http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html wrote:
The Relativistic Rocket
<<The theory of relativity sets a severe limit to our ability to explore the galaxy in space ships. Given that the galaxy is about 100,000 light years across there seems little hope for us to get very far in galactic terms unless we can overcome our own mortality.
A way to get around the problem may be to use the relativistic effects of time dilation and length contraction to cover large distances within a reasonable time span for those aboard a space ship. If a rocket accelerates at 1g (9.81 m/s2) the crew will experience the equivalent of a gravitational field with the same strength as that on Earth. If this could be maintained for long enough they would eventually receive the benefits of the relativistic effects which improve the effective rate of travel.
In theory you can travel across the galaxy in just 12 years of your own time. If you want to arrive at your destination and stop then you will have to turn your rocket around half way and decelerate at 1g. In that case it will take nearly twice as long in terms of proper time T for the longer journeys.
Here are some of the times you will age when journeying to a few well known space marks, arriving at low speed:
Code: Select all
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
Sadly there are a few technical difficulties you will have to overcome before you can head off into space. One is to create your propulsion system and generate the fuel. The most efficient theoretical way to propel the rocket is to use a "photon drive". It would convert mass to photons or other massless particles which shoot out the back. Perhaps this may even be technically feasible if we ever produce an antimatter-driven "graser" (gamma ray laser).
Remember that energy is equivalent to mass, so provided mass can be converted to 100% radiation by means of matter-antimatter annihilation, we just want to find the mass M of the fuel required to accelerate the payload m. The next chart shows the amount of fuel needed (M) for every kilogramme of payload (m=1 kg).
Code: Select all
d Not stopping, sailing past: M
4.3 ly Nearest star 10 kg
27 ly Vega 57 kg
30,000 ly Center of our galaxy 62 tonnes
2,000,000 ly Andromeda galaxy 4,100 tonnes
This is a lot of fuel—and remember, we are using a motor that is 100% efficient!
What if we prefer to stop at the destination? We accelerate to the half way point at 1g and then immediately switch the direction of our rocket so that we now decelerate at 1g for the rest of second half of the trip. The calculations here are just a little more involved since the trip is now in two distinct halves (and the equations at the top assume a positive acceleration only). Even so, the answer turns out to have exactly the same form: M/m = exp(aT/c) - 1, except that the proper time T is now almost twice as large as for the non-stop case, since the slowing-down rocket is losing the ageing benefits of relativistic speed. This dramatically increases the amount of fuel needed:
Code: Select all
d Stopping at: M
4.3 ly Nearest star 38 kg
27 ly Vega 886 kg
30,000 ly Center of our galaxy 955,000 tonnes
2,000,000 ly Andromeda galaxy 4.2 thousand million tonnes
One major problem you would have to solve is the need for shielding. As you approach the speed of light you will be heading into an increasingly energetic and intense bombardment of cosmic rays and other particles. After only a few years of 1g acceleration even the cosmic background radiation is Doppler shifted into a lethal heat bath hot enough to melt all known materials.>>