Where the focus is
A line, not a point.
A light ray grazing the Sun’s limb is deflected by four times the gravitational parameter divided by the product of the speed of light squared and the impact parameter. For a ray at the solar radius that is 8.49 × 10⁻⁶ radians, or 1.75 arcseconds — the Eddington measurement of 1919.
The focus lies where the deflected ray crosses the axis, at a distance equal to the impact parameter divided by the deflection angle. For a grazing ray that is 8.20 × 10¹³ meters, or 547.8 AU.
Because the deflection falls as the inverse of the impact parameter, rays passing farther above the limb focus farther out. The focus is therefore not a point but a line, running from 547.6 AU outward indefinitely. In practice a node wants to sit beyond about 600 AU, so its Einstein ring forms above the densest part of the corona rather than through it. From a node on the line the ring appears at a radius of about 1.75 arcseconds — the same angle as the deflection that made it.
The amplification
And why it favors visible light.
The optical amplification of the solar lens is approximately 4π² times the Schwarzschild radius divided by the wavelength. The Sun’s Schwarzschild radius is 2,953 meters.
| Wavelength | Amplification | Effective aperture of a 1 m telescope | Angular resolution |
|---|---|---|---|
| 2.0 microns | 5.8 × 10¹⁰ | 241 km | 3.0 × 10⁻¹⁰ arcsec |
| 1.0 micron | 1.17 × 10¹¹ | 342 km | 1.5 × 10⁻¹⁰ arcsec |
| 0.5 micron | 2.33 × 10¹¹ | 483 km | 7.4 × 10⁻¹¹ arcsec |
Effective aperture is the diameter of an unaided telescope with the same light-gathering area, which is the physical aperture times the square root of the amplification. Angular resolution is set by the lens geometry — roughly the wavelength divided by twice the solar diameter — rather than by the telescope.
The amplification scales inversely with wavelength, so the solar lens is better in the optical than in the radio. That is the opposite of almost every other instrument in astronomy, where longer wavelengths buy sensitivity at the cost of resolution; here they cost both. The instrument wants to be an optical telescope, which is convenient, because the things one wants to look at — surface features, atmospheric absorption bands, ocean glint — are optical phenomena.
The resolution figure deserves a caveat the popular accounts skip. The diffraction limit of the lens at 1 micron corresponds to about 29 meters at Proxima’s range. The published practical figures are far coarser, tens of kilometers, because signal-to-noise, deconvolution of the point-spread function, coronal background and image motion each degrade the theoretical limit by a large factor. The gap between 29 meters and tens of kilometers is not a rounding error. It is where the entire engineering problem lives.
You raster-scan a physical image
This changes the character of the mission.
The lens projects a real, physical image of the target into the focal region. The image diameter is the source diameter scaled by the ratio of node distance to target distance.
| Target | Distance | Node at | Image diameter | Sampling for a 1,000-pixel image |
|---|---|---|---|---|
| Proxima b (1 Earth radius) | 4.25 ly | 548 AU | 26 km | 26 m steps, 10⁶ positions |
| Earth analog at Alpha Cen A | 4.34 ly | 548 AU | 26 km | 26 m steps, 10⁶ positions |
| Earth analog at 30 pc | 98 ly | 650 AU | 1.3 km | 1.3 m steps, 10⁶ positions |
To build a thousand-by-thousand-pixel image of Proxima b, a spacecraft must sample a 26-kilometer image at 26-meter intervals: a raster of one million telescope positions. The nearer the target, the larger the projected image, so proximity buys the best photon budget per pixel and imposes the largest area to cover. Proxima is both the easiest and the most laborious target in the set.
One-way light time at 548 AU is 3.2 days, so a round trip is 6.3. That is well past the Ceres threshold: the node plans and executes its raster campaign locally and reports.
The image moves
20 kilometers per second per year, forever.
The projected image does not sit still. The planet orbits its star, and that orbital motion is scaled into the focal plane by the same factor.
Proxima b orbits at 0.0485 AU with an 11.19-day period. Scaled to a node at 548 AU, that traces an ellipse roughly 30,000 kilometers across, completed every 11.19 days. The mean image velocity is about 96 meters per second, and following an ellipse of that radius at that speed requires a sustained centripetal acceleration of 6.2 × 10⁻⁴ meters per second squared.
Tracking the image of Proxima b costs roughly 600 meters per second of Δv every 11 days, or about 20 kilometers per second per year, sustained, forever. That is not a station-keeping budget. That is a propulsion program. And it is a consequence purely of the planet being close to its star, which is a consequence of the star being an M dwarf.
Run the same arithmetic for an Earth analog at 1 AU around Alpha Centauri A. The focal-plane ellipse is about 600,000 kilometers across, but it is completed in a year rather than 11 days. The image velocity is a comparable 60 meters per second, but the required acceleration is 50 times lower, and the tracking cost falls to roughly 370 meters per second per year. That is an ordinary electric-propulsion budget.
Two independent arguments converge, and this is the shape of the whole problem. The lens prefers wide-orbit planets around bright stars. Photon braking prefers exactly the same thing, for reasons that have nothing to do with imaging. Two unrelated physical arguments agree that Sun-like stars are the tractable targets and M dwarfs are the hard ones. Only two considerations point the other way: mission duration, and the fact that every known rocky habitable-zone planet happens to orbit an M dwarf.
One node, one target
The cost nobody puts on the front page.
Voyager 1 recedes from the Sun at about 3.6 AU per year, which would put 548 AU 152 years away. The mission requires roughly 20 AU per year, which means either a solar sail released at a very close perihelion or a nuclear-electric stage. At 20 AU per year the cruise is 27 years.
And then the part that is usually omitted. The focal line is target-specific, so a multi-target program is a constellation, not a telescope.
The line for a given star runs from that star through the Sun and outward on the opposite side. Moving to a different target means moving to a different focal line, a lateral displacement of order the full 548 AU. One node images one target, or at best a small family of targets within a narrow cone. Six candidate systems means six nodes and six 27-year cruises.
Launched from the 2040s, such a constellation is productive from the 2070s, which is precisely the horizon this site treats as its primary case.
The only national program currently building toward that distance is Chinese. Interstellar Express, also called Shensuo, is a CNSA program of two or three probes for heliosphere and interstellar-space exploration, rescheduled from 2024 to 2032–2033. A January 2026 paper in China’s Journal of Deep Space Exploration outlined two probes aimed at the heliosphere’s nose and tail: IHP-1 with a Quaoar and Weywot flyby, and IHP-2 with a Neptune and Triton flyby in 2038. Each masses about 200 kilograms and carries over 50 kilograms of instruments, using radioisotope thermoelectric generators, Long March 5 launches, and gravity assists at Earth and Jupiter, with a thermoelectric fission reactor under development for a possible third probe. The stated goal is 100 AU by 2049, the centennial. That is not a lens mission — 100 AU is a fifth of the way to the focal line — but it is the only flight program anyone is building on the outbound corridor, and it is the cruise-speed and autonomy problem rehearsed at a fifth scale.
The lens as a receiver
The larger half of any probe program.
Apply the amplification to the downlink budget. Received power scales with collecting area, so replacing a 30-meter receiver with a 342-kilometer effective aperture multiplies the link by 1.3 × 10⁸.
The full table is on the data-return page: a four-bit-per-second trickle becomes a 550-megabit channel, 17 megabytes a year becomes 2.2 petabytes, using a one-meter telescope.
The geometry works out, which is worth checking rather than assuming. A probe at Proxima b sits 0.0485 AU from its star, an angular separation of about 0.037 arcseconds as seen from here. The lens resolves 1.5 × 10⁻¹⁰ arcseconds, so the probe is separated from the star by roughly 250,000 resolution elements: it is not swamped. In the focal plane the probe’s image sits about 15,000 kilometers off the star’s optical axis, which is a maneuver rather than an obstacle.
Three caveats keep this honest. The solar corona is the noise floor, because the light arrives through it, and coronal brightness and its variability set the achievable contrast. The node must know where the probe is to within its focal-plane offset, which means the probe must be where the mission said it would be, based on a plan made 4.25 years earlier. And a node cannot image the planet and track the probe at the same time if the two are separated by more than the instantaneous field, which they generally are.
The strategic verdict
The highest ratio of return to risk.
The solar gravitational lens is simultaneously the targeting system, the primary science return, and the communications infrastructure of any interstellar program, and it never leaves the solar system.
If the 21st century produces exactly one outward program, this is the one with the highest ratio of return to risk. Its justification does not depend on any star mission ever flying, which is exactly the property that separates a program surviving a change of government from one that does not.
It is also the reason the relay chain may be the real interstellar architecture: the first thousand AU pays for itself on astronomy alone, and everything further out is then an increment rather than a commitment.