View Full Version : The Photon pressure of a beam of UV radiation

max8166

2007-Sep-11, 06:46 PM

How much momentum (http://en.wikipedia.org/wiki/Momentum) would a beam of UV light (http://hyperphysics.phy-astr.gsu.edu/hbase/ems3.html#c3) exert on a 100kg solar sail (http://en.wikipedia.org/wiki/Solar_sail) and what would it's acceleration (http://en.wikipedia.org/wiki/Acceleration) be in Meters per second2?

Assuming that the beam of light to has 1 billion eV (http://en.wikipedia.org/wiki/Electronvolt)

The Speed of light to be 300,000,000 meters per second,

The Frequency of the UV to be 3 x 1016 Hz

And ignoring Solar wind, extraneous radiation etc,

My calculation would be:

Each Photon has an energy of 124 eV so a billion eV makes 100000000/124 Photons per Second. = 806,451.613 lets call 800,000

Now each Photon has momentum (http://en.wikipedia.org/wiki/Momentum#Momentum_in_relativistic_mechanics)

http://upload.wikimedia.org/math/4/8/f/48f8677cc71abebebb4542c7302f07ad.pngfrom the Wiki link

So the sail should have a force on it of 800,000 x 124/300,00000 or about 3.3 meters per second2

Divide by the mass of the sail 100 kg = 0.033 meters per second2

Is that right?

StupendousMan

2007-Sep-11, 07:20 PM

How much momentum (http://en.wikipedia.org/wiki/Momentum) would a beam of UV light (http://hyperphysics.phy-astr.gsu.edu/hbase/ems3.html#c3) exert on a 100kg solar sail (http://en.wikipedia.org/wiki/Solar_sail) and what would it's acceleration (http://en.wikipedia.org/wiki/Acceleration) be in Meters per second2?

...

Is that right?

Is your sail shiny silver or a dull black? It makes a significant difference....

max8166

2007-Sep-11, 07:58 PM

Oh well if its dull black it absorbs, and if it can reflect the energy beam it will get double the momentum so I guess we want it to not get hot and reflect the energy beam. (shiny)

korjik

2007-Sep-11, 08:00 PM

How much momentum (http://en.wikipedia.org/wiki/Momentum) would a beam of UV light (http://hyperphysics.phy-astr.gsu.edu/hbase/ems3.html#c3) exert on a 100kg solar sail (http://en.wikipedia.org/wiki/Solar_sail) and what would it's acceleration (http://en.wikipedia.org/wiki/Acceleration) be in Meters per second2?

Assuming that the beam of light to has 1 billion eV (http://en.wikipedia.org/wiki/Electronvolt)

The Speed of light to be 300,000,000 meters per second,

The Frequency of the UV to be 3 x 1016 Hz

And ignoring Solar wind, extraneous radiation etc,

My calculation would be:

Each Photon has an energy of 124 eV so a billion eV makes 100000000/124 Photons per Second. = 806,451.613 lets call 800,000

Now each Photon has momentum (http://en.wikipedia.org/wiki/Momentum#Momentum_in_relativistic_mechanics)

http://upload.wikimedia.org/math/4/8/f/48f8677cc71abebebb4542c7302f07ad.pngfrom the Wiki link

So the sail should have a force on it of 800,000 x 124/300,00000 or about 3.3 meters per second2

Divide by the mass of the sail 100 kg = 0.033 meters per second2

Is that right?

Second to last line should be 3.3 N

If I am reading it right this is a beam perfectly absorbed into a black sail. Double it for perfectly reflecting, I think.

tony873004

2007-Sep-12, 12:00 AM

Here's a javascript calculator I made for light sails. It uses total luminosity rather than a specific wavelength.

This computes your maximum velocity using a sail powered from starlight, which falls as in inverse square, rather than a beam as you suggest.

It's interesting to note that if the mass of your spacecraft is insignificant compared to the mass of the sail, as you double the surface area of the sail, you also double its mass and that cancels all the benefit of a larger sail.

http://orbitsimulator.com/gravity/articles/sailformula.html

The difficult thing about a beam is aiming it. Even if your sail were 1 kilometer wide, that's a pretty small angular target once the craft gets a few thousand kilometers from Earth. As it distances itself further, the pointing precision quickly exceeds by many magnitudes anything we have ever developed.

Gsquare

2007-Sep-12, 03:53 AM

My calculation would be:

Each Photon has an energy of 124 eV so a billion eV makes 100000000/124 Photons per Second. = 806,451.613 lets call 800,000

Now each Photon has momentum (http://en.wikipedia.org/wiki/Momentum#Momentum_in_relativistic_mechanics)

http://upload.wikimedia.org/math/4/8/f/48f8677cc71abebebb4542c7302f07ad.pngfrom the Wiki link

So the sail should have a force on it of 800,000 x 124/300,00000 or about 3.3 meters per second2

Divide by the mass of the sail 100 kg = 0.033 meters per second2

Is that right?

What??? I don't think so Tony.

First, you cannot use ev and kg.- m./sec in the same equation...you need to convert to joules first....

The conversion is 1.6 x 10^-19 joules/ ev

This is the problem when you try to do these calcs. in terms of ev....

Better to do it in flux units....watts/ meter^2

Now try again...and I think you will get MUCH smaller acceleration.

G^2

Ken G

2007-Sep-12, 03:58 AM

You can also think of F=ma as F= rate of deposition of momentum, that's the connection to momentum.

Gsquare

2007-Sep-12, 04:19 AM

You can also think of F=ma as F= rate of deposition of momentum, that's the connection to momentum.

OK, I see what he doing using 1 billion as the rate... so I've corrected myself to include only his conversion mistake...

The force is far too large.....ev is extremely tiny amount of energy....

1 billion photons /sec may seem like a lot but it is very tiny on a macroscopic scale and certainly not sufficient to give 3 newtons of force.......making the conversion correction will show that to be true.

G^2

max8166

2007-Sep-12, 09:42 AM

Huh? The conversion correction?

Is that just multiply 1.6 x 10-19 then x2 (reflection) is that the newton force we'd expect?

3.3 N x 1.6 x 10-19 x2 = 1.056 x 10-18 N ?

How would that translate to meters per kilo per second? (is it 9.8 Newtons to kilo?)

Ken G

2007-Sep-12, 02:28 PM

It's 10-10 joules/s. Note you divided out the eV per photon only to multiply it back in later-- you don't need the concept of the energy per photon here, just divide the energy rate by c to get a momentum rate (and multiply by 2 if it bounces straight back). So for Newtons, you divide 10-10 by 3 times 108 m/s to get about 3 times 10-21 Newtons, times 2. That's Gsquare's point-- it's minute if applied to any macroscopic object.

Huh? The conversion correction?

Is that just multiply 1.6 x 10-19 then x2 (reflection) is that the newton force we'd expect?

3.3 N x 1.6 x 10-19 x2 = 1.056 x 10-18 N ?

How would that translate to meters per kilo per second? (is it 9.8 Newtons to kilo?)

1N = 1Kg accelerated at 1m/s^2.

crosscountry

2007-Sep-12, 04:47 PM

one of my optics questions on the final exam went like this

suppose an astronaut had a flashlight that would never run out of juice. if he shined it (with so and so intensity) in one direction - how long would it take for him (70kg) to reach 1m/sec speed.

the answer was several orders of magnitude of years.

Ken G

2007-Sep-12, 05:01 PM

Let's check-- we'll say the flashlight is 1 watt, does that seem reasonable? Then that's 3 times 10-9 kg m/s2 (i.e., N) of force, applied to 70 kg gives about 4 times 10-11 m/s2 of acceleration. That takes about 2 times 1012 seconds, or of order 100,000 years. Put differently, this means that in his lifetime, he might get almost to a millimeter per second-- i.e., a (barely) perceptible speed!

neilzero

2007-Sep-12, 05:40 PM

Yes one watt is the output of a powerful flashlight or typical of the input power to the incandecent bulb in an average flash light. Most LED flashlights produce less than one watt, but the LED stoplights and back up lights on some new cars likely have several watts of photon output. It appears we need megawatts of photons for practical spacecraft propulsion. Neil

max8166

2007-Sep-12, 06:02 PM

Looking for a high powered laser I found

"The highest power industrial laser diodes, with power up to 10 kW," here (http://en.wikipedia.org/wiki/Laser#Semiconductor_lasers)

So we mount this near the sun with a collector to convert sun light into laser light and point it at our 100kg reflective space vessel with a excellent pointing device accurate up to a billion miles (ok probably not viable but it's a thought experiment)

Let's see if I understand this right.

So the laser power is 10000 watts, that's 3 x 10-4 kg m/s2 x2 (reflection) divide by 100 (kg)

Equals 6 x 10-6 m/s2

So after a minute the craft would be moving at 3.6 x 10-4 m/s

And after an hour the craft would be moving at 2.16 x 10-2 m/s

And after a day(24 hours) the craft would be moving at 5.184 x 10-1 m/s

Is that 51 cm a second?

Or have I got all my figures wrong again? And can someone explain this so I can understand... probably in terms of the momentum of a photon versus the momentum of the reflective vessel.

crosscountry

2007-Sep-12, 07:11 PM

Looking for a high powered laser I found

"The highest power industrial laser diodes, with power up to 10 kW," here (http://en.wikipedia.org/wiki/Laser#Semiconductor_lasers)

So we mount this near the sun with a collector to convert sun light into laser light and point it at our 100kg reflective space vessel with a excellent pointing device accurate up to a billion miles (ok probably not viable but it's a thought experiment)

Let's see if I understand this right.

So the laser power is 10000 watts, that's 3 x 10-4 kg m/s2 x2 (reflection) divide by 100 (kg)

Equals 6 x 10-6 m/s2

So after a minute the craft would be moving at 3.6 x 10-4 m/s

And after an hour the craft would be moving at 2.16 x 10-2 m/s

And after a day(24 hours) the craft would be moving at 5.184 x 10-1 m/s

Is that 51 cm a second?

Or have I got all my figures wrong again? And can someone explain this so I can understand... probably in terms of the momentum of a photon versus the momentum of the reflective vessel.

you also forgot some reflective momentun from the solar rays - those that aren't absorbed by the 20% efficient solar panels.

Ken G

2007-Sep-12, 07:33 PM

you also forgot some reflective momentun from the solar rays - those that aren't absorbed by the 20% efficient solar panels.

More importantly, he forgot the gravity of the Sun! That means you don't get the factor of 2-- you don't want to point the thrust outward you want to point it sideways. Further, if he is going to use solar energy to power his laser, he can do no better than to just reflect the sunlight to begin with.

max8166

2007-Sep-13, 12:23 AM

Well it would be in orbit so like the ISS is in orbit around the earth, it feels the gravity but only relatively. And I was using the laser so I didn't have to have to have a big sail, just a small mirror. That aside are we in agreement with the figures, acceleration of about 1/2 a meter a day? (optimally)

crosscountry

2007-Sep-13, 02:15 AM

1/2 meter per day is a velocity.

and Ken G, you got it!

max8166

2007-Sep-13, 10:21 AM

1/2 meter per day is a velocity.

Sorry, 1/2 meter per day per day (or day2)

Sorry, 1/2 meter per day per day (or day2)

Actually, more like 43,200 m/day2, or 1/2 m/s/day

max8166

2007-Sep-14, 10:13 AM

Actually, more like 43,200 m/day2, or 1/2 m/s/day

What?

Oh I see, first day starts at 0 meters cumulative acceleration gets it up to velocity of 1/2 m/s (end of first day) but you've assumed 1/2 m/s, so a 60 x 60 x 24 (seconds x minutes x hours) = 86400 x 0.5 =43,200m first day

So I see where your figures are coming from but I think you should half it 'cos you would want to average out the velocity.

Nope - it accelerates by 43,200 m/day/day.

Half of that would be its average speed over the first day, but the acceleration is simply ending speed minus starting speed over time, or (43200 m/day - 0m/day)/1 day.

mugaliens

2007-Sep-18, 05:55 PM

[QUOTE=max8166;1068580]Looking for a high powered laser I found

"The highest power industrial laser diodes, with power up to 10 kW," here (http://en.wikipedia.org/wiki/Laser#Semiconductor_lasers)

So we mount this near the sun with a collector to convert sun light into laser light and point it at our 100kg reflective space vessel with a excellent pointing device accurate up to a billion miles (ok probably not viable but it's a thought experiment)

Let's see if I understand this right...

Light's a horrible way to acceleration anything. But the sun is a giant nuclear furnace with massive heat output.

Add that heat to some reaction mass, and you'll have all the acceleration you can stand.

More to the point, use mirrors to collect it, focusing on a reaction chamber with, say, water, and, pardon the pun, you'll go zooming off like a rocket.

Alternatively, if you're in for the long haul, collect the energy, convert it to electricity, and employ that to power an ion rocket.

But solar sails suffer horribly from diminishing returns as direct drives. Aluminized mylar is just way too heavy. Even spider-silk-backed super-thin aluminum has a practical limit when it gets so thin that it's letting more of the light through than it's catching.

Ken G

2007-Sep-19, 05:03 PM

More to the point, use mirrors to collect it, focusing on a reaction chamber with, say, water, and, pardon the pun, you'll go zooming off like a rocket.

You may have missed where I made the point that if you are collecting light in the first place, you can do no better than to simply reflect that light back along the direction you are moving. There's no benefit in converting it to some other form of energy and then back into light, only lost efficiency. It would be like driving a boat with a wind turbine that powered a fan that shot a wind out the back of the boat-- a sail works much better!

max8166

2007-Sep-20, 11:03 AM

You may have missed where I made the point that if you are collecting light in the first place, you can do no better than to simply reflect that light back along the direction you are moving. There's no benefit in converting it to some other form of energy and then back into light, only lost efficiency. It would be like driving a boat with a wind turbine that powered a fan that shot a wind out the back of the boat-- a sail works much better!

I am misunderstanding something here. On a perfect reflection the energy of the photon remains the same, and yet the sail has some extra kinetic energy?

If the sail was already moving I could visualize some Doppler change and the reflected photon losing some energy. If the laws of conservation of energy are to be preserved however and a photon gets a perfect reflection then how can a stationary object start moving?

Ken G

2007-Sep-20, 11:31 AM

I am misunderstanding something here. On a perfect reflection the energy of the photon remains the same, and yet the sail has some extra kinetic energy?Ah, good question. Ask yourself: on what basis do you say that a perfect reflection imparts no energy? There is always recoil, so there is always some energy lost from the photon. How much depends on what reference frame you are in, i.e., how fast the sail is already moving when you add the recoil. That's typical for energy transfer: it depends on reference frame. The momentum transfer doesn't for nonrelativistic motion, so it's a more intuitive way to conceptualize the interaction.

If the sail was already moving I could visualize some Doppler change and the reflected photon losing some energy. If the laws of conservation of energy are to be preserved however and a photon gets a perfect reflection then how can a stationary object start moving?Yes, you do see the importance of whether or not the sail is moving, but note this is actually just a reference frame issue-- even once the sail is moving I can always "go into its frame" and ask your question again. The answer is recoil-- that happens even for things that are not moving. If the recoil is very small then there is not much energy there, as the energy goes like the square of the tiny v, while momentum just scales with v. So you tend to see the momentum effect first and the energy effect later, if you are moving with the sail at first, but it all works out-- that little bit of energy is all you need to "get over the hump" and start getting more and more energy. The result you get from the momentum consideration is consistent with the energy considerations, it's something you have to think through. Note the same holds for getting a feather to move by blowing on it-- you're just bouncing air molecules off it, and none of those air molecules can impart much energy but a tiny recoil is all you need to get the ball rolling. Anyone clever enough to see that question can also work through the answer with some thought, it's all consistent.

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