Rate of loss of mass of a meteorite

[PeterH]

Is there a general or approximative equation for the loss of mass, of a meteorite as it travels through the atmosphere?
For example as a function of something like its speed, surface area, the drag force experienced by the meteorite.

 

[Danger]

All of the above, and more. The mass loss is due to "disintegration" as parts are broken off by aerodynamic shock, melted or vaporized by the heat of compression (and to a lesser extent friction), and even chemical interaction with components of the air (such as burning). What is the specific air density at all points along the path? Is it spinning? Stuff like that. A lot of data about a specific rock is needed to try any sort of calculation.

 

[PeterH]

I see. My problem is that I am to model the motion a meteorite as it travels through the atmosphere, and I am working with a very limited number of pages.
This is what I know:

• Stony meteorite, specific heat: c_sm = 1.2 * 10^3 J kg^-1 K^-1
• Stony meteorite, thermal conductivity: k_sm = 2.0 W m^-1 K^-1
• Stony meteorite, density: p_sm = 3.3 * 10^3 kg m^-3
  
• Stony meteorite, melting point: T_sm = 1.7 * 10^3 K
  
• Stony meteorite, specific melting heat: L_sm =2.6 * 10^5 J kg^-1

Furthermore, I know the velocity of the meteorite, 50 km above, perpendicular to the surface of the earth: v = (19.76 km/s, -12 km/s) (which is equal to a speed of 28.6 km/s) where x is the horizontal speed, and y is the vertical speed (which means that it enters Earth's atmosphere at an angle, relative to where it impacts).

The formulation of the assignment, states that the mass of the meteorite is 0.025 kg when it hits earth, and that I must take into account the loss of mass at it moves through the atmosphere.

I have functions describing the density of the atmospheric air as a function of height (which are approximations based on a 50% reduction of air density each 5000 m) and the surface area of the meteorite as a function of its mass (based on the assumption that it is a sphere).

As to whether it is spinning, its shape, its drag coefficient and other factors like that; they're unknown, which means that I may make assumptions as I like, just as long as I argue why the assumptions are made and estimate their validity.

Therefore, any general equation, describing the loss of mass, as a function of anything I have included here or time (if one like that exists) would be greatly appreciated.

 

[Danger]

Oh, man... you seem to already have all of the necessary information. In that case, I can't help you: I don't do math. I was just pointing out what sort of stuff you have to know in order to start. You already know it, so you'll have to wait for someone else to assist you with formulae. Happy hunting.

 

[PeterH]

In any case, thank you for your help so far!

 

[Danger]

You're welcome. I wish that I could do more. Unfortunately, I was born before the meteors, so my education never included them.
Just for the sake of technical accuracy, though, I will point out some definitions that you should keep straight when making your presentation. A chunk of rock schmoozing around in space is a meteoroid. When it hits the atmosphere, and during the entire entry process, it is a meteor. Upon hitting the ground (or ocean), it becomes a meteorite. Some people think that the terms are interchangeable, but they aren't.

 

[PeterH]

I'll definitely keep that in mind.
Just for the fun of it, here's a video of the meteor my project is based upon (and it's frames from this video, that I've based my calculations of its velocity on):

 

[Danger]

here's a video of the meteor my project is based upon

Jeez! Somebody could have lost an eye!