Star Observation Calculation Homework

[evergreengiant]

Homework Statement

The intensity of the Sun's radiation is about 1380 Wm^-2 at Earth's distance, 1.5x10¹¹m. Earth absorbs this radiation as a black body, and radiates its own energy back into space.

a) How much Energy per second falls on the Earth's surface? (Diameter of Earth = 12800km)
b) What temperature would Earth's surface need to be to radiate this much energy back into space (i.e equilibrium)
c) Why is Earth's actual average surface temperature a bit higher than this
d) Ceres, the largest asteroid, orbits around 4.1 x10¹¹m from the sun:
(i) What would be the Sun's intensity on Ceres
(ii) Find the average temperature of its surface.

Homework Equations

P=AoT⁴ where o = 5.6697x10^-8Js^-1m^-2 K^-4
I = P / 4 x pi x D² where D is the distance from the star

The Attempt at a Solution

a) P = 1380 x 4pi x (1.5x10¹¹)²
don't think this is right...
b) T = fourth root of P / 4pi x r² x o
c) global warming?? greenhouse effect??
d) (i) Just use the ratio of Earth's distance : Ceres' distance, plug in the intensity
(ii) Don't even know where to start, considering we don't have the radius...

 

[Noctisdark]

Hi,
I agree with you in the first question since energy/sec is just watt, so assuming the sun shine on the whole Earth P_{on earth} = P*A
Also does agree with 2, it's a straighforward application of stephan's law,
Because It doesn't radiate all the energy that it absorbs due to something, maybe global warming and a small contribution go to heat the Earth's surface
And repeat the same scénario to answer the last two, good luck !

 

[evergreengiant]

Hi,
I agree with you in the first question since energy/sec is just watt, so assuming the sun shine on the whole Earth P_{on earth} = P*A
Also does agree with 2, it's a straighforward application of stephan's law,
Because It doesn't radiate all the energy that it absorbs and a small contribution go to heat the Earth's surface
And repeat the same scénario to answer the last two, good luck !

Hey there, My attempt at question 1 and 2 must be incorrect as I come out with a Power of 3.9x10²⁶, and therefore a surface temperature of over 1million Kelvin which just isn't right? HELP!

 

[Noctisdark]

No idea, we have no radius of ceres, maybe google it ?
Just to correct one thing 1380 is the sun intensity at earth, so I = 1380, calculate P (You've done that), assume that R being the radius of ceres and for it to radiate back that energy into space then P = 4πR²*σ*T⁴, and solve for T