Acceleration

How long would it take to travel to Alpa Centaurai if one were to accelerate at , say, 10m/s/s for half the distance and then decelerate at the same rate for the other half? 10 years anywhere near it?

Let's start with the basic kinematics equation:

s-s0 = v0*t+0.5*a*t^2
where:
s-s0 is change in position
v0 is initial velocity
a is acceleration
t is time

let's just set s0 and v0 equal to 0

solving for t, we get:

t=sqrt(2*s/a)

s in this case is half the distance from earth to Alpha Centauri, which is 4.36 ly away, or 4.1248*10^16 m

Therefore, at 10 m/s^2, it will take 6.422*10^7 s, or about 2 years, to get half way.

So, you're looking at 4 years to get there.

Oh yeah, one little problem: you'll be going twice the speed of light when you start your deceleration.

That is quite difficult, because special relativity and accelerated observers requires a lot of math to solve. This site (Baez' site is really great!) has an explanation which contains this formula:

t = c/a arccos ( a*d/c^2 + 1)

where c is the speed of light, a the acceleration, d the distance in the earth frame and t the time of those inside the spaceship.

Because we accelerate half the way, for us the formula becomes:

t = 2*c/a arccos ( a*1/2*d/c^2 + 1)

t = 2*300*10^5 arccos( 10*1/2*40,5*10^15/ (300*10^6)^2 + 1)

This gives you a time of 110834765 seconds or 1282,8 days or 3,51 years.

[edit on 13-6-2004 by amantine]

Thanks for that, it's a little bit beyond my abilities when it come to the relativistic calculation. The reason I'm asking and used A.C. as an example, is that if anyone seriously wishes to travel through space then one would have to move at very high speeds or it would take forever to get anywhere. (Supernatural or Magical forces aside). What sort of propellentless fuel could we actually use today with the technology currently at our disposal?

Ion engines are pretty handy in space. They use very little fuel and generate very little thrust, but after a lot of time they will achieve great speeds. The problem is getting a ship with an ion engine into space. The engine is way too weak to overcome the gravitational pull of the earth.

The folks from the Advanced Propulsion Technology Group at JPL have put together a great site discussing the many forms of propulsion: www.islandone.org...

As Amantine said, ion engines are very promising. However, scaling them up is proving rather difficult. Fusion and antimatter is probably the most promising. A friend of mine just did his master's thesis on using Antimatter-Catalyzed Micro-Fission/Fusion (ACMF) for a manned mission to mars. Fuel is typically the limiting factor for deep-space missions (theoretical, of course), but the mass of the pellets used for ACMF is negligible, meaning you're now limited by human factors, the most prominent being radiation.

A helicopter can overcome the force of gravity by pushing against the air. It must be using a force of appox 10N/kg or more if I remember school days correctly. As it goes up the air get less and has nothing to push against I suppose. What if it were possible to push against something that we take with us, like a fly-wheel for example? The re-action force stored as angular momentum and released later? I've been thinking for a long time and wonder if the solution might be simpler than we imagine. Overcoming gravity can't be that difficult, after all, I got out of bed this morning and have been jumping around ever since!! What is ion-drive? Could I make one?

Thanx for that link, I know what I'll be doing for the rest of the day now!!

[edit on 2004-7-2 by Teknik]

Of course, were space folding ever to be perfected....then it would be a moot point.... Instead of the shortest distance between two points being a straight line....it would simply bring point A to right next to point B, with NO travel time.....

While not exactly at our disposal yet, I have read of solar sails in conjunction with orbital-based lasers/fresnel type lenses as a potential way to achieve (relatively) close interstellar travel...