1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Radiation pressure

  1. Oct 19, 2005 #1
    Ok, i got a problem that reads as followed.

    Suppose that a perfectly reflecting circular mirror is initially at rest a distance R away from the sun and is oriented so that the solar radiation is incident upon, and perpendicular to, the plane of the mirror. What is the critical value of mass/area for which the radiation pressure exactly cancels out the force due to gravity?

    Ok so lets start with the given:, I know mass of the sun is 2.0 x 10^30 kg
    intensity of sunlight as a function of the distance R from the sun = 3.2x10^25(1/R^2) (w/m^2)
    and the gravitational constant is 6.67x 10^-11

    Radiation pressure ecerted on a perfectly reflecting surface is P= 2S/c where C is the speed of light and S is the poynting vector? I know the answer is going ot be mass/area in which the mass is mass of the sun. The answer will also be in kg/m^2. Now i am not sure how to setup this problem.
  2. jcsd
  3. Oct 19, 2005 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    The counter-force to radiation force is the weight of the reflecting surface (mass of mirror x acceleration due to gravity ([itex]F=mGM_{sun}/r^2 [/itex]). In terms of pressure this is:

    [tex]P = F/A = \frac{\rho*Ad*GM_{sun}}{Ar^2} = \frac{\rho*d*GM_{sun}}{r^2}[/tex]

    Equating the two:

    [tex]P = \Phi_E/c = \frac{\rho*d*GM_{sun}}{r^2}[/tex]

    where [itex]\Phi_E = \frac{E}{4\pi r^2}[/itex] is the energy flux (E/A)

    You should be able to work it out from that.
    Last edited: Oct 19, 2005
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook