# Why can't we go to the center of the galaxy?

At 10% c, relativistic effects only amount to a 2% difference in elapsed Earth time and elapsed ship time. (You just shave 2 1/2 months off for every 10 lys traveled.)

it's even worse than that..

at 14% c you have only a 1% time dilation (99,49874371% true time)

here is my handy Geometrodynamics Table as a reference

which includes the Formula for calculating time dilation

at 10% c there is only a 0,5% time dilation (half of 1%) so you only save 433 seconds per day of travel (more accurately - 0,50125629% time dilation)

so 1 day would equal 85966,91 seconds rather than 86400 s

a relative calendar year would equal 31398770,7931 seconds
rather than 31556952 seconds - (158181,2069 seconds less)

one would save: 1 day - 19 hours - 56 minutes - 0,35 seconds per year of travel

so in relativistic terms 10% c is not much faster than a school bus

to make matters even worse - the Bussard Fusion Ramjet must accelerate to 6% c - using conventional impulse propulsion before the Ramjet can even be engaged

a spacecraft with humans onboard can only accelerate at 1g for long durations - and accelerating at 1g (9,80665 m/s/s) would require 21 days 5 hours 30 min to reach 6% c - and 35 days 9 hours to reach 10% c

a 40 TW Fusion Ramjet would be lucky to acheive 50% efficiency
so it's doubtful that even 10% c would be reached using this method of propulsion

(the maximum period of time a spaceship can accelerate at 1 g is 30570322 seconds - or 353 days 19 hours 45 minutes 22 seconds - at 30570323 seconds the spaceship would reach c - which is impossible according to The Special Theory

the only proposed propulsion system capable of velocites approaching c
is warp drive - which expands the space behind the spaceship whilst compressing the space in the direction of travel

incidentally this is the propulsion system used in the Star Trek series

using this method of propusion - theoretically - it would be possible to acheive the effect of FTL velocity without actually reaching c

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Stingray
Your ship would probably get destroyed from collisions with random space junk and highly blueshifted radiation.

John Baez gives a duration of the trip to the center of the galaxy (first acelerating at 1g, and then at the middle of the trip decelerating by the same amount) of 21 years for the people of the ship. Well, I think that I'm nitpicking here
http://www2.corepower.com:8080/~relfaq/rocket.html [Broken]
Surprisingly using the same technique, the voyage to Andromeda galaxy is only of 29 years for the people of the ship!. Suddenly, Andromeda galaxy doesn't seem so far away

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Doc Al - how can the exhaust velocity be 10% purely in respect to the rocket? ...10% c relative to the rocket and what else? relative to the local speed of light? that would contradict the michelson-morley experiments for sure...

Janus - okay, it sounds like you are talking about a drag effect here that limits velocity, countering the momentum of 'stationary' hydrogen ...this is very interesting in that it offers some practical limitations to the intra-galactic relativity principle, i.e. what is our absolute motion in relation to the interstellar hydrogen?

Växan -

(the maximum period of time a spaceship can accelerate at 1 g is 30570322 seconds - or 353 days 19 hours 45 minutes 22 seconds - at 30570323 seconds the spaceship would reach c - which is impossible according to The Special Theory
don't forget that you're now involving the reference frame of a 'stationary' observer...this limitation has no effect on the inertial reference frame of our traveling spaceship where time dilation and the shrinking of space accomodate the constant speed of light...my point was, to the passengers on board the ship there is no speed limit in relativity, the only speed limit is set by the limitations of fuel for acceleration...

meteor -

Surprisingly using the same technique, the voyage to Andromeda galaxy is only of 29 years for the people of the ship!. Suddenly, Andromeda galaxy doesn't seem so far away
exactly...the article you gave was a little vague about the practical matters of fuel/acceleration but the point that relativity really sets no speed limit within a discrete inertial reference frame is an important one i think...

Doc Al
Mentor
billy_boy_999 said:
Doc Al - how can the exhaust velocity be 10% purely in respect to the rocket? ...10% c relative to the rocket and what else? relative to the local speed of light? that would contradict the michelson-morley experiments for sure...
I really don't understand your question. Why is there an issue with an exhaust velocity of 0.1 c? Exhaust velocity is the speed at which fuel is ejected--relative to the rocket. I don't know what you mean by "purely in respect to the rocket". I don't know what you mean by "and what else". What do you mean "relative to the local speed of light"? And what is the connection with Michelson-Morley?

(You're not using your personal definition of speed again, are you?)

This is an incredibly interesting conversation. But a few q's from a complete neophyte here if you don't mind.
Three actually.
1) Even in REALLY deep DEEP interstellar space, the "vacuum" of space is no "vacuum" right? I mean there are ALWAYS at least SOME stray molecules floating around in every cubic foot of space right?
So even if the "vacuum" of space looks like a "vacuum" at mach 18, at .1c wouldn't the "vacuum" of space start to look a lot more like a kind of soup?
2) Wouldn't hitting just random molecules along the way essentially irradiate the living piss out of any potential crew?
3) What would happen if you tried to tear ass through the Sagittarius Nebula at something like .1c? Wouldn't that wind up being a bit like diving head first into a shotgun blast?

Staff Emeritus
Gold Member
Dearly Missed
You are describing the "relativistic ramjet" idea. This was popular a couple of decades ago but detailed studies showed that the drag would exceed the reaction generation. So we're back to carrying your reaction mass along.

Of course there are "new physics" (i.e. crank) proposals all the time. "Vacuum propellers" or coupling to the zero point energy was one. And there are always the weird solutions of Einstein's field equations, like wormholes and the Alcubiere warp drive.

Nereid
Staff Emeritus
Gold Member
MonstersFromTheId said:
This is an incredibly interesting conversation. But a few q's from a complete neophyte here if you don't mind.
Three actually.
1) Even in REALLY deep DEEP interstellar space, the "vacuum" of space is no "vacuum" right? I mean there are ALWAYS at least SOME stray molecules floating around in every cubic foot of space right?
So even if the "vacuum" of space looks like a "vacuum" at mach 18, at .1c wouldn't the "vacuum" of space start to look a lot more like a kind of soup?
2) Wouldn't hitting just random molecules along the way essentially irradiate the living piss out of any potential crew?
3) What would happen if you tried to tear ass through the Sagittarius Nebula at something like .1c? Wouldn't that wind up being a bit like diving head first into a shotgun blast?
The ISM is (mostly) a plasma, so, being charged, there is a way - in principle! - to reduce the multiple hazards of colliding with lots of ions and electrons (really intense and well-designed magnetic fields). However, this doesn't work so well for neutral particles.

I'm sure all readers realise that denizens of the ISS, Shuttle, etc are doing a real-life experiment with the effects of impacts with relativistic particles ... right now. Cosmic rays are comprised of both neutral (few) and charged particles (mostly protons), and the Sun emits copious quantities of them too (though not really 'relativistic'). We here on the surface of the Earth are being hit in the head by ~6 CRs per second (IIRC); effect? And that's with a few hundred kms of air.

I suspect the infrequent collision with micron-sized ISM dust grains would be far more hazardous than even the ISM neutral gas at 0.1c :tongue2:

Anyone like to suggest a back-of-the-envelope calculation? (It's not all that difficult)

russ_watters
Mentor
meemoe_uk said:
12 years to travel to the centre which is thousands of light years away? are you sure.. if so....
that means as far as the travelers are concerned, they are moving towards the centre faster than light. It's a funny bit of SR. first you get your head round the idea that nothing can travel faster than light so you'd think it'd take thousands of years even from the travels point of view, then you realize space contraction effect cancels it out so things can appear to travel faster than light, in this case, the centre.

Does this case work for any old particle flying towards the earth?
Not quite. The length contraction cancels out time dilation in such a that they would not percieve themselves travleing faster than C. They wouldn't travel 33,000 ly in 20 years, but rather they'd travel 17 ly (guess) in 20 years (according to them), never exceeding C.

DOc Al - okay, i think i understand the 'exhaust velocity' idea a bit better, but i don't see how the exhaust velocity would limit accrued speed, it simply limits the gradient of acceleration...

nereid - very interesting, could we really design a magnetic 'shield' to neutralize charged particles? what about the dust grains? would there be any (theoretical) way to use the energy and rest mass of these dust grains to our advantage in the same way that we can funnel interstellar hydrogen into our (again, theoretical) fusion drive?

russ - this is a very important point, length contraction and time dilation adjust themselves in such a way that no one can ever measure his speed to be greater than c...but i think, too often, the popular impression is one that ignores length contraction, and time dilation, and insists on using simple earth-based measurements of distance to prohibit travel to the rest of the galaxy...within the bounds of relativity there is no limit to where you can travel in a certain amount of time...

billy_boy_999 said:
the "speed of light" relative to what? to earth? relative to earth, yes it would take a very long time but remember time dilation and the principle of relativity...as far as the crew of the space ship is concerned there is no speed limit...

the time it would take to get to the center of the galaxy is only limited by the gradient of acceleration...the gradient of acceleration is only limited by the thrust of the rockets and the mass of the ship, if we can make nuclear thrust technology very efficient i think the journey is a perfectly plausible one...
Slightly erroenous, the speed of light is constant for all observers. The travelers are still limited to the speed of light, the velocity they would measure for the objects moving apst them. But because of length contraction they would say they were traveling at the speed of light, but convering a shorter distance. This is what causes the shorter travel time by the moving clocks.

let's just face the fact that no existing propulsion system will ever result in interstellar travel

it will take breakthrough physics to accomplish that

and breakthrough physics discoveries are few and far between

the current prospects of joining the federation of planets are dismal

so just get used to watching perpetual space shuttle launches for the forseeable future - as far as propulsion technology is concerned - there has been no progress since the 1960's

the last moon landing (11 December 1972) tolled the end of manned planetary exploration for the 20th century (nearly 32 years ago!) who knows how long it will be before the next moon landing - 32 more years maybe? (most likely with 60's technology) and manned missions to mars are just a dream until the next generation of propulsion becomes reality

since the cold war ended - the days of cowboy rocketscience are over
(those were the days) I would guess that interplanetary manned missions (within this solar system) may happen by the end of the 21st or 22nd century

missions to the nearest stars?
possibly 300 to 1000 years into the future (maybe)

galactic missions?
possibly never
current physics notwithstanding

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it seems to me that it would be rather silly to send huge primates and chunks of plastic/steel- if I were considering such a long journey- I think that it would be more prudent to encode the crew/environment/ and a copy of all human knowledge into some quantum-scale computing system- you would transmit or project the ship to it's destination- I would be quite dissapointed in the engineers if the vessel were big enough to be visable by the human eye-

BTW- hello I'm new! (^_^)- I'm not a physicist- I'm a computermusic composer and incorporate some AI/AL/cog sci research into my art- [physics was my first declared major-I was going to go into cosmology but this was the late 80's and my love of the human brain and AI [and sythesizers] won me over so I ended up swept up into the great attractor that was the Santa Fe Inst in the early 90's- when the party was over I settled down into life as a self-styled crackpot/ chaos-shaman/ artist/ polymath/nutter [with a day-job]- thanks to excessive research into psychotropics and too much free time/money (as most of my collegues at SFI did- I think) ]

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