Calculating Radiation Pressure Needed to Balance Sun's Gravity

Pepsi24chevy
Messages
65
Reaction score
0
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.
 
Physics news on Phys.org
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
 
Last edited:

Thread 'Please tell me where I am going wrong in this integral'

##|\Psi|^2=\frac{1}{\sqrt{\pi b^2}}\exp(\frac{-(x-x_0)^2}{b^2}).## ##\braket{x}=\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dx\,x\exp(-\frac{(x-x_0)^2}{b^2}).## ##y=x-x_0 \quad x=y+x_0 \quad dy=dx.## The boundaries remain infinite, I believe. ##\frac{1}{\sqrt{\pi b^2}}\int_{-\infty}^{\infty}dy(y+x_0)\exp(\frac{-y^2}{b^2}).## ##\frac{2}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,y\exp(\frac{-y^2}{b^2})+\frac{2x_0}{\sqrt{\pi b^2}}\int_0^{\infty}dy\,\exp(-\frac{y^2}{b^2}).## I then resolved the two...
View full post »

Thread 'Direction of the magnetic field of an oscillating charge'

Hello everyone, I’m considering a point charge q that oscillates harmonically about the origin along the z-axis, e.g. $$z_{q}(t)= A\sin(wt)$$ In a strongly simplified / quasi-instantaneous approximation I ignore retardation and take the electric field at the position ##r=(x,y,z)## simply to be the “Coulomb field at the charge’s instantaneous position”: $$E(r,t)=\frac{q}{4\pi\varepsilon_{0}}\frac{r-r_{q}(t)}{||r-r_{q}(t)||^{3}}$$ with $$r_{q}(t)=(0,0,z_{q}(t))$$ (I’m aware this isn’t...
View full post »

Thread 'Initial conditions for orbits around a wormhole'

Hi, I had an exam and I completely messed up a problem. Especially one part which was necessary for the rest of the problem. Basically, I have a wormhole metric: $$(ds)^2 = -(dt)^2 + (dr)^2 + (r^2 + b^2)( (d\theta)^2 + sin^2 \theta (d\phi)^2 )$$ Where ##b=1## with an orbit only in the equatorial plane. We also know from the question that the orbit must satisfy this relationship: $$\varepsilon = \frac{1}{2} (\frac{dr}{d\tau})^2 + V_{eff}(r)$$ Ultimately, I was tasked to find the initial...
View full post »

Similar threads

I Sun gravitational lensing forces
Replies
11
Views
1K
Calculations using the Standard Solar Model & Solar Equations of State
Replies
1
Views
2K
Atmospheric pressure as a function of altitude
Replies
15
Views
3K
Poynting-Robertson effect on an object orbiting the sun
Replies
1
Views
3K
Change of radiation pressure of sunlight w.r.t. distance
Replies
6
Views
2K
Radiation Pressure: Exam Prep Questions & References
Replies
1
Views
2K
Radiation pressure on sphere orbiting earth
Replies
3
Views
3K
Average Pressure Radiation on Perfectly Absorbing Surface
Replies
6
Views
3K
Estimate the radiation pressure
Replies
4
Views
2K
Analytic solution of the Earth's orbit around the Sun
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top