L10aGH09Small_SS_Bodies_IVAsteroids_Come

L10aGH09Small_SS_Bodies_IVAsteroids_Come - Small SS Bodies...

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February 5, 2009 comets Small SS Bodies IV: Asteroids-II; Comets-I •Lecture topics: ¾ asteroids: heating and cooling ¾ comets: appearance, properties, orbits, origins •Text reading: Chapter 6: especially 6.5, 6.6 Chapter 7: especially 7.3, 7.5, 7.6
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February 5, 2009 comets Asteroid Heating: Impacts Two asteroids orbit the Sun in virtually identical orbits. One has a radius of 40 km and a density of 3300 kg/m 3 . The other has a radius of only 100 m, and the same density. Due to a small difference in initial velocity, the two asteroids approach each other and are attracted gravitationally. •H o w m u c h h e a t i n g might be expected from this collision? What is the typical collision time between asteroids?
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February 5, 2009 comets Asteroid Heating: Solar Radiation • Radiation from the Sun heats the surface of planets, asteroids to a temperature that depends on distance. ¾ Assume a fraction (1-A v ) of the solar flux is absorbed at a distance r ¾ , and reradiated as a blackbody. ¾ Assume body is rotating, so is heated evenly all over surface () 2 / 1 4 / 1 / 280 1 1 AU r K A A T IR V = • What is the temperature of the piece of coal, orbiting at 3AU, assuming its infrared albedo is similar to its visible albedo?
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February 5, 2009 comets Asteroid Internal Heating: Radioactivity • Radioactive heating? ¾ unstable isotopes present in solar or carbonaceous chondrite mixture can be powerful sources of energy ¾ …especially at earlier times when more of the radioactive isotope was available. Heating rate Isotope Half-life (10 9 yr) Isotope fraction in present-day chondrites Element abundance Isotope (J/yr/kg) Chondrite (J/Gyr/kg) 238 U 4.5 0.993 8.2x10 -9 2970 2.4x10 4 Total: 1.1x10 5 40 K 1.25 0.00011 5.6x10 -4 920 5.7x10 4 87 Rb 50.0 0.293 2.2x10 -6 0.544 3.51x10 2 232 Th 13.9 1.00 2.9x10 -8 837 2.4x10 4 235 U 0.71 0.0072 8.2x10 -9 18000 1.1x10 3 what is the maximum T increase from radioactive heating for a typical rocky body?
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February 5, 2009 comets Asteroid Internal Heating: Gravity • Gravitational energy? R GM E g 2 5 3 = • For Ceres, what is the maximum temperature increase possible from gravitational assembly? • The heat capacity of typical rock is K kg J c V / / 840
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February 5, 2009 comets Cooling: Conduction where A is the surface area, dx is the distance over which the heat is transmitted, k c is the thermal conductivity of the material. dx dT A k t Q c = Δ Δ For a spherical asteroid, radius R, assume the surface temperature is T=0, and the T gradient is linear. How long will it take to radiate away all its internal energy? In solid rock, the main method of heat transport is conduction. The rate of heat loss (dQ/dt) is related to the conduction efficiency and temperature gradient:
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February 5, 2009 comets Asteroid Cooling • For rocky material, the thermal diffusivity k c / ρ c v =1x10 -6 m 2 /s so τ yr ~1x10 4 R km 2 ¾ A body the size of an asteroid (R~500 km) will lose any internal energy in less than ~2.5 Gyr.
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This note was uploaded on 04/15/2009 for the course PHYS 275 taught by Professor Harris during the Winter '09 term at Waterloo.

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L10aGH09Small_SS_Bodies_IVAsteroids_Come - Small SS Bodies...

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