How to calculate laser thrust?

[CosmicVoyager]

Greetings,

I want build an interstellar probe.

Given the power of the laser beam and the mass of a mirrored object a laser is shining on, how does one calculate the thrust or acceleration?

Thanks

 

[tiny-tim]

Hi CosmicVoyager!

Use conservation of momentum …

the increase in momentum of the probe equals the total change in momentum of the photons in the laser when they bounce off the mirror

 

[Naty1]

Why are you using a mirror for laser thrust in an interstellar probe??

 

[D H]

The laser isn't on the spacecraft . The mirror is.

 

[K^2]

For laser, Thrust = Power / Speed of Light.

 

[mrspeedybob]

While at first this may seem like the least efficient way possible to propel a spacecraft he may be on to something.

Suppose you have 2 mirrors, one on the ground and one on the space craft. Each can be precisely angled so that when light bounces off the ground mirror it will be directed to where the spacecraft will be and when light bounces off the spacecraft it will be directed to where the ground station will be. Each mirror can also be distorted to compensate for beam divergence. On top of the ground based mirror you have a quantity of lasing material which is kept in an excited state. The two mirrors and the lasing material now form a single laser with no outlet. If the engineering works out what you would have is continuous, albeit low level thrust. You would also have the additional benefit of the spacecraft not having to cary any reaction mass for its propulsion system.

 

[K^2]

mrspeedybob, it won't work because of the Red Shift and the fact that laser cavity has to be the right length to resonate.

 

[Naty1]

"The laser isn't on the spacecraft . The mirror is."

Ah ha! Thanks DH...good grief...
so what happens to net laser power delivered wrsp to distance? and with interstellar gas and planets and things intruding??

Why not put the laser on the probe? And just accelerate photons out the back?? Sure, you have to provide local power and accelerate the additional weight of the laser apparatus, but it sure seems to eliminate a lot of issues...either doesn't seem such a probe will never be able to land and return.

Has a space probe ever been powered by a remote laser?

 

[D H]

Why not put the laser on the probe?

Because the ideal rocket equation is one mean SOB.

One way to get around the nasty implications of the rocket equation with regard to interstellar travel is to simply not take the fuel with you. Otherwise, getting to even the closest of stars is a bit like trying to get to Millinocket: You cahn't get theyah from heah" (Aside: this must be http://www.bangordailynews.com/external/bertni/bunker2.mp3" .)

The idea is not new; it goes back to at least 1984 with Robert Forward's paper "Roundtrip interstellar travel using laser-pushed lightsails" (http://adsabs.harvard.edu/abs/1984JSpRo..21..187F). Greg Landis refined the concept in 1999 in this white paper: http://www.niac.usra.edu/files/studies/final_report/4Landis.pdf.

 

[K^2]

@Naty1:

No. There have been a few projects, but they involved a propellant. Laser on a planet/station delivers heat to the probe where some cheap propellant (like water) is heated to high temperatures and used for propulsion.

If you look at the formula I provided, and consider the fact that building a 1MW laser is a huge challenge, it should be clear why this isn't done.

 

[Redbelly98]

For laser, Thrust = Power / Speed of Light.

It has been a while since I derived this myself, but I believe thrust is twice as much as you said if you are using a mirror. For each photon, the change in momentum is Δp = 2p, where p is the photon's momentum.

 

[D H]

Correct, assuming a perfect mirror and ignoring redshift. A factor of two, however, doesn't help much. That a 1 megawatt laser will generate 1/150 Newtons of thrust instead of 1/300 Newtons doesn't help all that much.

 

[K^2]

It has been a while since I derived this myself, but I believe thrust is twice as much as you said if you are using a mirror. For each photon, the change in momentum is Δp = 2p, where p is the photon's momentum.

With a mirror, you also have to figure in the red shift, so it's a bit more complicated. I gave the value for thrust of laser by itself.

 

[D H]

K^2, your factor of one ignores that the photons are reflected. Saying that thrust is power / speed of light, F=P/c, assumes that the photons are absorbed rather than reflected. Since the photons are reflected, the thrust is (ignoring redshift) F=2P/c\,\cos\theta where \theta is the angle of incidence.

 

[Redbelly98]

I didn't realize we were considering relativistic speeds. Otherwise we wouldn't be concerned with Doppler effects, which are of order v/c. But I guess for interstellar travel we would want to.

 

[Naty1]

DH... Thanks for the reference in your post #9...I skimmed the 1999 paper and the practical problems enumerated there are formidable...

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.

The thing that's astonishing to me is that's the received power/force conversion not the emitted power thousands or millions of miles or more distant...

Maybe that overall difficulty is just as well as I'd hate for such a probe to be really, really easy...we'd be overrun with alien snoops and maybe even weapons systems...

 

[CosmicVoyager]

"Why not put the laser on the probe? And just accelerate photons out the back??"

One could not reach relativistic speeds carrying the fuel. The point of the laser is the engine isn't on the craft. An indefinitely powerful laser or lasers could be used.

Imagane of countless square miles of solar panels in space powering gigawatts of lasers.

 

[CosmicVoyager]

Greetings,

Thanks for the replies :-)

I want to get some idea of how many gigawatts or terawatts or whatever of laser power would be needed to propel a kilogram for example to somewhere between half the speed of light to the speed of light over a period of years.

Once I know how much laser power I need I can figure out how many millions of square miles of solar panels in space I need for power.

Someone posted that a megawatt laser generates 1/150 Newtons of thrust. How much would that accelerate a kilogram?

I'm sorry I'm lacking the mathematical knowledge.

Thanks