Stargazing How Can a Grain of Sand Create a Bright Meteor?

[Electron Spin]

I understood megacal's question very clearly. I wondered the same, Meg's question... How large and how far were these visible "shooting stars", from my observation point?
Davenn's earlier posts laid a good foundation, I think.

Throw all the definitions away!

I always guessed that they were about the size of a marble or so, but the distance was always a puzzlement for me, even though I always noted the inverse square law when observing it's tail or light, and all the little other obvious factors such as shape, angle of attack, velocity, composition and the like, now I know... using the ?relative? visual magnitude figure given in the Meteoroid Size Classification Chart.

DId I noticed that the visual magnitude figure is not based on anything?; no visual output such as luminosity, intensity, or the like, but no matter. The comparison can be made now.

I wanted to mention, that I have used meteoroid scattering, or ionization to communicate via RF for years, fun to do on the HF bands. Just another tool for an old key pounder.

I am really happy that megacal posed this question...I always wondered about how big and how far those little buggers were. Alas, my guesses were real close, so I am happy.

PS: I knew the figure for appx. 2.5 Km. for the candle/distance/human eye sensitivity thing too!. : )

 

[megacal]

Electron Spin,
glad it was profitable for you, as it was for me.

It just didn't seem reasonable for the average meteor to be created by such a small mass as a "grain of sand" even at 72km/sec.
B-B's. marbles, baseballs, yes.

Or to be able to see a candle 30mi away.
Just not intuitive.

 

[davenn]

baseballs, yes.

a baseball sized object will give an extremely bright trail that's a very significant meteor

 

[Electron Spin]

Megacal,
Yes it was and mfb's chart helped me anyway.

davenn, from an old pyrotechnician; A baseball sized rock with the right elemental compositions would give a nice colourful show I would hope! Very nice indeed. Someone correct me if I'm wrong (I know that you will ) without knowing the actual distance its kinda hard to know the true intensity, I believe. It appears to be a relativistic thing for the eyeballs.

Also, and off track, a good rule of thumb for estimating a rough line of sight distance for microwave antenna putter uppers is, Distance = $\sqrt 2ht +\sqrt 2hr$
Nice to know in a pinch I guess.

 

[DaveC426913]

I have never heard the streak itself - as distinct from the object creating it - being called a meteor.

I always understood that a meteor was the object. A meteor 20km long is non-sensical. A meteorite is a meteor that has reached the ground.

 

[Chronos]

I'm a little confused, is the OP questioning the reality of meteors or the physics? Meteors obviously exist, so what exactly is in doubt?

 

[Chronos]

The 500 eV energy calculation applies to individual atoms, not the entire mass of a meteoroid entering the atmosphere, so a massive meteoroid obviously produces a vastly brighter trail than a micrometeoroid.

 

[mfb]

Epsilon Eridani is a nice mag 3.7 star: clearly visible in a clear dark night sky, still visible from most cities. The visibility limit for perfect viewing conditions is usually given by mag 6, a factor 8 weaker. Epsilon Eridani's total power emission (including infrared+UV) is 1.3*10²⁶ W and its distance is 10.5 light years. To have the same brightness, assuming the same spectrum, a shooting star 100 km away needs a power of 130 W. If it lives for one second, this corresponds to 130 J of energy. The visibility limit is at 16 J. If the spectrum has more infrared or more UV it needs more energy, but we are still talking about hundreds of Joules.

A 1mg-object at 20 km/s has an energy of 200 J. At 40 km/s it has 800 J.

 

[megacal]

davenn,

a baseball sized object will give an extremely bright trail that's a very significant meteor

Yes, I didn't mean to imply it was the average. It would be spectacular.

YDaveC426913,

I have never heard the streak itself - as distinct from the object creating it - being called a meteor.
I always understood that a meteor was the object. A meteor 20km long is non-sensical. A meteorite is a meteor that has reached the ground.

I always thought a "meteor" was the object, too, but according to Wiki and the American Meteor Society, the meteor is the ionized gas
trail we see. So "meteor trail" is redundant (as someone said earlier), and Meteor Crater would be "Meteorite Crater".

Chronos,

I'm a little confused, is the OP questioning the reality of meteors or the physics? Meteors obviously exist, so what exactly is in doubt?

Does "OP" refer to the one who starts the thread?
If so, no, I'm not questioning the reality of meteors or the physics...just the common statement I'd seen that
meteors (assuming the average brightness) is due to a "grain of sand".

mfb,

Epsilon Eridani is a nice mag 3.7 star: clearly visible in a clear dark night sky, still visible from most cities. The visibility limit for perfect viewing conditions is usually given by mag 6, a factor 8 weaker. Epsilon Eridani's total power emission (including infrared+UV) is 1.3*1026 W and its distance is 10.5 light years. To have the same brightness, assuming the same spectrum, a shooting star 100 km away needs a power of 130 W. If it lives for one second, this corresponds to 130 J of energy. The visibility limit is at 16 J. If the spectrum has more infrared or more UV it needs more energy, but we are still talking about hundreds of Joules.
A 1mg-object at 20 km/s has an energy of 200 J. At 40 km/s it has 800 J.

I did a search, and found this:

How much one sand grain weighs? Let's assume that we are dealing with quartz grains. Quartz has a density of 2.65 grams per cubic centimeter. A grain with a diameter of 2 millimeters makes up only little more than four thousands of a cubic centimeter, and it weighs approximately 0.011 grams.

Then a grain of sand weighing 11mg (0.011g) would put out ~ 2000 J at 20km/s, and ~8000 J at 40km/s? And only 130 J are needed to produce a 1s 3.7 magnitude streak?

 

[mfb]

Then a grain of sand weighing 11mg (0.011g) would put out ~ 2000 J at 20km/s, and ~8000 J at 40km/s? And only 130 J are needed to produce a 1s 3.7 magnitude streak?

Yes. Clearly visible.

 

[Chronos]

The velocity of a meteoroid entering the atmosphere ranges from 11 km/sec to 72 km/sec. Even at minimum velocity, the kinetic energy of a meteoroid is around 6 x10⁴ joules per gram of mass. Only about 1% of the original kinetic energy of a meteoroid can be converted into visible light - re: http://abyss.uoregon.edu/~js/glossary/ablation.html.

 

[megacal]

mfb,
sorry, just realized that a mass of 11mg was based on a 2mm grain of quartz sand, and we have been talking about 1mm grain which may be
more or less dense than quartz.

But your calculation of 200 J to 800 J is for something 1/5 the size of a 1mm grain, right?
That seems much too small for a visible if not average meteor, but will research it more.

Only about 1% of the original kinetic energy of a meteoroid can be converted into visible light - re: http://abyss.uoregon.edu/~js/glossary/ablation.html.

So only 1% of the 200 J to 800 J becomes visible light, but not bright enough to
be seen as a meteor. (?)

 

[mfb]

1 mg is about 1/3 a cubic millimeter. A sphere with a diameter of 1 mm has a volume of 0.52 cubic millimeters.
Meteors don't have as much visible light as stars (relative to their power), see the post by Chronos, so my estimate was a bit too bright. If I take that 1% compared to the 42% for Epsilon Eridani, we need 5 kJ of energy for mag 3.7, and 700 J for mag 6. The 1mg-object (a quartz sphere with a diameter of about 1 mm) at 40 km/s is sufficient for mag 6.

 

[Electron Spin]

Epsilon Eridani is a nice mag 3.7 star: clearly visible in a clear dark night sky, still visible from most cities. The visibility limit for perfect viewing conditions is usually given by mag 6, a factor 8 weaker. Epsilon Eridani's total power emission (including infrared+UV) is 1.3*10²⁶ W and its distance is 10.5 light years. To have the same brightness, assuming the same spectrum, a shooting star 100 km away needs a power of 130 W. If it lives for one second, this corresponds to 130 J of energy. The visibility limit is at 16 J. If the spectrum has more infrared or more UV it needs more energy, but we are still talking about hundreds of Joules.

A 1mg-object at 20 km/s has an energy of 200 J. At 40 km/s it has 800 J.

Now this makes sense...

130 watts/sec = about Epsilon Eridani.

Yes, I would have guesses a mere 1mg object would have less light, but on second thought... I have seen a few gram sized objects with our common elements contained... about 500 wts. for a few seconds@ the avg. of ≈40 km/sec.

 

[megacal]

Conundrum deleted.

 

[mfb]

130 watts/sec = about Epsilon Eridani.

Either W or J/s. W/s doesn't fit. And you cannot assign that value to the star. It is scaled to the distance of a meteor.

 

[Electron Spin]

Did I get the mass wrong?
11mg = 0.011g = 0.000011kg ...but that was based on a 2mm diameter quartz grain, and we originally were specifying
a 1mm diameter grain, which (unless I'm wrong), should = 5.5mg.

Only 400 J for a gram, i.e. 1000mg??
According to mfb,

Sounds like a conundrum.

No, forget what I posted...I deleted it.. made a mistake..How did you copy that after I deleted it? Now that's magic!

And everybody's units are correct, but mine!

I'm outta' here! for now anyway!

Either W or J/s. W/s doesn't fit. And you cannot assign that value to the star. It is scaled to the distance of a meteor.

Snap! You got me mfb! W/s does not fit... is nonsense, sorry..!

 

[megacal]

How did you copy that after I deleted it? Now that's magic!

It's gone down a black hole.

 

[Chronos]

I hate to be repetitious, but, we have it on pretty good authority [NASA] that most meteors are produced by space debris about the size of a grain of sand [~2 mm]. Irrespective of the mathematical trivia, meteors are frequently observed in dark sky regions across the globe - sometimes over 100 an hour. I'm just saying who would know better or have any better reason to know than NASA?

 

[megacal]

I hate to be repetitious, but, we have it on pretty good authority [NASA] that most meteors are produced by space debris about the size of a grain of sand [~2 mm].

I just wish we had a way to fire a known mass, e.g. ~5mg (1mm grain of quartz) at 30km/s at the atmosphere to see
for ourselves. That's the only way to know for sure.
Otherwise, NASA is probably right.

 

[Chronos]

NASA has a super rifle they use for such things, it can fire projectiles over 17,000 mph [around 8 km/sec]. They use it, among other things, to test shielding of spacecraft against meteoroid impacts.

 

[mfb]

It fires projectiles onto solid targets in a vacuum.
Here is a large object at 2.5 km/s moving through air at sea-level pressure - the trail is not from the cannon, it is just from the flight through air.

 

[Gary Weller]

According to this website
http://www.amsmeteors.org/meteor-showers/meteor-faq/ most meteoroids are between the size of a grain if sand and a small pebble and weight less than 1-2 grams. The light we see is caused by the KE ionizing atmospheric molecules.

I'm late to the thread, but I was going to say this. The only explanation for why something seemingly incapable of being visible due to its low energy output (that I can think of) is ionization of surrounding particles. This would not only create a larger area of light, but a wider spectrum as well.

 

[Steve Dutch]

So far there's a lot of arm waving but no actual math. So here goes. Imagine a speck of rock, density 3000 kg/m3. It's 1mm across, with a volume 10-9 m3 and mass 3 x 10-6 kg. If it hits at Earth's orbital velocity, 30 km/sec (30,000 m/sec) then its kinetic energy is 1/2 mv2 = 1/2 x 3x10-6 x (3x10^4)^2 = 4.5 x 10^2 joules. Now, if it takes a second to flame out (typical for the small meteors I've seen), then it's radiating 450 joules/sec = 450 watts. Crudely, auto headlights are around 50 watts and can be seen many miles away at night. So our meteor is about ten times that.

How do we convert our meteor to actual brightness? Incandescent lights are very inefficient. But then again, our meteor is also emitting due to incandescence, although more efficiently since it's a lot hotter. The Sun delivers 1361 watts per meter squared on earth. The apparent magnitude of the Sun is -26.7. Sirius is just about 25 magnitudes fainter or 5 steps of 5 magnitudes or one ten billionth as bright, so its energy flux on Earth is 1.36 x 10^-7 W/m2. Now, if our meteor is 100 km away (slant range) it will emit 450W/4pi x 100,000 x 100,000)m2 = 3.6 x 10-9 W/m2 at the observer's location. It's about 1/38 as bright as Sirius, or about 4 magnitudes, about M = 2.5. That's roughly as bright as a star in the Big Dipper.

 

[mfb]

So far there's a lot of arm waving but no actual math.

Did you miss page 3 and 4? We have those calculations already, with the same approach but with more accurate resuts: Comparing the shooting star power to a real star gives an error of a factor ~40 in brightness.

 

[Electron Spin]

So far there's a lot of arm waving but no actual math. So here goes. Imagine a speck of rock, density 3000 kg/m3. It's 1mm across, with a volume 10-9 m3 and mass 3 x 10-6 kg. If it hits at Earth's orbital velocity, 30 km/sec (30,000 m/sec) then its kinetic energy is 1/2 mv2 = 1/2 x 3x10-6 x (3x10^4)^2 = 4.5 x 10^2 joules. Now, if it takes a second to flame out (typical for the small meteors I've seen), then it's radiating 450 joules/sec = 450 watts. Crudely, auto headlights are around 50 watts and can be seen many miles away at night. So our meteor is about ten times that.

How do we convert our meteor to actual brightness? Incandescent lights are very inefficient. But then again, our meteor is also emitting due to incandescence, although more efficiently since it's a lot hotter. The Sun delivers 1361 watts per meter squared on earth. The apparent magnitude of the Sun is -26.7. Sirius is just about 25 magnitudes fainter or 5 steps of 5 magnitudes or one ten billionth as bright, so its energy flux on Earth is 1.36 x 10^-7 W/m2. Now, if our meteor is 100 km away (slant range) it will emit 450W/4pi x 100,000 x 100,000)m2 = 3.6 x 10-9 W/m2 at the observer's location. It's about 1/38 as bright as Sirius, or about 4 magnitudes, about M = 2.5. That's roughly as bright as a star in the Big Dipper.

Yes we all have done the math. As you applied 3 milligrams of space stuff hitting us perpendicular and at Earth's orbital velocity. Applying our dear KE formula we all love so dearly. Most of us just do it in our heads with nice round numbers as you used, nice indeed.
The arm waving helps us lose some weight so we remain attractive and tan with about 1.4 kw as a tanning agent as you indicated.

Did you miss page 3 and 4? We have those calculations already, with the same approach but with more accurate resuts: Comparing the shooting star power to a real star gives an error of a factor ~40 in brightness.

With your calc. being one of the complete ones, unlike mine mfb.

 

[Electron Spin]

I'm late to the thread, but I was going to say this. The only explanation for why something seemingly incapable of being visible due to its low energy output (that I can think of) is ionization of surrounding particles. This would not only create a larger area of light, but a wider spectrum as well.

Good point Gary. The wider perceived bandwidth or visible spectrum due to more or added elements ionizing in the surrounding Earth's atmosphere than the original rock/ice chemistry. You just can't beat 'fly by the wire gas spectrometry' (if there is such a thing).

 

[Chronos]

This is all basic physics, unless I missed something relevant. The KE, and physics, of meteoroids entering the atmosphere is understood well enough to allow to return astronauts to earth. Next question.

 

[TeethWhitener]

If the spectrum has more infrared or more UV it needs more energy, but we are still talking about hundreds of Joules.

I'm late to the thread, but I was going to say this. The only explanation for why something seemingly incapable of being visible due to its low energy output (that I can think of) is ionization of surrounding particles. This would not only create a larger area of light, but a wider spectrum as well.

One of the most fascinating talks I had the pleasure of attending in grad school was given by Dudley Herschbach on this very topic. He went through the basic kinematics and worked out the blackbody spectrum for an average meteor and concluded that, if that's all there is, then we shouldn't be able to see meteors. Then he delivered my all-time favorite line: "If it isn't physics, it must be chemistry!" and went on to explain that a good chunk of the light that we see comes from the sodium D line (smack dab in the middle of the visible spectrum). The talk then meandered its way through the existence of sodium and iron layers in the upper atmosphere (http://www.albany.edu/faculty/rgk/atm101/sodium.htm). Research in atmospheric chemistry has been focused for so long on things like ozone/CFCs, carbon dioxide, and acid rain, that his talk was a nice break from the doom and gloom often associated with the field.

 

[megacal]

TeethWhitener,
thanks for adding that fresh info to the conversation from the chemist's perspective.
Would love to have been a fly on the wall to hear Dr.Herschbach's presentation.

 

[Electron Spin]

TeethWhitener,
thanks for adding that fresh info to the conversation from the chemist's perspective.
Would love to have been a fly on the wall to hear Dr.Herschbach's presentation.

Me too megacal, me too!
TeethWhitener, See the later portion of post #77 and #73 ... There was some spectro suggested there.