Dyson Sphere Spaceship?

[TwelveParsecs]

If some alien civilization would build a Dyson Sphere, and put a gigantic engine on the back with the power of the star, how fast would it travel?

 

[sanctus]

Well you need a bit more assumptions for an answer to that. Following the Kardashev scale https://en.wikipedia.org/wiki/Kardashev_scale that would be a Type II civilaztion. But leaving all science-fiction a part the dyson sphere out (although without what seems SF to us it is hard to build a dyson sphere), then not so quick, apporaching c is still requiring exponentially more and more energy.

[CraigD]

Welcome to hypography, TwelveParsecs, and thanks for your interesting question! Please feel free to start a topic in the introductions forum to tell us something about yourself.

 

If some alien civilization would build a Dyson Sphere, and put a gigantic engine on the back with the power of the star, how fast would it travel?

Let’s start with an easier to calculate problem, and leave out the gigantic engine, having instead a Dyson sphere with a small hole in it that lets out the star’s light.

 

Let’s use the Sun as an example star. Its power P_Sun is about 3.846 x 10²⁶ W, mass M_Sun about 1.988 x 10³⁰ kg. The momentum of light is E/c.

 

From this we can calculate the acceleration of our Dyson sphere spaceship as

P_Sun / M_Sun / c = 6.4531 x 10^-13 m/s/s

 

This isn’t much. In 5,000,000,000 years, the remaining lifetime of the Sun, it could result in a change in velocity (delta V)of about 102000 m/s = 0.00034 c, about the same speed as the Andromeda galaxy relative to out Milky Way galaxy. People who plan very long-term could use even such a small acceleration for some interesting maneuvering, changing the Sun’s orbit in the Milky Way, but the time scales would be on the order or millions of years.

 

To do better than this, you need to do what the original question asks, and build a gigantic rocket motor. The delta V of this is given by the rocket equations,

[math]\Delta v = v_\text{e} \ln \frac {m_0} {m_f}[/math]

(This is the intuitive, non-relativistic one, but the relativistic equation will give similar results)

 

Assuming the engine can effectively use up nearly all of the mass of the star, [math]\frac {m_0} {m_f}[/math] can be big, and assuming it ejects it at a very high speed [math]v_\text{e}[/math], this means it’ll be able to go as fast as it can survive. The problem then shifts from one of rocket motors to one of surviving friction with the medium of space – that is, how to keep the ship from being burned up by heating from collisions with many small bodies, such as atoms of hydrogen, or explosively shattered by collisions with larger ones. The details can get very complicated here, but hint that its wise to keep speeds below 0.5 c.

 

In short, a star-powered rocket could get you practically anywhere in the galaxy on time scales on the order of a few 100,000 years, but not produce speeds where time dilation becomes so dramatic that a passenger could get anywhere in the galaxy within their lifetime. Space travel in a star-powered rocket is still slow, but you get to take a lot of luggage. ;)