A spaceship crew could happily accelerate away from the Earth at 1g (i.e. at Earth gravity), indeed they would feel "at home" under such an acceleration. Using 1g ( i.e. 9.8 meters/sec/sec) of acceleration, how long would it take to get to the nearest star and return?

Conveniently 1g is very close to an acceleration of 1 light year/year/year (it converts more accurately to 9.5 m/s/s). This makes the calculation straightforward by measuring the distance in "light years" and the time in years. For the trip to the nearest star, we accelerate at 1g to the half way point (2.15 light years distant) and then decelerate at 1g to the star.

Then using the usual equation of motion (distance s=u*t+a*t*t/2) with a small start velocity (i.e. u=0), and acceleration a=1 in our units, then substituting a distance s of 2.15 lightyears gives a time to half way of 2.07 years. The total journey time for the round trip is 4 times this, that is 8.3 years. This is the time the astronauts will have taken (and aged) on the trip.

However this is not the time the people on Earth think the astronauts have been away ! Due the relativistic effects, according to the people on Earth, the clocks on the speeding spaceship have been running slow. To find the Earth time for the trip, the change in the velocity with acceleration of the spaceship is not a=dv/dt but

acceleration a=d(v/sqrt(1-v*v/c*c))/dt

With the acceleration a=1, this gives on integration a velocity after t years of v=t/sqrt(1+t*t). Expressing v as ds/dt where s is the distance in light years and integrating again gives t=sqrt{s(s+2)} With s=2.15 light years, the time to the half way point is 3.0 years.

That is the total journey time in Earth time is 12 years(1). Although the Earth people will have aged nearly 4 more years than the astronauts, neither the journey time for the astronauts or the return time for Earth dwellers is prohibitive. Thus trips, at least to the nearest stars, are possible for man within current physics, but one must not belittle the enormous problems of providing the acceleration and protecting the astronauts from radiation. Even greater distances could be contemplated. For example within 9 light years of Earth we might expect about 8 stars. These could be reached with an astronaut journey time of 12 years and an Earth time of 22 years. More distant stars however would really only be accessible to galactic wanderers or unmanned spaceships. Although we cannot contemplate a trip to the stars in the near future, we can dream that one day we can go there.

1. This figure agrees with Professor Hawkins recent quote of about 6 years to get to the nearest stars.

Modified Oct 2007