It’s a long way from the back of an envelope to a deployed spacecraft, which is one reason why scientists write papers in journals and gather at conferences. Such venues are where ideas get shaken out, problems identified and solutions proposed. We sometimes talk about realistic technologies like solar sails as if all that remained were to build them, but as Roman Kezerashvili demonstrated at the recent conference in Aosta, there is a range of problems that we are only beginning to consider.

Kezerashvili (City University of New York), working with colleague Justin Vazquez-Poritz, has identified a significant area of concern for mission concepts that pass close by the Sun. Often called ‘Sundiver’ missions (a Gregory Benford coinage, if memory serves), these sails would be so constructed as to survive an extremely close solar pass. Perhaps protected behind an occulter until periherlion, the sail would then be unfurled to receive the full force of the Sun’s photons at extremely close range.

How close? No previous mission has ventured closer than 0.3 AU to the Sun. But Kezerashvili points to one recent study that showed deploying a sail at 0.1 AU could produce accelerations sufficient to reach 200 AU in 2.5 years, the Sun’s gravitational focus at 550 AU in 6.5 years, and the inner Oort Cloud at 2550 AU in thirty years.

Close passes work. We need highly reflective, low density sail materials that are extremely heat tolerant to withstand the conditions they will encounter, but there is no reason to think these are unattainable in the future. Kezerashvili believes that perihelion distances may be reduced as low as 0.05 AU – 0.1 AU as we develop the needed materials.


Image: From the recent Aosta conference, a snapshot taken in the Italian Alps. Left to right: Giovanni Vulpetti, Roman Kezerashvili, and Justin Vazquez-Poritz. Photograph courtesy of Roman Kezerashvili.

All of which is good news, but the problem that now emerges is one of navigation. Any time we venture so close to the Sun, we have to take account of General Relativity. The sail may be in close proximity to the Sun for only a short period of time, but this is also the period when the outward acceleration due to Solar radiation pressure is the greatest. The results of applying these calculations are stunning — our sail could be taken well off-course.

From the paper:

“…we consider a number of general relativistic effects on the escape trajectories of solar sails. For missions as far as 2,550 AU, these effects can deflect a sail by as much as one million kilometers. We distinguish between the effects of spacetime curvature and special relativistic kinematic effects. We also find that frame dragging due to the slow rotation of the Sun can deflect a solar sail by more than one thousand kilometers.”

For deep space purposes, this strikes me as the most significant result to come out of the Aosta sessions. Without the kind of trenchant analysis Kezerashvili and Vazques-Poritz offered up in two papers at the conference, a seemingly workable mission concept would have lacked a fundamental navigation solution. The duo examined as well more exotic factors such as the slowing of the passage of time near the Sun due to relativistic effects. An observer on Earth at 1 AU measures about 31 more seconds per year than an observer at 0.01 AU, leading to a redshift in the wavelength of sunlight whose effects on the optimum thickness of the sail turn out to be negligible.

Some relativistic effects are minor, then, but some are not. Indeed, we see the effects of General Relativity play out in terms of crusing velocity. Kezerashvili and Vazques-Poritz look at the motion of a sail from 0.01 AU outwards, one whose cruising velocity is 480 kilometers per second. With the effects of curved spacetime in mind, the radial component of its velocity turns out to be faster than what we would expect under a purely Newtonian approximation by about 1.65 meters per second. This is a difference, the authors note, that “…remains constant throughout most of the voyage and therefore has a cumulative effect.”

General Relativity, then, is a significant consideration in making a Sundiver mission a reality. Spacetime curvature can cause large deflections depending on our targets, but in any scenario, precision demands a full accounting of each of these variables. Not long ago we discussed the options for a fast mission to Haumea, an orbiter that was also discussed at Aosta. Obviously, the effects Kezerashvili and Vazques-Poritz studied would bear upon the navigational inputs for any sail mission to Haumea using a close solar pass.

The paper is R. Ya. Kezerashvili and J. F. Vazques-Poritz, “Escape Trajectories of Solar Sails and General Relativity,” (accepted for publication at Physics Letters Bpreprint available). Orbital issues relating General Relativity to solar probes are discussed in the same authors’ “Solar Radiation Pressure and Deviations from Keplerian Orbits,” Physics Letters B 675 (2009), pp. 18-21 (abstract).