Please help I have tried every method possible to get these answers but I keep c
ID: 2278555 • Letter: P
Question
Please help I have tried every method possible to get these answers but I keep coming up with the wrong answers, please include work with answers so I can know how to obtain them in future problems. Thanks!
A star has a radius of 8.5x10^9m and acts like a blackbody of temperature 4,300K. A planet of radius 2.7x10^7m orbits the star at a distance of 7.5x10^11m.
a. At what wavelength is the star's emmision the strongest?
b. What is the intensity of radiation at all wavelengths leaving the star's surface?
c. How much energy leaves the star's surface at al wavelengths each second?
d. How much energy leaves the star's surface in a time of one (Earth) year?
e. What is the intensity of radiation emitted by the star at all wavelengths at the position of the star's planet?
f. If it takes the planet 3.7 earth-years to orbit its star once, then how much energy is incident on the planet at all wavelengths during one orbital period, assuming that the planet's orbit it circular?
Explanation / Answer
a) wiens law
lamba T = 2.898E-3
so lambda = 2.898E-3/4300=6.74E-7 m = 674 nm
b) stefan boltzmann law
I = e sigma T^4 = 1*5.67E-8*4300^4=1.94E7 W/m^2
c) E per second = I A = 1.94E7*4*pi*8.5E9^2=1.76E28 J
d) 1.76E28*365.25*24*60*60=5.55E35 J per year
e) I = E /(4 pi R^2) where r is the radius of hte planet andR is the distance from star to planet
I = 1.76E28/(4*pi*1.75E11^2)=45730 W/m^2
f) E = I A t = 45730*pi*2.7E7^2*2.7*365.25*24*60*60=8.92E27 J