If a starship could accelerate at 9.8 meters per second squared then its crew would experience artificial gravity equal to that normally experienced on Earth. How long would it take them to reach places like Jupiter, Pluto, the nearest star to the sun or the nearest galaxy to us given that they would have to decelerate from the half way point to maintain artificial gravity?
Would they have the speed of light to contend with as a barrier to this possibility?
Yes, the speed of light and other relativistic effects become a problem.
Try the calculator here - use the Long Relativistic Journey calculator.
For Jupiter, at ~5AU, we get 6.4 days at 1g with turnaround, minimal relativistic effects.
For Alpha Centauri, 4.5 light years, we get 6.1 years earth time, 3.6 years ship time (average velocity .75c).
For Andromeda Galaxy, 2.5 million light years, we get 2.5 million years earth time, 28.6 years ship time.
However, while this calculates relativistic effects, it does not calculate kinetic ones. The closer you get to the speed of light, the more energy it takes to maintain 1g (as the relativistic mass of the spaceship increases). Unless you have a near infinite energy supply, you will not be able to maintain your 1g acceleration beyond a certain point.
Si
Thanks Si,
The calculator that you pointed me to is just the tool that I was looking for. All this is for no real reason, just idle curiosity, so I don’t need to worry about the kinetic problems.
I used to be able to understand and even work out my own answers to some of these questions but that was a long time ago and now I just look for the answers instead of working at them.
Thanks again
What I always find amazing is that if you accelerate at 1 G, you reach the speed of light in less than 1 year – Newtonian calculation of course as you never reach c under Relativity.
I might be misunderstanding you, or misapplying my relativity — but won’t you be burning fuel at a constant rate, to maintain a constant 1g, as measured in the reference frame of the ship?
That’s with the simplifying assumption that the ship’s total mass, including fuel, isn’t changing. You’d actually burn fuel at a decreasing rate as your mass decreased, in order to keep a constant acceleration. (Constant for the ship that is, and not as seen from Earth.)
The speed of light does not become a problem. It is the relativistic effects that enable you to get to Andromeda in in 29 years instead of 2.5 million years.
And Bytegeist is correct. Under the assumption that you have infinite fuel of zero mass, it does not get any harder to maintain an acceleration of g in the rocket’s reference frame. If the fuel has finite mass, it gets easier as the fuel is burned up.
The problem is acheiving a 1 g acceleration when the rocket is filled with enough fuel to burn for 29 years (even 29 minutes would require an enormous rocket to carry the fuel in a craft capable of carrying a person).
If I travel from here to the next galaxy that is 2.5 million years away, and according to ship time it only took 29 years then doesn’t that mean I travelled faster than light? I had a known distance divided by a known time it took to arrive gives me a speed greater than C. From my frame of reference, I exceeded C.
What am I missing? Something obvious i’m sure. Is it because when I arrive I will find that 2.5 million years have actually passed, and that’s the time I have to go by now? Still, it seems that from my frame of reference, for 29 years I am going faster than light. I didn’t think that was possible in ANY reference?
You need to take into account the relativistic contraction of length (Fitzgerald Contraction). In your frame of reference, you aren’t moving at all and nothing is moving faster than the speed of light. Andromeda is rushing toward you at nearly light speed and the distance is contracted from 2.5 million light years to tens of light years.
Classic Physics Limerick:
There was a young fellow named Frisk
Whose fencing was exceptionally brisk
So fast was his action
The Fitzgerald Contraction
Reduced his rapier to a disk
Another good essay here:
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html
4.3 ly nearest star 3.6 years
27 ly Vega 6.6 years
30,000 ly Center of our galaxy 20 years
2,000,000 ly Andromeda galaxy 28 years
n ly anywhere, but see next paragraph 1.94 arccosh (n/1.94 + 1) years
For distances bigger than about a thousand million light years, the formulas given here are inadequate because the universe is expanding. General Relativity would have to be used to work out those cases.
You are probably right. I was thinking about applying an accelerating force external to the relativistic object, where increasing amounts of energy are required due to relativistic mass.
In the spaceship frame of reference, fuel burns at a constant rate to maintain 1G no matter the velocity.
Si