Is it possible to get an impulse, if you shoot at a solar sails with lasers mounted on the spaceship?
If so, why doesn't a laser create a force, if it fires/releases a photon?
Is the impulse conservation rule broken with such a construction?
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Yes, it is entirely possible for lasers to give a propulsive power. In fact, there is a fairly commonly discussed idea of pointing a large laser at a solar sail to accelerate it faster than would be possible by just the sail itself. The key is, the lasers cannot be on the spaceship, they have to be away from the spaceship.
And yes, given these laws, lasers do in fact exert a small force back on the object they are launched from. It's just that the momentum is so tiny, it's barely noticed with highly sensitive devices and powerful lasers. The most powerful laser in the world is the laser located at NIF. It can produce a pulse at 500 trillion watts, albeit only for an instant. If you concentrated that on a single point, it would exert a force of about 367 N for an absorptive surface. That same force would be applied to the sail, except doubled as it would be reflected (Ideal). It should be noted that while this is actually quite a bit of momentum, it can only happen for a very small fraction of a second, making it more difficult to apply.
So, you are on a spacecraft, and you want to propel yourself with a laser stationed on the spacecraft itself. What do you do? There are two options you could do. First of all, if you bounce the light off of a reflective surface, then the light will bounce back, in essence, it will provide a slight bit of momentum, because the net effect is that light is being pushed off of the sail and outside of the spacecraft. But, there's a better way. Instead, point the laser as you would a rocket engine, and use it for thrust. Then you would get 100% of the thrust from said laser, and you'll be slowly accelerating in the direction you want to go.
Of course, one has to ask where the power comes to power this laser. The only conceivable source in the long run is solar power. And to do that, you might as well use solar sailing, it will give you the same return on your space, with less weight.
Bottom line, the only way that makes sense to use this is if a laser from a remote location is firing at you. Otherwise, it just wouldn't make any sense.
I'm going to borrow an analogy from Baron Münchhausen (see Fig. 1) later on to illustrate the Newton's three laws of motion that are in effect with such a system you're proposing and why it wouldn't be possible to create a propulsive force, if the lasers and the solar sail are a part of the same closed system (or a single body), but let's first go through these laws of motion:
- First law: When viewed in an inertial reference frame, an object either is at rest or moves at a constant velocity, unless acted upon by a force.
- Second law: The acceleration of a body is directly proportional to, and in the same direction as, the net force acting on the body, and inversely proportional to its mass. Thus,
F = ma, where
Fis the net force acting on the object,
mis the mass of the object and
ais the acceleration of the object.
- Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction to that of the first body.
Now, the first two laws seem promising, but I've promised to illustrate the problems of your proposal with an analogy, so here it is:
Fig. 1 - Baron Münchhausen pulls himself out of a mire by his own hair. Source: Wikipedia
I'm not trying to be smart, or mock your proposal in any way whatsoever. I just genuinely love Baron Münchhausen's stories since I was a kid, and this one, where Münchhausen allegedly pulled himself and the horse on which he was sitting out of a swamp by his own hair, is as good of analogy as I can currently think of, and it taught me the very same dynamics of a closed system that I'm describing here when I was a kid and didn't yet even hear of Newton until then.
So yes, while lasers will exert radiation pressure upon solar sails (see @PearsonArtPhoto' answer for more information), they will also exert a force equal in magnitude and opposite in direction on the vehicle's body, as per Newton's third law of motion. And because the lasers are a part of the same system (not two separate bodies, as quoted in Newton's third law of motion - they're attached to the vehicle and it to the solar sails, possibly by some long tether), this force on the solar sail will be canceled out by the equal and opposite force on the lasers that are emitting the photons. It would stretch the tethers the sails are connected to with the spaceship, but that's about it.
This is a bit of generalisation, as lasers work as concentrators of photons (optical amplification) and travel many times back and forth within the gain medium, but they travel exactly one length of the gain medium longer in the direction of the output coupler, so our initial presumption still stands.
Simple point in case (reusing Münchhausen's "idea", but let's make it less potentially painful and unpleasant) - put your hands around your waist and try lifting yourself up without moving your legs at all. You will find it quite impossible, unless you exert some force on another body that is not a part of yours, and that you can push against.
Now, if the laser was stationed on another body, such propulsion would be quite possible. It could also be used to constantly change direction (spin on its axis), even if it was part of the same body, but it wouldn't work as a long term propulsion in any desired direction. Not by targeting the photon emitting lasers on a sail attached to the same vehicle. If would work without a sail though. Sadly, there's no free lunch here, not even with photons.
Edit to add: I see in the comments that my and @PearsonArtPhoto's answers have caused some concerns over their accuracy, due to supposed "free lunch" concept of pushing on solar sails using an onboard generated laser beam. So what follows is a bit of background on the actually proposed mode of propulsion, as found in scientific papers. If anyone can find a proposed solution that does this in a closed-loop system, and propels a spaceship in any direction by focusing a laser beam that is aboard the spaceship on the solar sails attached to the same spaceship, I'll be extremely interested to read the paper.
The beam has to have a large diameter so that only a small portion of the beam misses the sail due to diffraction and the laser or microwave antenna has to have a good pointing stability so that the craft can tilt its sails fast enough to follow the center of the beam. This gets more important when going from interplanetary travel to interstellar travel, and when going from a fly-by mission, to a landing mission, to a return mission. The laser or the microwave sender would probably be a large phased array of small devices, which get their energy directly from solar radiation. The size of the array obsoletes any lens or mirror.
Right. Not really directly dismissing the idea of carrying the source of the laser beam aboard the spacecraft, but it is suggested the beam source would have to be stationary by implying the greater radii (due to angular resolution) the more distant the spaceship is to the energy beam source. Let's take this a step farther and quote actual scientific papers, not only Wikipedia (which is fine in most cases, but one can't trust conclusions there with any degree of certainty, unless also absolutely certain it doesn't change implied meaning of its quoted sources);
1.11 Beamed-energy Propulsion (pages 4-6)
An alternative solution to the problem of the mass ratio required for high velocity flight is to use beamed energy. In beamed-energy propulsion, the energy source is left stationary, and the probe is pushed at a distance. Since the propulsion system does not move, the weight of the energy source is not critical, and fuel does not have to be carried.
An example of the beamed-energy propulsion is the photon-pushed sail. Since a photon has momentum, a photon beam can “push” a reflective sail. In practical terms, the force produced by reflecting a light beam is 6.7 newtons per gigawatt of light reflected. This force comes with no expenditure of fuel whatsoever. Thus, it is extremely favorable for high delta-V missions.
So there we have it. Such systems describe a stationary beam source, and a moving spaceship pushing against the momentum force reflected photons exert upon the solar sail.
I have also watched the first laboratory tests performed on feasibility of using this momentum of the photons targeted at an extremely light solar sail, but sadly don't exactly remember where this study was conducted, or who the publisher was (it was a fair bit ago, probably around 10 years?). Still, the test system was assembled in a vacuum chamber with the high-power laser stationary, and a small (roughly 1 square inch in size) solar sail held in place by an extremely sensitive lever that didn't impart movement of the test piece of the solar sail in the direction of the light beam. The forces measured were extremely tiny, but the concept worked and the method proposed was confirmed. Again - by using a stationary laser beam source!
Hope this clarifies things a bit.
The others covered some essential points concerning use of remote beam sources as propulsion to solar sails. Let me add something else:
The solar sail is huge to gather a lot of relatively weak, scattered solar energy and use its (very weak) kinetic component to push against (huge but cheap) mirror surface - Sun shines in all directions and you need enormous surface to catch its energy to provide reasonable propulsion to your vehicle (but the surface can be any cheap, light reflective material).
If you use light source of higher intensity than sunlight, concentrated over a small area, you might be better off exploiting the photovoltaic effect of the beam. Concentrate the laser beam over much smaller (but more expensive to build) area of a solar cell. While shining laser at ten square meters of solar batteries you're unlikely to generate direct kinetic push of magnitude comparable to a square kilometer of solar sail, you'll give it a fairly good voltage which then can be used to accelerate minuscule amounts of matter to relativistic speeds providing quite efficient propulsion in form of ion drive, that uses very little of solid fuel, and produces thrust proportional to amount of electricity you pump into it.
So, if you decide to shine a laser at a craft, don't use that laser to push that craft. Use it to power the drive of that craft.
If you used a laser connected to your "lightship" to push against the sail then only that portion of reflected light from the sail would propel your "lightship" forward. Any light that was absorbed by the sail or reflected by the sail back to the ship would be wasted. Pointing the laser out the back of the ship would give the best propulsion with the same laser.
A ground based laser pushing against your sail would use all the light hitting it to propel your ship, but if you used a sail that reflected that laser light then you would almost double the amount of acceleration from the same laser. You would get the transferred momentum from the light hitting the sail and the added thrust of the light reflecting off the sail being bounced back toward its source. In low volume high velocity water turbines they use a blade shaped like two bowls and direct the jet of water to the middle of the two bowls. That momentum is absorbed and turns the wheel but the water continues to travel across the bowls inner surface and exits in nearly the same direction from which it came adding that reaction to push the turbine even faster. A mirrored light sail would be nearly twice as effective as an absorbent sail.