Energy requirements for a relativity launcher

[Jota]

Energy requirements for a relativity "launcher"

I read about an interesting concept for space travel in the book "the Millennial Project: colonizing the galaxy in eight easy steps". Unfortunately, I forgot what exactly the author called it, and so have dubbed it a "relativity launcher". It was basically a method of rapid travel between vast distances in space, using the old concept of going at relativistic speeds to 'slow down' the time involved in travel. It was based on building incredibly large, star-powered rail guns. The "shuttle" carrying the passengers from point A to point B would be aimed precisely at the "barrel" of their end destination, then "fired" ( or more accurately slowly accelerated) out of the gun/launcher (point A). Eventually, it would "land" right in the barrel of the gun/launcher at point B, which would then use electromagnetic forces to slowly bring it to a stop.

Now, this might incite debate about the group dynamics of creating interstellar societies, the psychology of passengers dealing with everything else aging after they stop, etc. but please set these aside for now so that I can ask the main question. Also understand that I wish I was smart enough to answer it myself, but am unfortunately far too ignorant of mathematics, science, and physics to so. The question (preceded by the necessary assumptions) is this: Assume the device was built near a star that was more or less identical in every way to our own sun., Assume the device had no replenishment of energy from any other source. Assume the energy extraction method from the star is 50 percent efficient. Assume that it was firing payloads at relativistic speeds that would make a distance of one billion light years traversible in just one year of time for any passengers. Approximately How much mass could be shot out before entirely consuming the energy of the star?

 

[chroot]

It doesn't really matter how much power you have available. You can't accelerate people at more than a couple of g's without killing them, and a couple of g's doesn't really require much power to accomplish.

So, really, the rest of your questions are meaningless, but I'll answer them anyway, just to give you a sense of the numbers involved.

If you want to travel a billion light-years in one year of proper time, you (essentially) need gamma = 1 billion. To accomplish this, you need v > 0.9999999999999999994 c.

If you have a spaceship with two billion kilograms of mass (a thousand times the mass of the space shuttle), it'll require about 2 * 10³⁵ joules of energy to accelerate to the required speed.

$E = \gamma m_0 c^2 - m_0 c^2 = (\gamma - 1) m_0 c^2$

This is roughly the amount of energy the Sun liberates in 15 years.

- Warren

 

[pervect]

If you assume that the fundamental limit is acceleration, one could travel to Andromeda (about 2 million light years, not 2 billion) in 28 years, including braking - i.e, one would accelerate for 14 years at 1g, and deaccelerate for 14 years at 1g.

See for instance http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html

One starts to needs GR to consider corrections for trips longer than this according to the FAQ.

Thus the "gun" idea really doesn't work, the closest thing that would work is probably something like a laser-pumped light sail, converting some fraction of the sun's energy into a laser beam and putting it through a very large lens. (The largest lens I've seen proposed is Robert Forward's Jupiter sized Fresnsel lens. This is of course beyond our current technological ability.)

Taking 4*pi*1 Au^2 * 1366 watts/m^2, one gets a total energy output of the sun of about 3.7*10^26 watts. This could generate a thrust of 2.5*10^18 Newtons, so one could initially accelerate a very large mass at 1g with just a fraction of the sun's output.

Howver, as you get farther and farther away, and travel faster and faster, you'll run into problems. You won't be able to keep the laser beam focussed on the spacecraft .

Using the formula from http://www.sff.net/people/Geoffrey.Landis/lightsail/Lightsail89.html

for a spot size of 2.44 * lambda * (distance / aperature)

lambda being the wavelength of the light

for 1 1000 km lens at 1 light year using blue light (400 nm), one would have a spot size of 10 km.

If the light sail could also be 1000 km (which is probably generous), you could maintain focus for at most a few hundered light years.

If one works around this focusing problem somehow (perhaps a civilization has spread through the galaxy and uses a chain of stations to accelerate the spaceship) at high values of gamma the beam will be severly redshifted, dropping it's thrust by a factor of gamma^2.

The gamma^2 factor is slightly counter-intuitive, there is a reduction in the energy per photon by a factor of gamma, there is also a reduction in the rate at which photons arrive by a factor of gamma. The total energy flux, and hence the total thrust, decreases by gamma^2.

Thus our thrust of 2.5*10^18 Newtons would go down to 2.5*10^6 Newtons with a gamma factor of a million, using the entire suns output, assuming we could somehow focus it on a distant space-craft.

Keeping the solar sail from melting is another engineering problem, left to the reader.

It's a lot easier and probably more practical to postulate advances in medical science and/or a working nanotechnology resulting in an extended lifespan than the sort of physics it would take to get ultra-relativistic time dilation. One would then just live with the long trip times at 10-20% of light speed.