By Hello World


2014-05-15 14:19:11 8 Comments

Photons have no mass but they can push things, as evidenced by laser propulsion.

Can photons push the source which is emitting them? If yes, will a more intense flashlight accelerate me more? Does the wavelength of the light matter? Is this practical for space propulsion? Doesn't it defy the law of momentum conservation?

Note: As John Rennie mentioned, all in all the wavelength doesn't matter, but for a more accurate answer regarding that, see the comments in DavePhD's answer .

Related Wikipedia articles: Ion thruster, Space propulsion

4 comments

@Ralph 2014-05-17 20:44:06

See Solar Sails http://en.wikipedia.org/wiki/Solar_sail.

As other people have pointed out, this is extremely inefficient energy-wise, but has the advantage of being purely passive - no need to carry an energy source, and few or no moving parts to fail.

@Hello World 2014-05-19 08:34:17

Solar sails is about being pushed by an external source, like laser propulsion. Although related, this is not the same.

@Dohn Joe 2014-05-15 16:59:31

This does not directly answer your question, but this is related. If you are floating in space the photons that hit you are also exerting a force. When you float in space a large number of photons emitted by the sun will hit you. These photons exert a force, this mechanism is referred to as radiation pressure. This force is significant enough that you can actually control a spacecraft with it.

NASA is doing that with the Kepler space telescope. The space telescope lost one of its reaction wheels. Reaction wheels are used to alter a spacecraft's orientation. With the remaining reaction wheels, the orientation of the telescope cannot be controlled with the accuracy needed for scientific missions. NASA devised a way to make use of the radiation pressure for controlling the spacecraft's orientation.

@Kyle Kanos 2014-05-15 19:48:37

Actually, two of the reaction wheels are broken. With 3 of the 4 working, it could do its mission; once the 2nd broke it stopped being useful as an extremely sensitive planet finder

@rob 2014-05-16 19:13:03

@KyleKanos Actually there is an announcement today that the technique Dohn Joe describes has been funded and NASA will try to revive Kepler.

@Kyle Kanos 2014-05-16 19:19:55

@rob: That was made known to the community back in February (the white paper was back in September, I think). It won't be as stable as the original mission, hence it isn't an extremely sensitive planet finder, just a sensitive planet finder (plus, it's going to be looking at things that aren't planets).

@Blackbody Blacklight 2014-05-18 15:41:29

Interesting about Kepler, but they found a way to balance it using reflected solar radiation. What OP describes is radiation, not reflection. The Pioneer Anomaly is a better real-life example.

@DavePhD 2014-05-15 14:33:03

Can photons push the source which is emitting them?

Yes, photons have momentum and momentum must be conserved. The source is pushed in the opposite direction of the photons.

If yes, will a more intense flashlight accelerate me more?

Yes, more photons means greater momentum.

Does the wavelength of the light matter?

Yes, shorter wavelength photons have higher momentum. $p = h / \lambda $

Is this practical for space propulsion?

Possibly, see Prospective of Photon Propulsion for Interstellar Flight (or use Alternative download site for pre-print version ) The concept of photon recycling is considered, for a potential enhancement of thrust/power ratio by several orders of magnitude.

Doesn't it defy the law of momentum conservation?

No, photons have momentum in one direction, the source has momentum in the opposite direction, so momentum is conserved.

@paqogomez 2014-05-15 15:45:07

So which is it? @JohnRennie says wavelength doesnt matter, but yours says yes.

@C4stor 2014-05-15 15:48:10

@JohnRennie provided verifiable equations to make his point, so I'd go with him.

@DavePhD 2014-05-15 15:51:06

@paqogomez momentum per photon = (Planck's constant)/wavelength.

@garyp 2014-05-15 16:00:36

@JohnRennie expressed his answer in terms of the power of the flashlight. That is the sensible way to approach it IMO, and in those terms the wavelength doesn't matter. But wavelength does appear in the analysis. It would be possible to ask a similar but different question for which wavelength does matter, so pay attention to the exact wording of a question.

@DavePhD 2014-05-15 16:02:58

@C4stor The question "does the wavelength of the light matter" is somewhat vague, I'm saying it matters on a per photon basis, and John is saying it doesn't matter on a per total energy basis, so I don't think there is any disagreement.

@Hello World 2014-05-15 16:32:49

So the same energy either generates X photons with M wavelength or X+k photons with M+n wavelength? And in both cases momentum output is the same? (All variables are positive numbers)

@DavePhD 2014-05-15 16:41:52

@HelloWorld yes, but it would be better to say: the same energy could be transformed to nX photons of nM wavelength, to yield the same total momentum, even though the momentum and energy per photon is different

@Hello World 2014-05-15 16:55:41

That's indeed a better way to say it, n has to be a constant. Does this constant have a name?

@DavePhD 2014-05-15 17:10:32

@HelloWorld I wouldn't says n is a constant. If we said X=1, then n would just be the number of photons. Otherwise, n is a ratio of the number of photons in the two situations, and n is also a ratio of the wavelengths in the two situations.

@John Rennie 2014-05-15 14:47:44

Can photons push the source which is emitting them?

Yes.

If yes, will a more intense flashlight accelerate me more?

Yes

Does the wavelength of the light matter?

No

Is this practical for space propulsion?

Probably not

Doesn't it defy the law of momentum conservation?

No

In fact that last question is the key one, because photons do carry momentum (even though they have no mass). Photons, like all particles obey the relativistic equation:

$$ E^2= p^2c^2 + m^2c^4 $$

where for a photon the mass, $m$, is zero. That means the momentum of the photon is given by:

$$ p = \frac{E}{c} = \frac{h\nu}{c} $$

where $\nu$ is the frequency of the light. Let's suppose you have a flashlight that emits light with a power $W$ and a frequency $\nu$. The number of photons per second is the total power divided by the energy of a single photon:

$$ n = \frac{W}{h\nu} $$

The momentum change per second is the numbr of photons multiplied by the momentum of a single photon:

$$ P/sec = \frac{W}{h\nu} p = \frac{W}{h\nu} \frac{h\nu}{c} = \frac{W}{c} $$

But the rate of change of momentum is just the force, so we end up with an equation for the force created by your flashlight:

$$ F = \frac{W}{c} $$

Now you can see why I've answered your questions above as I have. The force is proportional to the flashlight power, but the frequency $\nu$ cancels out so the frequency of the light doesn't matter. Momentum is conserved because it's the momentum carried by the photons that creates the force.

As for powering spaceships, your 1W flashlight creates a force of about $3 \times 10^{-9}$ N. You'd need a staggeringingly intense light source to power a rocket.

@John Odom 2014-05-15 15:31:34

Hypothetically, how much force would you need to power a spaceship if it was done this way?

@John Rennie 2014-05-15 15:41:24

@JohnOdom: it depends entirely on how much thrust you want to generate. The only realistic scenario I've seen for using light as propulsion is a solar sail. In that case it's the light from the Sun generating the force, and although the force is very small it's continuous so over time even the very small acceleration can build up high speeds.

@zwol 2014-05-15 15:46:51

According to Wikipedia, an ion thruster typically consumes 1–7 kW of power and produces 20–250 millinewtons of thrust. To get the same amount of thrust from a photon source would require roughly 6–80 megawatts of power. That's not trivial, but it's not totally infeasible either; a modestly sized nuclear fission reactor and several thousand halogen lamps would do it. (Lamp efficiency doesn't matter because any wavelength will do; reflector efficiency does matter, though.)

@zwol 2014-05-15 15:49:11

... The thrust-to-weight ratio of such a contraption is obviously terrible compared to just about any other option, but it would never run out of reaction mass.

@Carl Witthoft 2014-05-15 15:51:52

@Zack I think that's the important point about "photon drive technologies" : if you can build a source whose energy density is near-infinite, then you're better off in the long run.

@ratchet freak 2014-05-15 16:10:58

@JohnOdom for 1 N of thrust you need 1 GW of power

@Hello World 2014-05-15 16:49:08

Can the process be somehow made more efficient?

@user6972 2014-05-15 22:41:58

@HelloWorld The technology you are looking for is called an Ion Thruster. en.wikipedia.org/wiki/Ion_thruster

@Hello World 2014-05-16 13:38:02

It is indeed more efficient, but an ion thruster is not a photon gun. The "problem" with ion thrusters is that they lose mass, while a flashlight doesn't.

@dominicbri7 2014-05-16 14:30:36

I've read HERE (physics.stackexchange.com/a/2233/4634) that "a photon does have relativistic mass proportional to its momentum." and that "photons have 'mass' inversely proportional to their wavelength!" So wouldn't the wavelength matter in this question then? I'm probably wrong but I couldn't help but ask

@John Rennie 2014-05-16 14:41:02

@dominicbri7: the mass in the equation I quoted is the rest mass and that is zero for photons. The relativistic mass referred to in the answer you cite isn't a mass in the sense that you and I have mass.

@Hello World 2014-05-16 17:27:51

@dominicbri7 You might want to check the comments in DacePhD's answer.

@WernerCD 2014-05-16 18:08:56

Should ask XKCD to do a What If like it's Model Rocket question: what-if.xkcd.com/24

@The Quantum Physicist 2014-05-16 18:46:03

@JohnRennie You said the wavelength doesn't matter, while the amount of energy, i.e., momentum depends on the frequency, hence the wavelength. Can you explain this?

@Egor 2014-05-16 21:24:29

@TheQuantumPhysicist The momentum of each photon depends on the frequency, but for a flashlight of a certain power W it doesn't matter. With a higher frequency you end up ejecting fewer, but more energetic, photons. Your propulsion stays the same.

@The Quantum Physicist 2014-05-19 11:05:34

@JohnRennie hmmmmm... this assumes that you have like 100% efficiency in your flash-light and you predefine its power. So if I understand you correctly, the whole power of the flash-light is transferred to photons. From a technical point of view, if everything is ideal, then this is right. But talking about the physics, I wouldn't be so happy stating that the wavelength "doesn't matter". I would say that the wavelength matters per photon, and the number of photons determines your momentum.

@John Rennie 2014-05-19 11:08:34

@TheQuantumPhysicist: re your first point I was careful to say flashlight that emits light with a power W not flashlight that consumes a power W. Re the second point, the number of photons is proportional to $\lambda$ and the momentum of each photon is proportional to $\lambda^{-1}$. When you multiply these two numbers to get the total momentum change the $\lambda$s cancel out.

@The Quantum Physicist 2014-05-19 11:11:16

@JohnRennie You're right, I'm not saying you're wrong. It's just that when we talk physics, we ignore technicalities and concentrate on concepts. In other words: the concept that the energy of a photon determines its momentum linearly is much more important than that a flash-light with a constant power doesn't care about the wavelength. Peace!

@dr. honey 2016-10-20 15:27:05

But how it has a momentum it has no mass. how it can exert force.

@John Rennie 2016-10-20 15:32:30

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