Calculating Radiation Pressure Needed to Balance Sun's Gravity

In summary, the problem involves determining the critical value of mass/area for which the radiation pressure exactly cancels out the force due to gravity on a perfectly reflecting circular mirror initially at rest a distance R from the sun. The given information includes the mass of the sun, the intensity of sunlight as a function of distance from the sun, and the gravitational constant. The counter-force to radiation force is the weight of the reflecting surface, and equating this to the radiation pressure allows for the calculation of the critical value.
  • #1
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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  • #2
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 ([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.
AM
 
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FAQ: Calculating Radiation Pressure Needed to Balance Sun's Gravity

What is radiation pressure?

Radiation pressure is the force exerted by electromagnetic radiation on an object. It is caused by the transfer of momentum from photons to the object's surface.

How is radiation pressure calculated?

Radiation pressure can be calculated using the equation P = F/A, where P is the pressure, F is the force exerted, and A is the surface area of the object.

What is the Sun's gravity?

The Sun's gravity is a force of attraction between the Sun and other objects, such as planets, that is caused by the Sun's mass.

Why is radiation pressure important in balancing the Sun's gravity?

The Sun's gravity is constantly pulling on objects in space, but radiation pressure from the Sun's intense radiation helps to counteract this force and prevent objects from being pulled in towards the Sun.

How is the radiation pressure needed to balance the Sun's gravity calculated?

The radiation pressure needed to balance the Sun's gravity can be calculated using the equation P = GMm/r^2, where P is the radiation pressure, G is the universal gravitational constant, M is the mass of the Sun, m is the mass of the object, and r is the distance between the Sun and the object.

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