A. A comet has a nucleus with a diameter of 1 km and is at a distance of 1 AU fr

Question

A. A comet has a nucleus with a diameter of 1 km and is at a distance of 1 AU from the Sun. Under the assumption that most of the material lost from the comet is water vapour, estimate the mass of material lost from the comet each second. Assume that the albedo of the comet is 0.05, and take the luminosity of the Sun to be 3.8 x 1026 W and the latent heat of sublimation of ice to be 2.8 × 106 J kg-1 1;} B. Under the assumption that each time the coment returns to the inner solar system it spends approximately 3 months at around 1 AU from the Sun, make a rough estimate of how many times the comet will return before all the ice is melted. Take the density of ice to be 1000 kg m-3

Explanation / Answer

(A) I = P / (4 pi r^2)

I = 3.8 x 10^26 / (4 x pi x (1 x 1.496 x 10^11)^2)

I = 1351.2 W/m^2

Pabsorbed = (1 - albedo) I ( pi R^2) =

= (1-0.05) (1351.2) (pi (1 x 10^3)^2)

= 4.03 x 10^9 W

4.03 x 10^9 = (2.8 x 10^6) m

m = 1440 kg /s

(B) ice melted in 3 months = (1440) (3 x 30 x 24 x 3600)

= 1.12 x 10^10 kg  

total mass = (1000)(4 x pi x (10^3)^3 / 3)

= 4.19 x10^12

n = (4.19 x 10^12) / (1.12 x 10^10)

= 374 times

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