Conservation of momentum and laser powered solar sail

[nemesiswes]

I was watching a show on the science channel called "Alien Encounters". Well in one of them they showed a ship that looked as if it was propelling itself by firing a laser at it's solar sail. Now I am pretty sure that from what I understand about physics, that would not be possible.

Correct if I am wrong but when a laser is fired, the laser beam (electromagnetic waves) carry momentum, now since the laser beam carry's momentum then a reverse momentum must be created on the ship that it is firing from, only in the opposite direction. So now if you have a solar sail on that very same ship and the laser beam is absorbed or reflected from that solar sail, then the laser beam momentum is transferred to the solar sail. So now your momentum from firing the laser and the momentum absorbed from the solar sail should cancel out and thus your ship should not move at all. Is this correct?Don't atoms move the opposite direction that a photon is emitted from?

 

[phinds]

Yeah, I saw that same typically moronic show. I watch physics shows on the Science Channel when I feel the need to raise my blood pressure and scream obscenities at the TV.

You are of course correct.

NEVER take things seriously on those shows. They get an awful lot right, but you just never know when they are going to put it some really bone-headed statement just as though they had actually checked it with a real scientist.

EDIT: there have been numerous threads on this forum pointing out how laughable their "physics" is much of the time.

 

[nemesiswes]

Thanks, I figured there was something wrong there ,lol . I love watching the shows but I sometimes you just catch something that seems a bit off, lol

 

[256bits]

So now if you have a solar sail on that very same ship and the laser beam is absorbed or reflected from that solar sail, then the laser beam momentum is transferred to the solar sail. So now your momentum from firing the laser and the momentum absorbed from the solar sail should cancel out and thus your ship should not move at all. Is this correct?

Not entirely correct

If the light is reflected from the sail then the ship would move - I am quite sure you can realize that as the outcome.

Even if the beam is absorbed at the sail the ship would have a translation opposite the direction of the beam.

Don't atoms move the opposite direction that a photon is emitted from?

The engine part of the ship would experience a recoil as the photon is emitted. The sail part would experience a recoil in the opposite direction as the photon is absorbed. Diring the brief time interval while the photon is traveling from engine to sail, the engine part will have moved ahead, and the absorption would cancel out this movement. Since the emmision and absorbtion are not instantanious, the ship has translated froward a small distance.

 

[Drakkith]

Can anyone elaborate on how the reflection of light causes an object to move away from the source of the light? Does the light lose momentum after reflection? Otherwise I can't understand how it works.

 

[nemesiswes]

So wait would it actually work then?

I was just thinking about it and while it seems impossible, I don't think it is, lol.


Here is how I think of it.

1.Engine part creates laser beam
2. Laser beam will have momentum and the engine will have a opposite momentum causing the ship to move backwards.
3. laser traverses distance and meanwhile ship is moving backwards (backwards would be the actual direction you want)
4.laser is absorbed by sail imparting it's momentum on the sail which is the ship, this stops the movement.

conservation of momentum still holds because all momentum = 0


So what you said "256bits", just explained step by step. Wow if that is true then that is really cool, your basically taking advantage of the speed of light delay to move your ship.

The question I have though is theoretically, could you have 100% efficient solar panel that absorbs your laser which then turns that energy back into a laser with a 100% efficient electricity to laser generator then use this system to move your spacecraft through space. So you would just have to supply the energy in the beginning.

 

[Drakkith]

Nemesis, if the sail is bouncing the laser beam backwards, away from the direction you want to go, I believe it would work. This is similar to using nozzles to propel the exhaust of a rocket engine. You will feel a force opposite to the direction the exhaust is moving, no matter what direction it was initially in during combustion. I'm not understanding how 256bits explanation works however.

 

[Infinitum]

Can anyone elaborate on how the reflection of light causes an object to move away from the source of the light? Does the light lose momentum after reflection? Otherwise I can't understand how it works.

Momentum of light changes after reflection. It transfers the momentum to the object so that the total momentum is conserved. Consider a beam of light with energy E and momentum p, perpendicular to the face of a cubical reflecting box of area A.

$E = pc$

where c is the speed of light.

Now when the light is incident on the cube, the momentum of photons is E/c, and when it is reflected, the momentum is -E/c. So the change in momentum of light is 2E/c. Change in momentum implies force, which is exerted on the body.

http://en.wikipedia.org/wiki/Radiation_pressure

Edit : If the beam is absorbed, the change in momentum would only be E/c since the final momentum of photons is zero. So, this force would be half of that would occur due to reflection.

 

[Drakkith]

Hmm. I don't understand how momentum is conserved during reflection. If the light reflects and has the same energy/momentum, and the sail has gained some, where did it come from?

 

[nemesiswes]

Too drakkith,

The object moves away from the source of the light because light which is just electromagnetic fields can carry momentum. So if the light hits a object it can impart that momentum on it. If the light is reflected then only some of that momentum would be imparted on the object and the light (electromagnetic field) would lose some energy (drop in frequency). It would then be remitted with momentum in the opposite direction (less momentum due to less energy of emitted photon) to which it came in, there would also be momentum in the direction that it originally came in so as to cancel the momentum of the emitted light.

I think this is about right but I am not too sure about some of it which is why I asked the question below

edit: apparently I wrote this one too late, lol

to others,

Would the photon actually impart only some it's momentum when hitting the mirror or would it impart all it's momentum and then just get back some of that momentum when remitted?
Meaning that there is a net momentum in one direction.

Edit: yeah I am pretty sure it would impart all the momentum and the net momentum in one direction comes from the decreased energy of the emitted photon which would mean less momentum.

 

[Infinitum]

Hmm. I don't understand how momentum is conserved during reflection. If the light reflects and has the same energy/momentum, and the sail has gained some, where did it come from?

Light will not have the same momentum. The magnitude of initial and final momenta may be same. In the box case, momentum after reflection is -E/c. (Momentum is a vector!)

This change in momentum is transferred to the sailboat,

$$\frac{2E}{c} = M_{boat}V$$

Would the photon actually impart only some it's momentum when hitting the mirror or would it impart all it's momentum and then just get back some of that momentum when remitted?
Meaning that there is a net momentum in one direction.

From wikipedia,

The momentum the photons carry is a conserved quantity—that is, it cannot be destroyed—so it must be transferred to the surface; the result is that absorbing/reflecting the light beam causes the surface to gain momentum.

All of the photon's momentum is conserved. There will not be a net momentum in any direction.

 

[nemesiswes]

ok so then is it possible for the ship to move at all. I am pretty sure it will like how 256bits said. It would just move for a bit until the light hit the sail and stopped the motion. So while momentum is conserved everywhere, the ship still moved a bit. So would the show be correct in showing a ship with a sail and laser and be correct as a viable idea even if impractical for say energy reasons?

 

[Drakkith]

Light will not have the same momentum. The magnitude of initial and final momenta may be same. In the box case, momentum after reflection is -E/c. (Momentum is a vector!)

Alright, so the momentum is now changed. Has the light lost energy? IE will the reflected light be of the same frequency as it was prior to reflection from an observer stationary to the emitting source?

 

[Infinitum]

Alright, so the momentum is now changed. Has the light lost energy? IE will the reflected light be of the same frequency as it was prior to reflection from an observer stationary to the emitting source?

Considering a perfectly reflecting surface...The frequency of the emitted light will be same.

This can be verified from the equation I wrote above,

$E = pc$

For partially reflecting surfaces, it depends on how much fraction of the energy they reflect, and the frequency will change accordingly.

 

[Infinitum]

ok so then is it possible for the ship to move at all. I am pretty sure it will like how 256bits said. It would just move for a bit until the light hit the sail and stopped the motion. So while momentum is conserved everywhere, the ship still moved a bit. So would the show be correct in showing a ship with a sail and laser and be correct as a viable idea even if impractical for say energy reasons?

I'm somewhat confused by this explanation. There can't be a net displacement with no external force acting on the light-boat system. My idea to this is, the photon cannot stay in the atom of the sail forever, it -has- to be emitted out, since atoms hate excited states. This would result in the boat moving back again to its original position. I'm not entirely sure of this though...

 

[Drakkith]

Considering a perfectly reflecting surface...The frequency of the emitted light will be same.

This can be verified from the equation I wrote above,

$E = pc$

For partially reflecting surfaces, it depends on how much fraction of the energy they reflect, and the frequency will change accordingly.

Then I am confused lol.

 

[nemesiswes]

I drew a picture just so to make sure everyone knows what I am trying to visualize at least

 

[nemesiswes]

Now what if the solar sail was just 100% efficient solar panel? Your ship moves and you get the energy back as long as the laser engine is 100% too, lol, something is wrong

 

[256bits]

I'm somewhat confused by this explanation. There can't be a net displacement with no external force acting on the light-boat system. My idea to this is, the photon cannot stay in the atom of the sail forever, it -has- to be emitted out, since atoms hate excited states.

What has happened is that some energy has moved from one end of the system to the other end - all internal and nothing external needed at all.

This would result in the boat moving back again to its original position. I'm not entirely sure of this though

Correct. If the energy moves back to the original end.

 

[256bits]

Now what if the solar sail was just 100% efficient solar panel? Your ship moves and you get the energy back as long as the laser engine is 100% too, lol, something is wrong

Yes. Moving the energy from the sail back to the engine moves the ship in the reverse direction.

 

[nemesiswes]

Because the movement of the charges I assume? So with a solar panel there really would be no net movement. Without though, there would be a net movement if the laser was powered by say a nuclear reactor .

 

[Infinitum]

What has happened is that some energy has moved from one end of the system to the other end - all internal and nothing external needed at all.

Correct. If the energy moves back to the original end.

Assuming this is true...

Now what if the solar sail was just 100% efficient solar panel? Your ship moves and you get the energy back as long as the laser engine is 100% too, lol, something is wrong

Yes. You would get the energy back. To begin with, it didn't go anywhere if you consider the light-boat system. And the boat came back to its original position. No loss or gain of anything.

 

[nemesiswes]

And if the solar sail was a reflector then the movement would be double that of the absorber correct?

 

[Infinitum]

And if the solar sail was a reflector then the movement would be double that of the absorber correct?

You cannot have a reflecting solar cell-sail. You need to use up those photons to energize the electrons to exhibit photoelectric effect. The cell might be a partially reflecting one though, but that won't make it 100% efficient.

 

[nemesiswes]

what I meant was if it was just a reflector and not a solar panel, So no energy or very little absorbed.

 

[Drakkith]

And if the solar sail was a reflector then the movement would be double that of the absorber correct?

Per the wiki article I believe that is the case. I'm still having trouble with understanding the gain during reflection.

 

[Infinitum]

I'm still having trouble with understanding the gain during reflection.

Think of it like an elastic collision of a ball with the earth. The ball goes back with a momentum of -mv, so total change of momentum is 2mv.

 

[nemesiswes]

I was just thinking and obviously the ship would move

absorbed case:
The photon emitted has momentum +1 and the engine and hence ship has momentum -1, since photon is not part of the ship, the ship moves back with -1 momentum. Now when photon is absorbed (case 2 next) the photon imparts +1 momentum causing the ship to stop. Thus ship moved but then stopped. ship has no momentum. Momentum Conserved.

absorbed case 2:same thing up until absorption
Photon is absorbed on sail imparting +1 momentum causing ship to stop. Sail then re-emits photon in opposite direction with -1 momentum and causing the sail to have + 1 momentum. Photon leaves ship entirely out into space and the sail and hence ship continue moving out with +1 momentum. ship is moving with momentum. Momentum is conserved. -1 + 1 = 0

--------------------------------------------------------------------------------------

Reflected case: very very good reflector, almost no energy loss.
The photon emitted has momentum +1 and the engine and hence ship has momentum -1, since photon is not part of the ship, the ship moves back with -1 momentum. Now when photon is reflected, the photon imparts +1 momentum causing ship to stop, Then the reflected Photon now has momentum -1 and the ship will a opposite momentum of +1. Photon leaves ship entirely.
Ship is now moving with Momentum +1. Momentum is conserved. -1 + 1 = 0

Also the reason the reflected case the momentum is not double is because when the photon imparts it's momentum, the ship already had momentum but opposite and so they cancel out.

So I think that is right. The ship will move in any case, even if only momentarily.
Correct me anywhere I am wrong. I think i might have the relected case a bit wrong.

 

[nemesiswes]

So 256bits was always correct from his original post.

 

[Drakkith]

Think of it like an elastic collision of a ball with the earth. The ball goes back with a momentum of -mv, so total change of momentum is 2mv.

And does the Earth move away from the ball? If so where is the energy coming from?

 

[Infinitum]

And does the Earth move away from the ball? If so where is the energy coming from?

Yes, the Earth moves away from the ball. The initial kinetic energy and potential energy of the Earth and ball, and also the gravitational potential energy are the only energies in play here(assuming no friction, no heating up etc). And the total mechanical energy is conserved.

 

[A.T.]

And does the Earth move away from the ball? If so where is the energy coming from?

The idea that the photons / balls have exactly the same energy after reflection is an idealized one. It is based on the assumption that the reflector has infinite mass, so it doesn't begin to move during the interaction.

In reality the ball has a certain finite interaction time during which the Earth will slightly accelerate, so the ball doesn't regain it's full speed. The same is true for a pulse of light, which will be reflected with a Doppler red-shift at the end. But I'm not sure if you can break this down to a single photon being reflected.

 

[Drakkith]

The idea that the photons / balls have exactly the same energy after reflection is an idealized one. It is based on the assumption that the reflector has infinite mass, so it doesn't begin to move during the interaction.

In reality the ball has a certain finite interaction time during which the Earth will slightly accelerate, so the ball doesn't regain it's full speed. The same is true for a pulse of light, which will be reflected with a Doppler red-shift at the end. But I'm not sure if you can break this down to a single photon being reflected.

Now that makes sense.

 

[D H]

So I think that is right. The ship will move in any case, even if only momentarily.

Try calculating how little the ship will move in the absorbed case. It is essentially nothing. Even in the case of a perfect reflector (and there is no such thing), one is better off dispensing with the mirror. Even a perfect laser beam is not parallel. The beam will have diverged somewhat by the time it hits the mirror, so the reflection will not be as effective as just firing the laser opposite the desired direction of travel. Bottom line: Ditch the mirror. It's a Rube Goldberg device that adds nothing.

Propulsion via a ship-borne laser is a terrible choice for propulsion. Not much oomph and too much mass for the laser and all the associated machinery. The only possible exception is a laser powered by matter / anti-matter annihilation. This is pure sci-fi, however.

 

[haruspex]

The same is true for a pulse of light, which will be reflected with a Doppler red-shift at the end. But I'm not sure if you can break this down to a single photon being reflected.

You can. On an earlier thread I calculated the Doppler shift and found that the photon's lost energy matched the mirror's gain in kinetic energy.