How Bright is that Meteor - In Light Bulbs?

Rick Scott and Joe Ormon

How Bright is that Meteor - In Light Bulbs?

Martin Lewicki

Astronomy Educator Adelaide Planetarium. Astronomical Society of South Australia
Published in the Bulletin of the Astronomical society of South Australia May 2019

It was a question posed by a school student in the Adelaide Planetarium. I really had no idea. Just how many light bulbs worth of light does a particular “shooting star” emit? To work this out is a complicated process involving the meteor mass, composition, velocity,  angle of entry and atmospheric physics that had me rattling my brain for months. But there is also a simple rule-of-thumb I derived that can give a quick good-enough approximate answer in a few moments by consulting a look-up table.

Casual star gazers are well aware of these streaking particles of dust or rock incinerating in our upper atmosphere, sometimes putting on a meteor shower when Earth ploughs through a swarm of them. These remnants of early solar system formation, debris of asteroid collisions and particles left behind by visiting comets collide with the Earth’s atmosphere as it moves around the Sun at 30 kilometers per second. Meteors can plunge into our atmosphere anything from 11 km/sec to 70 km/sec heating up to thousands of degrees emitting a portion of its energy as light that we see as a “shooting star”.

After reading through a few (sometimes impenetrable) documents on what happens as a meteor burns up I was frustrated that there was nothing on how much light a typical meteor emits in user-friendly terms nor how to calculate it. What I was looking for was the lumen output of the meteor during incineration. This could be easily converted to light bulb brightness units. For example, a typical household light bulb emits 800 lumens (60W old fashion incandescent equivalent).  If you are star gazing and a meteor streaks across the sky overhead and reaches a maximum magnitude of say -3 (somewhat brighter than Jupiter) how many light bulbs worth of light is that meteor emitting?

An internet search found at least two pieces of program code both in BASIC. An old one from Sky and Telescope, January 1987 issue METEOR.BAS[1] and a more recent one from the Australian Space Academy METFLITE.BAS [2]. Both give somewhat different results for the same meteoroid input parameters but at least provide a guide. They work best for meteoroids less than 1 kilogram. Readers familiar with BASIC programming may download and try for themselves with the links at the end of this article. I will present an real meteor sighting as an example.

Both programs require an input of mass, density, velocity and zenith distance angle of entry. The programs then chew through the complex algorithms that models what happens as the meteor plunges into the atmosphere.  The results are a timeline table in steps of fraction seconds of the meteor flight ending its career as height, velocity, deceleration, mass loss and visual magnitude.  All this I was hoping will give me the info I needed. But the best these programs delivered was the meteor’s visual magnitude and energy in watts.

An attempt to derive lumens from visual magnitude had me juggling all manner conversions such as calculating the Sun’s magnitude knowing its lumen output from far enough away (light years) to match the magnitude of a meteor at a typical 70 to 100 kilometers altitude. I even thought of using a lux meter or a Sky Quality Meter to measure a standard 5mm LED light from one meter to fix a reading then have someone walk away with it to the other side of the oval at night, far enough until the LED visually matched the appearance of a choice first magnitude star in the sky that night.  I had a bee in my bonnet about solving this. Finally a direct conversion of magnitude to lumens turned up on the internet. The requisite formula is (for the math mined):

                                                  Lux = 10^((-14.18-Vm)/2.5) [3]

Lux is the amount of light received from the meteor at ground level. This gives us lumens once we know the meteor distance and its visual magnitude Vm. I added this as extra lines of code to the Sky and Telescope BASIC [4] program and finally got my meteoric LIGHT BULBS!

Here is an example of a meteor I observed in December. It was moving from the Gemini/Orion direction from the north-east in late evening. It was very slow and gradually built up in brightness greater than Jupiter but less than Venus. After several seconds it culminated in brightness almost overhead. Total time was around 5 or 6 seconds. I estimate magnitude about -3.0. Perhaps it was an early Geminid which are known for their slow burn[5]. After several attempts inputting experimental mass, density, speed and zenith distances into my modified Sky and Telescope METEOR.BAS code I received an output that seemed to match my observation. The meteor was an 8 gram rocky type with a density of 2500 kilograms per cubic meter, a velocity of 35 kilometers per second and entering zenith angle of 65 degrees. 

The program begins output (Table 1) when the meteor reaches magnitude 0.1 at three seconds into flight and continues to magnitude -3.1 about 5 seconds into flight when it glows with the light of more than 3000 light globes before it rapidly extinguishes.  This presumes a maximum brightness achieved near zenith as it was for my observation. If the meteor peaks at an angle lower than at zenith, then it is further away and is further dimmed due to atmospheric extinction. This means its intrinsic brightness must be greater than the same magnitude meteor at zenith. Readers can find approximate corrected values to the intrinsic brightness for zenith angles other than zero in Table 2.

It turns out those meteors less than 1 kilogram burn up at a height between 70 and 100 kilometers. Those in the range of a few tens of grams consistently reach peak magnitude around 75km. Armed with this knowledge it is possible to adopt a generic meteor model that relates magnitude to lumens directly, that is to light bulbs, without complex calculations but with less accuracy.  This is also provided by Table 2. Simply look up observed magnitude, its zenith angle (or altitude above horizon) and read off the light bulb value. Of course the mass, density and other properties of the meteor are not available in this simplified method but it should satisfy an audience at a dark sky site or in a planetarium wondering “how bright is that meteor really?”  Thanks to Andrew Cool for helpful discussions and program code assistance.

What are Lux and Lumens?

These are SI metric system standards referring to light received and light emitted. 1 lux is 1 lumen of light spread over 1 square meter at a distance of 1 meter from the source.  Its total emission in all directions like a globe will therefore be 4 x pi or 12.57 lumens, or 1 candela. 1 candela is about the brightness of a standard household candle as in “candle power”.  How bright a light source appears to an observer of course depends on its distance squared.  Double the distance is four times fainter, halve the distance is four times brighter.  If my 8 gram, magnitude -3.1 stony meteor shining at 3000 light bulbs was brought down to earth only 1.4 meters away it would glare at 120,000 lux or magnitude -26.7  --- as bright as the midday sun!

Links and References:

1. Sky and Telescope METEOR.BAS https://www.skyandtelescope.com/astronomy-resources/basic-programs-from-sky-telescope/    See note 4 for author’s modified code.

2.  Australian Space Academy: METFLITE.BAS for original code http://www.spaceacademy.net.au/watch/debris/metflite.htm

3. Magnitude to Lux  formula (forum discussion): https://physics.stackexchange.com/questions/340230/whats-the-conversion-between-apparent-magnitude-and-lux

4. Download the programs for QBasic and BBC Basic. QBasic versions include code lines for light bulbs output. Link: http://www.adelaideobservatory.org/darkskysa/program files/ 

5. Readers may wonder if I saw an Iridium flare. Note this is near midnight when any Iridium satellite is deep within the Earth shadow and is not capable of catching any sunlight, especially from overhead!

TABLE 1

OUTPUT OF METEOR.BAS {MODIFIED SKY AND TELESCOPE CODE)

INITIAL MASS (KG) 0.008

DENSITY (KG PER CUBIC METER) 2500

SPEED AT ENTRY (KM/S) 35

ZENITH ANGLE (DEG) 65

 TIME  HEIGHT   SPEED    DECEL   MASS   VISUAL  POWER   LUMENS     LAMPS

  (S)   (KM)     (KM/S)  (M/S/S)   (%)    MAG    WATTS            (800-LM)

 3.71    95.1    35.0      11     95.6   -0.1   2.5E+03  2.4E+05     304  

 3.82    93.5    35.0      14     94.4   -0.4   3.2E+03  3.1E+05     387  

 3.93    91.9    35.0      18     92.8   -0.7   4.0E+03  3.9E+05     492  

 4.04    90.2    35.0      23     90.8   -0.9   5.1E+03  5.0E+05     623  

 4.15    88.6    35.0      30     88.3   -1.2   6.4E+03  6.3E+05     786  

 4.26    87.0    35.0      40     85.2   -1.5   8.0E+03  7.9E+05     985  

 4.37    85.4    35.0      52     81.3   -1.8   1.0E+04  9.8E+05    1226  

 4.48    83.7    35.0      68     76.4   -2.1   1.2E+04  1.2E+06    1511  

 4.59    82.1    35.0      89     70.5   -2.3   1.5E+04  1.5E+06    1839  

 4.70    80.5    35.0     118     63.3   -2.6   1.8E+04  1.8E+06    2199  

 4.81    78.9    34.9     159     54.8   -2.8   2.1E+04  2.1E+06    2567  

 4.92    77.2    34.9     217     45.1   -3.0   2.4E+04  2.3E+06    2896  

 5.03    75.6    34.9     304     34.4   -3.1   2.5E+04  2.5E+06    3107  

 5.14    74.0    34.8     440     23.3   -3.1   2.5E+04  2.5E+06    3088  

 5.25    72.4    34.8     679     13.0   -3.0   2.2E+04  2.2E+06    2699  

 5.36    70.8    34.7    1179      4.9   -2.7   1.5E+04  1.5E+06    1840  

 5.47    69.2    34.5    2833      0.6   -1.6   5.2E+03  5.1E+05     637

Time; in seconds. Height; altitude overhead. Speed; kilometers per second  Decel; deceleration meters per second per second. Mass; percent remaining mass. Visual mag; visual magnitude at zenith. Power; energy in watts. Lumens; intrinsic amount of light emitted in the visual range. Lamps; equivalent light output in 800-lumen light bulbs.

TABLE 2

 

                        GENERIC METEOR AT ~75KM HEIGHT

                           VERY APPROXIMATE VALUES

                        METEOR ASSUMED LESS THAN 1 KG
                       (INCLUDES ATMOSPHERIC EXTINCTION)

                           METEOR LIGHT BULBS (800-LM)

                           ALTITUDE(ABOVE HORIZON)         

       90°       75°       60°       45°       30°       15°       10°

                                 ZENITH DIST

        0°       15°       30°       45°       60°       75°       80°

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

MAG    BULBS ---->

-6     55000    61307      85067     125400    440000    3119994   10214339

-5     20000    22293      30933     45600     160000    1134543   3714305

-4     9000     10032      13920     20520     72000     510545    1671437

-3     3000     3344       4640      6840      24000     170182    557146

-2     1500     1672       2320      3420      12000     85091     278573

-1     500      557        773       1140      4000      28364     92858

 0     200      223        309       456       1600      11345     37143

 1     90       100        139       205       720       5105      16714

 2     30       33         46        68        240       1702      5571

 3     10       11         15        23        80        567       1857

 4     5        6          8         11        40        284       929

 5     2        2          3         5         16        113       371

 6     1        1          2         2         8         57        186

In the above table read the visual magnitude in the left column then zenith distance (or the complementary altitude) in top rows to find a ball-park intrinsic light bulb luminousity of a meteor.  Bright meteors at zenith distances of 75° or more may require a meteor larger than 1kg so the brightness figures are wildly uncertain here but are included for the sake of completion. Example: You observe a meteor at magnitude 2.5 (typical) at a zenith angle 45 degrees. This meteor burns with the light of between 68 and 23 light bulbs. Rough interpolation for magnitude 2.5 suggests around 50 or so light bulbs.