5.76x10^-3 NRadiation Force on Echo II Satellite Ballon

[jabosh7777]

Homework Statement

The intensity of the suns' radiation just outside the Earth's atmosphere is approximately
8x10^4 joules/m^2*min
Approximately what force does this radiation exert on the Echo II reflecting satellite ballon? Echo II is a spherical shell of radius 20.4 m. Its skins consists of a layer of Mylar plastic, 9x10^-6 m thick, between two layers of aluminum, each 4.5x10^-6 m thick. The density of Mylar is 10^3 kg/m^3; of aluminum 2.7x10^3 kg/m^3..

This is problem 1-2 out of Special Relativity by A.P. French and the solution is 5.76x10^-3 N

Also the information on the densities are for the preceding question about the gravitational pull on the shell. I assume the force the radation exerts is independent of its mass.

Homework Equations

The Attempt at a Solution

8x10^4 joules/m^2*min / 60 = 1333 joules/m^2*sec
1333 joules/m^2*sec * 4(pi)(20.4m)^2 = 6972827.7 joules/sec

Here is where things break down. I tried dividing by the speed of light

(6972827.7 joules/sec) / (3*10^8 m/sec) = .0232426 N

 

[SimonZ]

the effective area is not 4(pi)(20.4m)^2, only (pi)(20.4m)^2

 

[kamerling]

why do you use $$4 \pi r^2$$ for the area? That is the area of the entire surface of the balloon. Dividing by the speed of light is Ok, since the energy of a photon is cp.
(with p the momentum).

 

[jabosh7777]

This is probably extremely intuitive, but why is it not 4(pi)r^2 or even 2(pi)r^2 since only half would be exposed?

 

[SimonZ]

the radiation is not perpendicular to all parts of the spherical shell and we only need the perpendicular component of radiation. This is something like the electric flux when using Gauss theorem in electrostatics. Suppose there's a uniform electric field, what is the flux passing through a sphere with radius R in the field? the answer is E*pi*R^2, not E*4pi*R^2, or E*2pi*R^2.