How big should asteroids be to

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In summary, the conversation discusses determining the size of a main-belt chondritic asteroid that would result in a maximal internal temperature exceeding the melting temperature of ice and rocks. The conversation mentions using the present-day chondritic heat production, thermal conductivity, and density to make a reasonable guess about the surface and melting temperatures. The individual also asks for reassurance on their approach using heat flux and thermal conductivity equations.
  • #1
Mattbro
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Consider main-belt chondritic asteroids. How large should be an asteroid so that the
maximal internal temperature exceeds the melting temperature of ice? Of rocks? For your
calculations, use the present-day chondritic heat production w = 4×10-12 W kg-1, typical
thermal conductivity of slightly fractured rock k = 2 W K-1m-1, and density r = 2700 kg
m-3 representative of chondritic materials. Make (and explain) a reasonable guess about
the surface temperature Ts and melting temperatures Tm of ice and rocks
 
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  • #2
Welcome to PF - you have to show some attempt to work out the homework before we can help.
 
  • #3
well i know heat flux = -k(dt/dr) this is change in temperature with depth and thermal diffusivity x= k/pC (here p is density and C is heat capacity). I just don't know how to apply heat production. I feel like I'm missing an equation and i have no idea what it is.
 
  • #4
Heat production is given per mass, so with the density it's easy to work out heat production/volume. If you assume a spherical asteroid you can get a heat prouction / radius relation
 
  • #5
the units for that would be W/m^3. this is almost heat flux (W/m^2). where would i go from there?
 
  • #6
asteroid size

How large should be the body so that the maximal internal temperature reaches given
temperature Tm (melting temperature)?

I'm thinking i can use F= K*[(Ta-Tb)/(Ra-Rb)]. where F is heat flux, K is thermal conductivity, T is change in temperature and R is change in depth.
I'm thinking the radius i need should be R=(K*(Tm))/F, but I'm not sure if it is that easy.

I need some reassurance.

Thank you
 
  • #7
(two threads on the same question merged into one)

(thread moved to Advanced Physics Homework Help)
 

1. How big should asteroids be to cause major damage on Earth?

The size of an asteroid needed to cause major damage on Earth depends on various factors such as its speed, composition, and angle of impact. However, on average, an asteroid with a diameter of 1 kilometer or larger can cause significant damage and destruction on a global scale.

2. How big should asteroids be to be classified as "potentially hazardous"?

Asteroids are classified as "potentially hazardous" if they have a minimum diameter of 140 meters and come within 7.5 million kilometers of Earth's orbit. However, this classification does not necessarily mean that they will collide with Earth.

3. How big should asteroids be to be visible to the naked eye?

The size of an asteroid needed to be visible to the naked eye depends on its distance from Earth and its brightness. On average, an asteroid with a diameter of at least 10 meters can be seen with the naked eye if it passes within 1 million kilometers of Earth.

4. How big should asteroids be to have an impact crater?

The size of an asteroid needed to create an impact crater depends on factors such as its speed, angle of impact, and the composition of the surface it hits. Generally, an asteroid with a diameter of at least 100 meters can create a visible impact crater on Earth.

5. How big should asteroids be to be considered "small" or "large"?

The terms "small" and "large" can be subjective when it comes to asteroids. However, in general, asteroids with a diameter of less than 10 meters are considered small, while those with a diameter of over 1 kilometer are considered large.

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