Effective cross

# Effective cross - lost asymmetrically it is possible this...

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Effective cross-section for collisions Our collision probability (for a comet to hit an inner solar system body) calculated above (10 -6 ), ignored the effective cross-section increase due to gravitational deflection. We can account for this to give an effective gravitational cross-section which is greater than the geometric cross- section (effective radius D >> real radius R). D will depend on the initial approach velocity. We use conservation of angular momentum and conservation of energy to calculate D: img/3C37-133.gif"> The critical offset D is given by: D = R(1 + 2GM/RV app 2 ) = R[1 + (V esc /V app ) 2 ] For a long period comet D/R is around 1.04, but if v app is as low as 2.2km s -1 then D/R = 26. Forces due to evaporation By considering a typical model of a comet - mostly water with "impurities" - see above - you can calculate how much material is lost at close encounter with the Sun (perihelion). Assuming this is

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Unformatted text preview: lost asymmetrically it is possible this could have a net accelerative effect on the body. Rough calculations (see Lewis pp286-7) shows this is unlikely to be more than of the order of magnitude 6 m s-1 , but this depends heavily on the assumptions made. The evaporation is ameliorated by dust which inhibits heating and slows gas loss. We have seen above how light pressure is balanced by gravity for grains of a certain size in interplanetary space. Similarly there will be a size above which gravitational attraction to the comet exceeds the gas pressure trying to detach the grains. Grains above this size accumulate. How much does depends on the maximum heating, and therefore the pressure, near the Sun. Comets with perihelia far enough out may lose their volatiles and become dust-covered and hence inactive....
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## Effective cross - lost asymmetrically it is possible this...

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