Technically if they exploded....we would see it only after 39 years.

SvennoJ said: darkenergy said: If only there was an exoplanet that that was only one light year away from Earth Yeah, then it would only take us 7,500 years to get there, instead of 300,000 In Elite Dangerous (sorta modelled on the real galaxy) there are star systems as close as .2 light years from each other. Ofcourse that close usually means a cluster of young stars with no habitable planets. Yet 1500 years is starting to get reasonable, hmm. Terraforming Mars might be a better waste of time :)

With a bussard ramjet  and nuclear fusion reactors we can probably accelerate to something like 20% of the speed of light before the drag on the ship becomes too overwhelming. Solar sails are also predicted to have a maximum velocity of 10% the speed of light, so they are a (slower) alternative. 

We'd have to be careful of collisions though. At 20% of the speed of light a 1Kg object would have a kinetic energy of approximately 3.7 Petajoules. That is about ten times the energy yield of Little Boy. Although it wouldn't likely impart all of that energy on the ship. Fortunately interstellar space is mostly empty, and the ship likely could avoid any objects as big or bigger than that. 

It would take 400 years  to get to the OP's system, a few years less from the perspective of the passengers. 

If we can perfect shielding technology and further eliminate drag we can go even faster. At 80% of the speed of light , the kinetic energy of a 1 Kg object  is 1.6 * 10^17 joules or 160 PetaJoules, which is on the same order of magnitude as the energy released by the Tsar Bomba. However, again, the object would probably not impart all of that energy when colliding with the ship, but that is plenty to pierce the ships hull, and damage things pretty badly. 

But at 80% of the speed of light we'd reach there in fifty years. 

There is more about this method of space travel here. 

https://en.wikipedia.org/wiki/Space_travel_using_constant_acceleration

I'd imagine we'd have technology that could achieve something like this a few hundred years from now (but maybe soooner or  maybe later.) 

I linked this before which already has a theoretical upper limit of 26% the speed of light in just 10 minutes.
http://www.zmescience.com/space/lasers-mars-travel-04232/
The problem is how to slow down, and ofcourse it only works with very little mass.

Yet that does open the door to send out probes build in the form of a distributed redundant system made of thousands of smaller components under constant communication. A swarm of tiny objects is much more likely to survive mostly intact than a space ship. A distributed AI can control the swarm, make observations and beam results back to Earth.

Shielding a spaceship at those speeds is a big problem when a grain of dust is already enough to cause severe damage. Plus we dont know how dirty interstellar space is. The densisty of stray objects is likely a lot higher than in interplanetary space where the sun and planets have been cleaning up for billions of years. Distributed probes will be a lot more successful, although not as sexy as sending out the Enterprise.

Who knows if swarms of relativistic probes have already passed through our solar system, they would be impossible to detect. Yet even if they detected us and beam signs of our intelligent life back to their origin it could still be many millenia before the slow boat arrives. Physics is more cruel than nature. Bringing a life sustaining spaceship up to 20% of the speed of light for now seems suicide.

Only 39 light-years away from us! That's actually close.

Drank a Westmalle to celebrate the discovery of the Trappist system :)

darkenergy said: If only there was an exoplanet that that was only one light year away from Earth

Still almost unreachable with current technology / resolve.