is a correction for acceleration time. – a4android Jan 10 at 1:36
• @Iona Not quite right, because they will still be moving during the acceleration phase, just at a slower average speed. The average speed during the acceleration/deceleration phases will be half of the full speed, so the trip time will be about (117+117)/2, or 177 days longer, which comes out to 31.8 years. – plasticinsect Jan 10 at 2:12

According to what I found online your spaceship should never stop accelerating so your rocket would eventually fly even faster than your given speed. (Of course only when the engines are on all the time)

So here is a scenario how this could work:

Assumption: Acceleration at the beginning = 1g (9.81 $$m/s^2$$) (acceleration decreases with speed as the Mass of your space ship increases)

This would be the most comfortable travel as it would ensure living like on Earth (when the mass of the passengers increases the acceleration decreases which leads to same weight felt throughout the whole trip)

Time needed (spaceship view): bit more than 472 days

Time needed (earth view): 11 years and 15,6 days

• thanks! could you point me to the research you did online? – Iona Jan 9 at 21:17
• physics.stackexchange.com/questions/109776/… I used this to generate my answer for the time Solution – Soan Jan 9 at 21:46
• youtube.com/watch?v=OHCHWDVjTZ4 and this for the infinite propulsion (yes light waves and gamarays are the same just that one of them are invisible to the eye) youtube.com/watch?v=LtPBqJ8XmWQ this was also part of it – Soan Jan 9 at 21:58
• At a glance, I find the 99 days to be very unlikely. It will take roughly a year to accelerate to close to light-speed, and another year to decelerate, and there will not be large time dilation for most of those years. – David Thornley Jan 9 at 22:13
• Yes I went over them again and discovered that i was indeed wrong – Soan Jan 11 at 21:39

At a minimum, assuming 1g acceleration of the ship, an outside observer would see them take something under 13 years -- about one year to accelerate to a high fraction of lightspeed, something like ten years in transit (because they'll cover about half a light year during acceleration, and the same to decelerate at the destination -- and it doesn't matter much if they coast or continue to boost, due to time dilation), and about one year to decelerate.

I'm not good with Lorentz equations, either, but the time experienced by the crew will be significantly less than that seen by an outside observer, and to them, it will make a noticeable difference if they boost continuously vs. coasting at 99% of lightspeed.

First you have got to see the acceleration then know if you want to decelerate at the system or not and how much fuel it has and if you are going to want to maneuver at all then you can begin your calculations leaving a margin for error.

Yes, time is affected, at a % of light speed I believe that time dilates causing it to feel shorter, be shorter. eg traveling at 90% the speed of light one year "earth time" will feel like 1 minute "ship time"
(i think that is how it works)

• I don't know where you got that value, but it's definitely wrong. At 0.9c 1 year of earth time is felt like 0.43 years. – L.Dutch Jan 9 at 12:42
• i don't actually know what the time dilation would be at any speed but i did read about this in a book, not a completely accurate one, i personally have no clue of the maths other than something happens like that :) – Dylan Bull Jan 9 at 16:17
• L. Dutch are you saying that those in the colony ship would have aged 43 years for every one earth year? I thought it would be the reverse – Iona Jan 9 at 21:18
• @Iona If you take Earth as a frame of reference (it's close enough to an inertial frame for these purposes) then the people on the ship would age slower. The ship over the course of the trip is not an inertial reference frame, since it first accelerates and then decelerates, so the point of view of the colony ship isn't all that useful. – David Thornley Jan 9 at 22:11