# One of the first successful satellites launched by the United States in the 1950's was essentially a large spherical (aluminized) Mylar balloon from which radio signals were reflected. After several orbits around Earth, scientists noticed that the orbit itself was changing with time. They eventually determined that the radiation pressure from the sunlight was causing the orbit of this object to change - a phenomenon not taken into account in planning the mission. Estimate the ratio of the radiation-pressure force by the sunlight on the satellite to the gravitational force by Earth's gravity on the satellite.

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.

`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`