by Chris Peterson » Thu Apr 23, 2015 6:18 pm
Wayne N. wrote:What are the calculations you use to compute the size that the "grain" must be to contain enough energy to create a streak of light in the sky of that magnitude? I'm still having a problem with a "grain" of only 1 cm diameter containing enough energy to create enough light to be observed for 10s of miles away.
Various models are used to determine the mass of a meteoroid from its radar properties (ionization mass) and optical properties (photometric mass). For the latter, the simplest model has the total intensity proportional to the product of the time derivative of the mass and the velocity squared (dating from work by Ceplecha in the 1950s). In recent years this has been tweaked quite a bit to take into consideration bulk material properties and other factors, as well as corrections from photometric mass to absolute mass. Still, it's substantially derived from the simple equation for kinetic energy.
The constant of proportionality is called the luminous efficiency, and relates the amount of energy given up as visible light to the total kinetic energy. This can be taken as around 0.005 for cometary fireballs. So for a 1 cm particle (density = 1) moving at 48 km/s and burning up completely in one second, the KE is 1 MJ, the optical energy is 5000 J, which corresponds to a 5000 W source persisting for one second. Certainly, a 5000 W source is very bright against the night sky even when viewed from 100 km away. (In reality, the density is probably higher than one, and the luminous efficiency could be as high as a few percent, depending on the material properties of the meteoroid.)
[quote="Wayne N."]What are the calculations you use to compute the size that the "grain" must be to contain enough energy to create a streak of light in the sky of that magnitude? I'm still having a problem with a "grain" of only 1 cm diameter containing enough energy to create enough light to be observed for 10s of miles away.[/quote]
Various models are used to determine the mass of a meteoroid from its radar properties (ionization mass) and optical properties (photometric mass). For the latter, the simplest model has the total intensity proportional to the product of the time derivative of the mass and the velocity squared (dating from work by Ceplecha in the 1950s). In recent years this has been tweaked quite a bit to take into consideration bulk material properties and other factors, as well as corrections from photometric mass to absolute mass. Still, it's substantially derived from the simple equation for kinetic energy.
The constant of proportionality is called the luminous efficiency, and relates the amount of energy given up as visible light to the total kinetic energy. This can be taken as around 0.005 for cometary fireballs. So for a 1 cm particle (density = 1) moving at 48 km/s and burning up completely in one second, the KE is 1 MJ, the optical energy is 5000 J, which corresponds to a 5000 W source persisting for one second. Certainly, a 5000 W source is very bright against the night sky even when viewed from 100 km away. (In reality, the density is probably higher than one, and the luminous efficiency could be as high as a few percent, depending on the material properties of the meteoroid.)