Calculating Radiation Pressure Needed to Balance Sun's Gravity

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To calculate the critical mass per area for a perfectly reflecting mirror to balance the Sun's gravitational force, one must equate the radiation pressure to the gravitational force. The gravitational force acting on the mirror is given by F = mGM_sun/r^2, while the radiation pressure on a reflecting surface is expressed as P = 2S/c, where S is the intensity of sunlight and c is the speed of light. The intensity of sunlight decreases with distance as 3.2x10^25(1/R^2) W/m^2. By setting the radiation pressure equal to the gravitational force per area, the equation can be solved for the mass per area in kg/m^2. This approach provides a framework to determine the necessary conditions for equilibrium between radiation pressure and gravitational force.
Pepsi24chevy
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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 let's 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.
 
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Pepsi24chevy said:
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 let's 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.
The counter-force to radiation force is the weight of the reflecting surface (mass of mirror x acceleration due to gravity (F=mGM_{sun}/r^2). In terms of pressure this is:

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

Equating the two:

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

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

You should be able to work it out from that.
AM
 
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