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So that’s why we are looking for a better Isp for reaching the outer planets. Let’s skip all the intermediate fuels and consider the best, photons. And of course the most famous photon driven rocket is the solar sail. How do they work?
Well, we are all aware that sunlight has energy, it warms our back and can even power our calculator. But it is also true that sunlight has momentum. From the Einstein relation, the momentum of a photon is its energy divided by the speed of light, c. At Earth orbit, the energy flux from the sun is 1.4 kWatts per square meter. Dividing by c, we get the pressure (in those pesky Systeme International units) 4.5 microPascals. Now if the light is reflected from the sail, it doubles the momentum transferred then if it is just absorbed, so we can achieve up to 9 microPascals.
Now to get to Pluto, the sail needs to accelerate, and because the light pressure is so low, the acceleration will be very, very small. The only way it can get there in 1.6 years will be if it is extremely light, and even then, it will be like a beer truck starting from the stop light, accelerating all the way. Knowing that it is accelerating constantly, I will cheat and pretend it is a constant acceleration even though the sunlight is getting weaker as the sail leaves the sun. This will give an acceleration far too small, but I can avoid some nasty calculus while still making my point. From freshman physics, the distance travelled is equal to half the acceleration times the square of the time, d=1/2 at2. Plugging in for the distance to Pluto and the time, we see that we need an acceleration of at least 0.004 m/s2 to make the trip.
Now we go back to Newton’s Law that says the force is proportional to mass times acceleration, F=ma, and then we divide both sides by an area. A force divided by an area is a pressure, whereas a mass divided by an area is a “mass loading”. Then the pressure of 9 microPascals divided by the acceleration of 0.004 m/s2 gives a mass loading of 2 g/m2. Since we have underestimated the necessary acceleration, the actual mass loading is even smaller, making this an upper limit.
Well, what are the current achievements in mass loading? We have aluminized Mylar materials that are 6 g/m2, and a new Carbon fiber felt that is all the rage at 5 g/m2. The photo on the slide shows the Carbon sail material floating like a sheet of duck down above the hand. But nothing that is close to 2 g/m2, or the even smaller values needed to reach Pluto quickly. Nor have we added in the dead weight of the booms that deploy the sail, or even of the spacecraft itself. Clearly it will be a while before sails can achieve this sort of mission to the outer planets.