Sling-Shooting Around a Star to Catch a Solar Flare

Question

How much thrust could a solar sail receive from sling shooting around the Sun and riding the wave of a solar flare during the escape? I found this link https://ww4.fmovies.co/film/the-ark-season-1-1630854809/ at 23:32 somewhat examples the maneuver.

Answer 1

The discussion around 23:30 of the clip you cite makes no reference to solar sails and instead talks about "faster than light travel" and "propelling ships through a quantum distortion bubble" - I'm afraid it's all more than questionable (from a physics point of view, although I'm not encouraged to watch any further).

A "solar sail" works by presenting a reflective surface to the electromagnetic radiation from the Sun. The change of momentum of photons bouncing off the sail will impart a force/thrust per unit area of $2f/c$, where $f$ is the solar flux (power per unit area) incident upon the sail.

The kind of "slingshot" manoeuvre you are talking about could mean furling in, or turning the sail sideways as you approach the Sun, to avoid any deceleration, and then unfurling or deploying it fully once the Sun was behind the spaceship in its desired trajectory.

If you were at a distance $r$ from the Sun, then the thrust per unit area of sail would be, assuming normal incidence, $$ \frac{2f}{c} = 2 \frac{L_\odot}{4\pi r^2c} \simeq 10^{-5} \left(r/{\rm au}\right)^{-2}\ {\rm N/m}^2\ , $$ where $r$ is expressed in astronomical units ($1.496\times 10^{11}$ m) and $L_\odot = 3.9 \times 10^{26}$ W is the solar luminosity. This is a rough estimate and assumes the full sail area can intercept the solar radiation normally to provide thrust directed along the orbital trajectory (which can't happen for any realistic orbit, so it is an over-estimate).

The presence or not of a solar flare would make very little difference to this number, since even a large solar flare results in only a very minor increase in the total flux from the entire solar surface.

Answer 2

The property of the coronal mass ejection (CME) that you need is called the momentum flux. This is simply the total momentum of all particles passing through a unit area per second. The reason this matters is that if those particles are hitting a solar sail and stopping, then the momentum change per second is equal to the momentum flux times the area of the sail, and the momentum change per second is equal to the force on the sail.

The problem is that I have found it very difficult to find figures for the momentum flux in a CME. I have found some figures in the paper Tracking the momentum flux of a CME and quantifying its influence on geomagnetically induced currents at Earth. This analyses a fairly standard flare from 2011 and reports that when the flare reached the Earth the proton density was about $\rho = 40$ protons per cm³ and that the proton velocity was about $v = 370$ km/s. The momentum flux is then simply $\rho v^2$ and this comes out as about $10^{-8}$ N/m².

So for this particular CME the force contributed by the CME was about $10^{-8}$ N/m², and as discussed by Rob above the force due to regular sunlight at the distance of the Earth is about $10^{-5}$ N/m², so the extra force due to the CME was about 0.1% of the total. This is not a insignificant increase, but the 2011 CME studied in this paper was not a particularly intense one and a really big CME could easily be a thousand times as large, which would make the force from the CME comparable to the force from regular sunlight. If the CME was $10^4$ times larger than the 2011 event the force would be dominated by the CME.

So a really big coronal mass ejection could indeed significantly boost the thrust from a solar sail, but I think we need to inject a note of reality. Firstly the force is still very small so even for a very large CME our solar sail powered spaceship would not be racing off as if its pants were on fire. Secondly CMEs large enough to dominate the force on the sail are exceedingly dangerous and would probably kill the occupants of the spaceship anyway. And of course thirdly solar flares do not happen to order. So while it is an interesting calculation, I don't think surfing a solar flare is likely to be a useful way of propelling a spaceship any time soon.