# How long would it take for a light sail to make it to Proxima Centauri and what speed would it get to?

The new discovery of a small planet keeping Proxima Centauri company prompted my imagination into overtime.

There are four parts to this:

1. If we were to deploy a small probe on a light sail how long would it take to get the distance to Proxima Centauri?

2. What speed would the sail reach before it had to slow down and how long would it take to reach top speed.

3. How long would it take to come to a stop.

4. Assuming it made it in one piece would the probe be able to beam data back to us for us to analyse? I know this would be a 4+ year transmission each way.

TL/DR: Over 2000 years for a ridiculously advanced craft travelling at the surface escape velocity of the sun, 620 km/s.

The effectiveness of a solar sail is determined by its "lightness factor", the thrust-to-weight ratio under solar gravity. (Since both gravity and radiation pressure obey inverse square law, this is independent of distance from the sun.) It is sometimes given in terms of the characteristic acceleration or characteristic thrust, which is the value at Earth's distance from the sun. The characteristic acceleration due to solar gravity is 0.005 m/s^2. (Edit: I should have written 0.0059 as 0.006. The basic conclusion will remain the same.)

The speed that can be achieved is limited by a number of factors. The maximum temperature that the sail can withstand (which limits how closely it can fly by the sun to gain speed) is one limit. Material strength is also an important factor, such a very thin material could easily be torn apart by radiation pressure when pulling against the inertia of a spacecraft near the surface of the sun. Furthermore, dust so near the sun is not that well studied and may pose a risk.

As an example, Wolfgang Seboldt & Bernd Dachwald discuss a number of solar sails in "Solar Sails: Propellantless Propulsion for Near- and Medium-Term Deep-Space Missions" (*1) One currently build-able of 400 m^2 at 87 g/m^2, one of 2500 m^2 at 38 g/m^2 likely build-able if existing technology is refined and one of 4900 m^2 at 23 g/m^2 that would require significant research but is considered realistically achievable. (Payload mass not included.) The third could achieve a characteristic thrust of about 40mN, giving a lightness factor of β = a/(0.005 m/s^2 ) = 0.07.

This is not enough to reach Proxima in any reasonable amount of time unless the sail is accelerated with large lasers. Instead of working it all out, I will show what happens with a lightness factor of 1 (*2), much higher than the craft above even without payload. If the spacecraft is on an orbit around the sun (ideally highly eccentric) and deploys its solar sail approximately at perihelion, we may assume that the sail exactly cancels solar gravity for the entire trip. This means that the spacecraft will escape the solar system with a constant speed equal to whatever its speed at perihelion was. Unless we also use another propulsion system, we must assume that we start from a bound orbit and so this can at most be the surface escape velocity of the sun, 617 542 m/s (*3).

(3.991 * 10^16 m)/(6.18 * 10^5 m/s) = 6.46 * 10^10 s, or about 2000 years.

The acceleration period for such a β = 1 craft will consist of the period where it falls in towards the sun, after which it will as already mentioned escape at constant speed. Falling in from Earth would give much less than the mentioned speed; if we assume a Jupiter flyby was used for perihelion lowering then the acceleration time (starting at Jupiter) would be just about a sixth of a Jupiter year, or two years. (Edit: Egg on my face. I wrote half a Jupiter year, when I should have said half an orbit at half of Jupiter's semi-major axis. That makes for 0.5 * 0.5^(3/2) of Jupiter's orbital period.)

(*1) Published in "Advanced Propulsion Systems and Technologies Today to 2020" edited by Claudio Bruno & Antonio Accettura, 2008. (American Institute of Aeronautics and Astronautics) p. 448-449

(*2) See "The Startflight Handbook: A Pioneer's Guide to Interstellar Travel" by Eugene Mallove & Gregory Matloff, 1989. (Wiley) p. 96-97.

(*3) From "Space Mission Engineering: The New SMAD" edited by James Wertz et al., 2011. (Microcosm) p. 955

Edward Guinan, an astronomer at Villanova University claims that 0.1C is possible with present technology and thus the trip would take less than 50 years.

I'm not sure what present technology is he referring to, laser propulsion and solar sail are still largely unproven.

In any case, if you get up to 0.1C, it makes more sense to do a flyby rather than to try to slow down. Having onboard propulsion system means extra weight, and on top of that having to slow down means you have to carry twice the propellent. If you use Earth based laser, you won't have any means of slowing down. That's basically why New Horizons did a flyby - they wanted to get there fast and had no means of slowing down.

Once you are there you can use radio or laser (still experiment) communications to return the collected science data. There will be a number of challenges - the solar system will be very small at that distance so the antenna has to be pointed very accurately, but I think it's doable.

There will be very little back and forth due to the large lag time, I would imagine that the spacecraft will have to do the final course corrections on it's own. Traveling at 0.1C, the spacecraft will cross the Proxima Centauri system in a few weeks, so obviously there is no time for any back and forth.

• I was under the impression that Solar Sail had already been demonstrated as with link? – CodePoint Aug 25 '16 at 14:50
• Additionally I read link where it is pointed out that you could use the star at the other end of the journey to slow the light sail down. – CodePoint Aug 25 '16 at 14:55
• @TenaciousC solar sails have been demonstrated, but the size of sail needed for such a distance would be gigantic by comparison, and that brings in a lot of new problems. Also the technology for the laser needed to propel it would need to be developed. – kim holder wants Monica back Aug 25 '16 at 15:48
• It has been demonstrated, sure, but that hardly makes it proven technology. It's mid TRL at best. Point taken though, I reworded my post. – ventsyv Aug 25 '16 at 16:24