1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculating Luminosity and Temperature of the Sun from Pluto

  1. Oct 6, 2015 #1
    Hey all, I think that I'm doing this problem correctly but I'm getting an answer that's a couple thousand Kelvins off. Sorry if I should have posted this in the "advanced" section.

    1. The problem statement, all variables and given/known data

    Part of a flat region of Pluto has the Sun directly overhead. Its surface temperature is 58 K. You have determined Pluto is 33 AU away from the sun, and the region of interest has an albedo of 0.5. Use all of this information to determine the Sun's luminosity temperature. Assume the Sun and Pluto are perfect black bodies.

    2. Relevant equations
    P/A of a black body is equal to σT4, where σ = 5.67x10-8 W*m-2*K-4.


    3. The attempt at a solution
    Pluto's temperature is 58 K. By the equation above, its power/area radiated outward is σ*584, which is 0.642 W*m-2. Because its albedo is 0.5, it receives double this power from the sun, so the power per area from the sun hitting the surface is 1.283 W*m-2.

    Because this power will fall off as the radius squared from the sun, I multiplied this by the square of 33 AU, which is 2.437x1025 square meters. I came away with a total luminosity of 3.13 W. Then, using the same equation above, I get that the effective surface temperature of the Sun is 3193 K, which is almost 3000 K away from the true value. Am I doing something wrong, or is this because of the imprecise variables that I was given in the problem?

    Thanks in advance.
     
  2. jcsd
  3. Oct 6, 2015 #2

    Bandersnatch

    User Avatar
    Science Advisor

    Why do you care for the power radiated from Pluto's surface, though?
     
  4. Oct 6, 2015 #3
    The power radiated from Pluto's surface is equal to half of the total power it receives from the Sun, because the albedo is 0.5. Right?
     
  5. Oct 6, 2015 #4

    Bandersnatch

    User Avatar
    Science Advisor

    Right, sorry. I posted without thinking. Give me a moment to go through it again.
    Tentatively, I'd probably look at the difference in areas that receive and reradiate the energy.
     
  6. Oct 6, 2015 #5

    Bandersnatch

    User Avatar
    Science Advisor

    I think this is the issue right here. To get the total power produced by the Sun, you need to take the flux you've just calculated at Pluto's orbit, and multiply it by the area of a sphere at that distance. That is, 4π times the radius squared. This gives the correct luminosity for the Sun.

    I'm not sure what method you used to get the temp. from luminosity, though. Don't you need to know the Sun's radius? In any case, with the correct luminosity you should get the correct temperature.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Calculating Luminosity and Temperature of the Sun from Pluto
  1. Luminosity of the sun (Replies: 2)

Loading...