We can use the definition of pressure to express the radiation force on the balloon. We'll assume that the gravitational force on the balloon is approximately its weight at the surface of Earth, that the density of Mylar is approximately that of water and that the area receiving the radiation from the sunlight is the cross-sectional area of the balloon.
The radiation force acting on the balloon is given by:
`F_r=P_rA`
Where `A` is the cross sectional area of the balloon.
Since the radiation is reflected, the radiation pressure is:
`P_r=2*(I/c)`
Substituting for `P_r` and `A` yields:
`F_r=(2I(1/4pi d^2))/c=(pi d^2I)/(2c)`
`d` is the diameter of the balloon.
The gravitational force acting on the balloon when it is near-Earth orbit is approximately its weight on at the surface:
`F_g=W_(balloon)`
`=m_(balloon)*g=rho_(mylar)*V_(mylar)*g=rho_(mylar)*A_(surface,balloon)*t*g`
Where `t` is the thickness of the Mylar skin of the balloon.
The surface area of the balloon is `A=pi*d^2` . Therefore:
`F_g=pi rho_(mylar)d^2*t*g`
Now express the ratio.
`F_r/F_g=((pi*d^2I)/(2c))/(pi rho_(mylar)d^2*t*g)=I/(2rho_(mylar)*t*g*c)`
Assume the thickness of the Mylar skin of the balloon to be `1 mm` . The value for `I` can be found in the attached graph and the first source I provided. Now substitute numerical values and evaluate `F_r/F_g` .
`(F_r/F_g)=(1.35 (kW)/m^2)/(2(1*10^3 kg/m^3)(9.81 m/s^2)(1 mm)(2.998*10^8 m/s))`
`(F_r/F_g) ~~ 2*10^-7`
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