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!

Hw help, its been a while since last physics course

  1. Jan 31, 2006 #1
    The Sun emits energy at a rate of about 3.9 · 1026W. At Earth, this sunshine gives
    an incident energy flux Ie of about 1.4kWm−2. In this problem, you’ll investigate
    whether any other planets in our solar systemcould support the sort of water-based
    life we find on Earth.
    Consider a planet orbiting at distance d from the Sun (and let de be Earth’s distance).
    The Sun’s energy flux at distance d is I = Ie(de/d)2, because energy flux decreases
    as the inverse square of distance. Call the planet’s radius R, and suppose that
    it absorbs a fraction α of the incident sunlight, reflecting the rest back into space. The
    planet intercepts a disk of sunlight of area πR2, so it absorbs a total power of πR2αI.
    Earth’s radius is about 6400 km.
    The Sun has been shining for a long time, but Earth’s temperature is roughly
    stable: The planet is in a steady state. For this to happen, the absorbed solar energy
    must get reradiated back to space as fast as it arrives (see Figure 1.2). Because the rate
    at which a body radiates heat depends on its temperature, we can find the expected
    mean temperature of the planet, using the formula
    radiated heat flux = ασT4.

    In this formula, σ denotes the number 5.7·10−8Wm−2 K−4 (the “Stefan–Boltzmann
    constant”). The formula gives the rate of energy loss per unit area of the radiating
    body (here, the Earth). You needn’t understand the derivation of this formula but
    make sure you do understand how the units work.
    a. Using this formula, work out the average temperature at the Earth’s surface and
    compare your answer to the actual value of 289K.
    b. Using the formula, work out how far from the Sun a planet the size of Earth may
    be, as a multiple of de, and still have a mean temperature greater than freezing.
    c. Using the formula, work out how close to the Sun a planet the size of Earth may
    be, as a multiple of de, and still have a mean temperature below boiling.
    d. Optional: If you know the planets’ orbital radii, which ones are then candidates
    for water-based life, using this rather oversimplified criterion?
     
  2. jcsd
  3. Feb 1, 2006 #2

    cepheid

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    What have you done so far on the question? Post your attempts, and we can help point you in the right direction.
     
  4. Feb 1, 2006 #3
    for a.) i know i need to solve for T.

    so is the radiated heat flux the same as incident energy flux Ie? If so then how do i solve for alpha, in the equation

    total pwr absorbed = pi x R^2 x alpha x I
     
  5. Feb 1, 2006 #4
    can anyone help me?
     
  6. Feb 1, 2006 #5

    chroot

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Does the problem really not give you a value for alpha (alpha is known as the "albedo")?

    The equation for energy in = energy out is:

    [itex] \pi r^2 \alpha I = \sigma A T^4 [/itex]

    Note that α on the left hand side is the albedo, while A on the right hand side is the surface area of the planet. They are not the same.

    Of these, you know pi, r, I, sigma, and A. You need to know alpha; too, then it's just a simple matter of solving for T.

    - Warren
     
  7. Feb 1, 2006 #6

    no it does not give a value for alpha, everything in the problem is in my orginal post.

    i am still lost on the other ones as well
     
  8. Feb 1, 2006 #7

    chroot

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Well, if I were you, I'd just pick a value for alpha, say 0.5, and explicitly write your assumption on your paper.

    Part b uses the same formula, using I = Ie(de/d)^2, T = 273 K (the freezing point of water), solved for d.

    - Warren
     
  9. Feb 1, 2006 #8

    but how do i get from the alpha x sigma x T^4 equation to the equation I = Ie(de/d)^2?
     
  10. Feb 1, 2006 #9

    chroot

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    The equation is the same for every problem in this set. Energy in = energy out:

    [itex] \pi r^2 \alpha I = \sigma A T^4 [/itex]

    where

    [itex]I = I_e \left( \frac{d_e}{d} \right)^2[/itex]

    Thus, the equation is, in full generality:

    [itex] \pi r^2 \alpha I_e \left( \frac{d_e}{d} \right)^2 = \sigma A T^4 [/itex]

    - Warren
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Hw help, its been a while since last physics course
Loading...