A stupid thing that's been bothering me. OK, so I was doing research for my own (hard SF - mostly) uni, and I was looking at a site comparing the different types of beamed propulsion for (realistic - STL) starships (particle beam, laser sail, sailbeam). One of the ones it talked about was the sailbeam, where you use a laser to shoot a bunch of tiny lightsails to some fraction of c and then slam them into the ship (as ionized gas, vaporized by on onboard laser). It mentioned one of the limitations was that as the ship sped up acceleration would drop off, because the sails have a finite speed and the faster the ship moves the longer it takes for them to catch up with it.
So I had a little fridge logic moment, and it occurs to me, hey wait a minute, what happens with a laser based system? I mean, the laser is light and that has a finite speed too. As the ship speeds up and gets farther away, wouldn't you have a similar effect?
For instance, say the ship accelerates at 2 m/s^2 and the final velocity is .8 c. This means acceleration time is around 8 years (compensating for relativistic effects. Now, the ship starts basically right on top of the laser, and gradually moves away from it. So by the time 8 years has passed it's a good couple of light years away. So the light emitted at that point will take several years to reach the ship. So...
At the beginning of the trip the ship is basically right on top of the laser. A certain amount of energy is imparted to it by the laser and it starts to accelerate. It always sees the laser shining behind it as it accelerates. At the end of 8 years (not accounting for time dilation), it's been getting hit by the laser for 8 years. Right so far? Except the tail end of the laser will take several years to reach it, right? So wouldn't that mean it's seeing the laser for several years longer than the laser is actually active?
This is probably a very stupid question, but that was a major WTF to me. For the life of me I can't wrap my brain around how this works. Does the ship's acceleration drop off as it gets further away from the laser, or what?
Physics-knowledgeable people, please enlighten me. Thank you.
Stupid laser lightsail physics/mechanics question
Moderator: Alyrium Denryle
Well the laser would be getting less effective at accelerating the ship as the ship gets further away for 2 reasons.
1. If the ship is so far away that the beam has spread out so that some of beam is not hitting the sail.
2. As the ship gets further away is has accelerated more, so there is a higher relative velocity between the ship and the source. This means that the laser will be redshifted and will appear to have lower energy/photon.
As momentum of a massless particle is U/c for U the KE, that means that as the laser is redshifted U decreases so will the momentum imparted per photon when it hits the sail. This means that for a faster ship a laser of given power will be less effective.
As for your "Ship perceives time differently to planet" problem, you cant really neglect time dilation and expect in general to be able to easily rationalise everything.
Consider someone being sprayed with a big firehose and pushed back:
The water has speed of 20m/s and pushes the guy back 5m over a time it is switches on of 4s.
So the hose operator turns it on at 0s and the guy starts to move back under the force of the jet.
At t=4s according to the operators watch he turns the hose off.
The poor sod then gets hit by the last of the water at t=4+5/20=4.25s
So here we see that even in a non relativistic case we have hose operator had the hose on for 4s and hosed guy was hit for 4.25s. There isn't actually any complex dilemma attached to the fact that the ship is hit by the laser for longer.
1. If the ship is so far away that the beam has spread out so that some of beam is not hitting the sail.
2. As the ship gets further away is has accelerated more, so there is a higher relative velocity between the ship and the source. This means that the laser will be redshifted and will appear to have lower energy/photon.
As momentum of a massless particle is U/c for U the KE, that means that as the laser is redshifted U decreases so will the momentum imparted per photon when it hits the sail. This means that for a faster ship a laser of given power will be less effective.
As for your "Ship perceives time differently to planet" problem, you cant really neglect time dilation and expect in general to be able to easily rationalise everything.
Consider someone being sprayed with a big firehose and pushed back:
The water has speed of 20m/s and pushes the guy back 5m over a time it is switches on of 4s.
So the hose operator turns it on at 0s and the guy starts to move back under the force of the jet.
At t=4s according to the operators watch he turns the hose off.
The poor sod then gets hit by the last of the water at t=4+5/20=4.25s
So here we see that even in a non relativistic case we have hose operator had the hose on for 4s and hosed guy was hit for 4.25s. There isn't actually any complex dilemma attached to the fact that the ship is hit by the laser for longer.