Radiation pressure

A$.$ On earth, the time$-$averaged electromagnetic energy flux $(($:$S$:$))$ from the sun is $0\mathrm{.}14$wat$\frac{t}{c}{m}^2.$

Consider steady sunlight hitting $1m^2$ of the earth: picture an imaginary box $($containing streaming

sunshine$)$ striking this area, with a "box height" of $1$ light$-$second. There is a certain amount of

momentum stored in that box, and in one second, ALL that momentum will strike the $1m^2$ area.

Assuming the EM wave is absorbed $($not reflected$),$ what force does that work out to$?$ How does the

radiation pressure from this light compare to atmospheric air pressure, Comment!

If the earth reflected the sunlight, how would that affect the radiation pressure $($qualitatively$)?$

B$.$ We $($a combination of private industry and NASA$)$ can launch tiny satellites $($CubeSats are $1$ liter

in volume, with a mass of about $1\mathrm{.}3kg)$ on the $($relative$)$ cheap into near$-$earth orbit. There is

currently a Kickstarter project to attempt to boost one of these out to lunar orbit by using a $32m^2$

reflective "solar sail" to utilize light pressure to propel the satellite $(!)$ The orbital mechanics of this

are complicated, but let's ignore all that and just figure out what the acceleration would be due

ONLY to the light pressure alone, and thus what the corresponding $($simple$,$ Phys $1110-$style$)$ time$-$

to$-$moon estimate would be$.$ What are some advantages and disadvantages of conventional

spacecraft?

C$.$ Fine particles of dust in interplanetary space are pushed out of the solar system by radiation

pressure from the Sun too. That's why the night sky is nice and dark and transparent. Derive an

expression for the size $($the radius$)$ of a particle $($located $1AU$ from the sun, so the solar flux is the

same as in part A$)$ that is at the critical size where the outward radiation pressure balances the

inward pull of gravity. Insert reasonable numbers in your expression and estimate this critical size.

$($Would the answer you get be different if you were closer, or farther, from the sun?$)$