Question

Question 6: (a.) The asteroid Vesta orbits the Sun with a semi-major axis of 2.362 AU. It has a rotational period of about 5 hr 21 min and an albedo of 0.38 (unusually reflective for an asteroid). (a) Estimate Vesta's surface temperature (b) Estimate what Vesta's surface temperature would be if it were instead tidally locked with the Sun so that it always kept the same side facing the Sun. State at what point on the planet this temperature is technically estimated for. (c) Assuming Vesta has a layer of subsurface ice, would you expect it to sublimate in case (a) and/or case (b)? Recall (from the Homework) that many ices start to sublimate at around 150 K.

Answer 1

Given the semi-major axis - 2.362 AV Time tau = 5hr 21 min flux = (l - a) m^2 s flux out = 4 m^2 s T^4 Q is dhx du M^2 is area of circle exposed to sunlight S - intensity of sunshine 67 w/m^2 S - Boltzman constant 5.67 times 10^-8 w/m^2/k^ T - temperature equating the flux inward and outward (t - a) m^2 s = 4m^2 sT^ S (l - a)/4 = ST^4 1367 w/m^2 (1 - 0.38)/4 = 5.67 times 10^-8 w/m^2/k^4 times T^4 211.885 = 5.67 times 10^-8/k^4 T^4 37.69 times 10^8 R^4 = T^4 247.24 k = 7 \r\n similarly flux In = (t - a) m^2 s/2 flux = out = 4m^2 ST^4 the flux we will get S (l - a)/8 = ST^4 13.67 w/m^2 (1 - 0.38)/8 = 5.67 times 10^-8 w/m^2/k^4 times T^4 105.94/5.67 times 10^8 k^4 = T^4 207 k = T this is the temperature on side exposed to sun will in both cares but faster on care (a) than (b)