Navigating by parallax: how New Horizons found itself among the stars

The oldest trick in astronomy

Hold a finger at arm's length and blink one eye, then the other. The finger jumps against the background; the distance between your eyes is the baseline. Astronomers measure the distances of nearby stars the same way, with Earth's orbit as the baseline. The parsec is defined by it: the distance at which one astronomical unit subtends one arcsecond.⁸

Here θ is the apparent shift in radians, b_⊥ the part of the baseline perpendicular to the line of sight, and d the star's distance. Even the nearest star is a long way off: Gaia DR3 puts Proxima Centauri at 1.30197 pc, or 268,551 au.³ From Earth's orbit its parallax is 0.768″, about the width of a coin seen from 6 km. Every spacecraft that leaves the inner solar system lengthens the baseline. Voyager 1 is now 171.9 au from the Sun; even so, it is less than a thousandth as far out as Proxima (about 1/1,560).⁹

Turned around, parallax is a navigation instrument. If you already know where the stars are (Gaia gives their directions to a few hundredths of a milliarcsecond at its 2016 reference epoch, a few tenths by 2020 for these fast-moving stars), then their apparent positions tell you where you are.

The 2020 experiment

New Horizons carries LORRI, a 20.9 cm telescope with a 1024×1024 CCD. For these observations it ran in 4×4-binned mode, giving 4.08″ pixels across a 17.4′ field. That is a coarse, undersampled camera for astrometry; it was built to photograph Pluto. On 22–23 April 2020 it imaged the fields around Proxima Centauri and Wolf 359 twice each in a 28-hour window, at three exposure lengths. Telescopes at Siding Spring, Australia and Mount Lemmon, Arizona imaged the same fields from Earth.¹

Each star's position was measured against Gaia reference stars in the same frame: about 230 for Proxima's crowded field, 14 to 18 for Wolf 359's sparse one. Measuring within the frame matters, because effects that shift the whole field cancel. The spacecraft's 13.97 km/s motion shifts the stars' apparent directions by 8.8″ and 7.3″ (stellar aberration), but the differential effect across the frame is 0.010″.¹

The "expected" values come from Gaia DR3 and JPL's ephemeris: the answers in the back of the book, as the authors put it. The authors call their measurements "not of research grade", but you can see the effect directly: the same star is in two different places for two observers at nearly the same moment.¹

From two directions to a position

A navigator doesn't need Earth's images at all. The spacecraft measures the direction to each star; the catalogue gives each star's position in space. A direction and a point define a line, the line of position, and the spacecraft must be somewhere on it. With two stars, it sits where the two lines (nearly) cross.

Every measured direction has an error σ, so each line can slide sideways. How far? A line anchored at a star a distance d away, tilted by an angle σ, moves by d·σ at the spacecraft's end. Put d in parsecs and σ in arcseconds, and the units fall out neatly:

This identity is simply the definition of the parsec run backwards. In Lauer and colleagues' words, it is "the distance for which a 1″ error in direction causes a 1 au transverse displacement of the line of position".¹ It explains almost everything that follows. Nearer stars make better beacons; a one-arcsecond camera looking at Proxima knows its position across the line of sight to about 1.3 au.

To combine stars, minimise the weighted squared distance from the spacecraft to every line. With s_k the star's position, p_k its distance and d̂_k the measured direction:

Q_k projects onto the plane perpendicular to the line of sight, so each star constrains only the two directions it can actually see. The covariance of the fix is σ²(ΣQ_k/p_k²)⁻¹. This is the formalism of Lauer et al., §3.1, following Kaplan (2011).¹ It is a linear least-squares problem, about twenty lines of NumPy.

Reproducing the fix

We took the two directions LORRI observed and the Gaia DR3 positions propagated to the observation date, all from the paper's Table 2. We took the stars' distances from Gaia DR3 parallaxes and used σ = 0.18″ per star, the paper's figure for six images. Then we solved Equation 3.

Our error ellipsoid has semi-axes of 0.442, 0.233 and 0.206 au, against the paper's 0.44, 0.23 and 0.21, with the long axis pointing roughly toward Proxima. The true position lies 0.95σ from the fix (the paper: 0.94σ). In plain terms, New Horizons located itself to about a third of the Earth–Sun distance, and placed its direction from the Sun within a quarter of a degree in both right ascension and declination.¹

Which stars to use

Equation 2 says to use the nearest stars. Geometry adds a second rule: the lines must cross at a healthy angle. Two stars in nearly the same direction give nearly parallel lines, which cross anywhere along a long stretch. The long axis of the error ellipsoid grows without limit as the separation approaches 0° or 180°. For two stars, the short axis doesn't care about the angle at all:

Recomputing every pair of the nearest usable stars from Gaia DR3 reproduces the paper's Table 4 to within 0.01 au/″:

Proxima Centauri and Barnard's Star, the two nearest stars after α Centauri A and B, are the best pair by a wide margin: 1.91 au per arcsecond. Proxima and Wolf 359, the pair actually used, is second at 2.45. The paper chose Wolf 359 because, seen along New Horizons' outbound direction in April 2020, Barnard's Star's baseline was foreshortened and its shift would have been smaller.

Two candidates are conspicuously missing. α Centauri A and B, and Sirius A, are brighter than Gaia's bright limit (G ≈ 3) and have no Gaia DR3 entries. A science camera exposing for faint reference stars would saturate on them anyway.^1,4 Another conclusion from the paper runs against intuition: with a fixed observing budget, "it is almost always more efficient to repeat an image of a closer star that has already been used, rather than to add an image of a third more distant star."¹ Bailer-Jones's 2021 analysis finds accuracy improving as 1/√N with more stars. That is not a contradiction. Bailer-Jones adds measurements as he adds stars, measuring angles between star pairs for a craft 0.1–10 ly out; Lauer et al. ask how best to spend a fixed number of images near the Sun.²

The error budget

Almost all of the error comes from one place: how well a small, coarse camera can centroid a star. Everything else is far smaller.

The third row is the elegant one. Gaia knows Proxima's distance to ±17 au, which sounds alarming when the answer is wanted to a fraction of an au. But an error in distance slides the star along the line we are measuring, so the line of position stays put. What matters is the star's position across the line of sight, and Gaia gives that to a fraction of a milliarcsecond.

How good can it get?

Because the error scales linearly with angular precision, the path to better fixes is mostly better cameras. Lauer et al. project 0.17 au from LORRI itself, with four times as many images and Barnard's Star in place of Wolf 359. A diffraction-limited telescope with a Nyquist-sampled detector, measuring to a few milliarcseconds, could reach about 0.01 au.¹ That is still far from radio tracking, as Figure 6 shows.

Radio wins by about six orders of magnitude,¹⁰ but only while a network of large dishes is listening. For a probe beyond the reach of tracking stations, or one that must make decisions faster than a round-trip light time allows, a camera and a catalogue are enough to know where you are to within an au or so. The camera is flight-proven; the processing has so far been done on the ground. X-ray pulsar navigation (NASA's SEXTANT, under 10 km) is the other autonomous candidate. As of 2025 it had been demonstrated only in low Earth orbit.^1,6 A 2026 study by Franzese simulates star-based navigation for the trajectories of Voyager, Pioneer and New Horizons, and finds sub-au accuracy out to 250 au.⁵

Checking our own datasheet

YS·NAV 7's datasheet listed its position fix as ±0.02 light-years. The pair geometry lets us check that in one line. 0.02 ly is 1,265 au. With the best pair near the Sun, Proxima and Barnard's Star at 1.91 au per arcsecond, that fix needs pointing good to about 660″, or 11 arcminutes. That is roughly a third of the Moon's apparent diameter.

Bailer-Jones notes that 1″ "can easily be achieved" by commercial star trackers, but those work on bright stars; Proxima and Barnard's Star are around magnitude 9–11.^1,2 A camera that reaches 1″ on stars that faint (LORRI already does better) gives about 1.9 au, or 0.00003 light-years. Labelled as a position fix, our figure was about 660 times looser than the geometry requires.

The number wasn't wrong so much as mislabelled. ±0.02 ly is what we guarantee for the whole crossing: decades of catalogue drift, dead reckoning between fixes, and a camera offline. A live fix is a different and much smaller quantity. The datasheet now lists them separately:

See the Navigation Systems datasheet.

One thing does get harder on a long crossing: the reference stars change. Proxima is the best beacon only near the Sun. Far out, the best beacons are whichever catalogue stars are nearest the ship, and Equation 2 still applies with those distances. The catalogue's transverse accuracy degrades slowly; Bailer-Jones notes that with Gaia's proper-motion accuracy of 0.02 mas/yr, catalogue positions degrade by only 2 mas in a century.²

Try it yourself

You don't need a spacecraft to test any of this. The geometry works at any scale, and Equation 2 tells you in advance how well a setup can do: error equals distance to the reference times pointing error. Here are three experiments, from an afternoon to a season. The planning script plan_experiment.py predicts the result for your own setup before you build anything. The figures below are its estimates, not measurements.

Level 1 · A tabletop model (an afternoon)

• The stars: two small LEDs 3–4 m away, well apart in direction, positions measured with a tape measure.
• The sky behind them: anything much farther away, such as rooftops or streetlights through a window, at least a hundred times the LEDs' distance. The camera measures each LED against this background, as LORRI measured stars against Gaia field stars. A nearer background has its own parallax, a small version of the 0.79″ field star in the error budget.
• The spacecraft: a phone or webcam on a tripod. Photograph, move the tripod, photograph again, and solve Equation 3 for each position.
• What to expect: at 30″ of pointing precision, about 0.7 mm (1σ), with 95% of fixes within 1.5 mm. Lens distortion is the usual limit: calibrate the camera, or keep the LEDs near the centre of the frame.

Level 2 · Navigate Earth by its own parallax (a season)

• The idea: Earth's orbit is a 2 au baseline. Barnard's Star (parallax 0.547″, Gaia G = 8.2) and Lalande 21185 (0.393″, G = 6.6) are bright, nearby, and 98° apart on the sky, close to the ideal geometry.³ Measure where they sit against background stars over several months, then solve for where Earth was in its orbit on each night.
• Equipment: a 20–30 cm telescope and an astronomy camera, or time on a robotic telescope network such as Las Cumbres Observatory, whose 0.4 m telescope took the paper's Earth-side Proxima image.¹ Plate-solve against Gaia reference stars.
• What to expect: averaging many frames to 0.05″ per star gives a 1σ long axis of 0.13 au (median simulated error 0.15 au). That locates Earth to about a seventh of its distance from the Sun, using only starlight.
• Watch for: atmospheric blur of a few arcseconds, which many frames average down. These red stars refract differently from bluer field stars, so use a red filter and observe at a similar height in the sky each time. Barnard's Star moves 10.4″ a year across the sky, so propagate Gaia's proper motions to each night.

Level 3 · See the 2020 shift with your own eyes (a few nights)

• The LORRI images and the authors' notebook are public on Zenodo.⁷ Blink a spacecraft frame of Wolf 359 against an Earth frame from the same April 2020 nights, and the star jumps about 15.7″ against the same background stars.
• Want to use your own Earth image instead? Wolf 359 (G = 11.0, near the celestial equator, so visible from both hemispheres) moves 4.7″ a year across the sky, about 30″ since 2020. Propagate its Gaia proper motion back to the spacecraft's epoch before comparing, or the drift will swamp the parallax.³
• This reproduces the parallax, not the navigation, but it is the most direct way to see it.

Limits of this note

• We reproduce the paper's solution from its published directions; we did not re-measure the LORRI images. Those images and the authors' notebook are public on Zenodo.⁷
• σ = 0.18″ per star is itself uncertain by about a factor of two, per the paper. Our ellipsoid scales linearly with it.
• Our pair geometry uses Gaia DR3 positions at J2016.0 and ignores the small drift of separation angles over a few years. Our Figure 4 curves place a second star at a fixed distance and vary only its angle, an idealisation.
• Quotes are from the arXiv version of Lauer et al. (v1), not compared line by line with the typeset AJ article.
• The radio-tracking entries in Figure 6 are an order of magnitude only: we scaled a per-measurement ΔDOR error to 47 au, while real orbit determination combines many passes with a dynamical model.

References

1. T. R. Lauer, D. H. Munro, J. R. Spencer, M. W. Buie, et al. "A Demonstration of Interstellar Navigation Using New Horizons." The Astronomical Journal 170(1):22, 2025. doi:10.3847/1538-3881/addabe; arXiv:2506.21666.
2. C. A. L. Bailer-Jones. "Lost in Space? Relativistic Interstellar Navigation using an Astrometric Star Catalog." PASP 133(1025):074502, 2021. doi:10.1088/1538-3873/ac0774; arXiv:2103.10389.
3. Gaia Collaboration, A. Vallenari, et al. "Gaia Data Release 3: Summary of the content and survey properties." A&A 674:A1, 2023. Values from VizieR I/355/gaiadr3, queried 2026-10-03.
4. ESA. Gaia Data Release 3 overview (bright limit G ≈ 3). cosmos.esa.int/web/gaia/dr3.
5. V. Franzese. "Star-based Navigation in the Outer Solar System." arXiv:2603.06247, 2026; accepted to the Journal of Guidance, Control, and Dynamics.
6. J. W. Mitchell, L. M. Winternitz, M. A. Hassouneh, et al. "SEXTANT X-Ray Pulsar Navigation Demonstration: Initial On-Orbit Results." AAS 18-155, 2018. ntrs.nasa.gov/citations/20180001252.
7. Lauer et al. data and notebook, Zenodo. doi:10.5281/zenodo.15359866.
8. IAU. "Measuring the Universe" (parsec, light-year), and IAU 2012 Resolution B2 (au = 149 597 870 700 m). iauarchive.eso.org/public/themes/measuring; IAU2012_English.pdf. The parsec as exactly 648 000/π au: E. E. Mamajek et al., arXiv:1510.06262.
9. JPL Horizons, Voyager 1 (−31), 2026-10-03 00:00 UT: 171.93 au from the Sun. ssd.jpl.nasa.gov/horizons.
10. JPL. DSN Telecommunications Link Design Handbook 810-005, Module 210 Rev. E, "Delta Differential One-way Ranging" (1.9 nrad, 281 m at 1 au), and Module 203 Rev. D, "Sequential Ranging" (~1 m). 210E.pdf; 203D.pdf.

Reproduce

Every computed number in this note comes from parallax_fix.py; values quoted from the literature (Figure 1's measured shifts, Figure 6's other methods) are entered, with their sources, in build_figures.py. You need Python 3.10+ and NumPy; it runs in about a second.

python code/ys-en-0002/parallax_fix.py      # solve, Monte Carlo, pair geometry → results.json
python code/ys-en-0002/build_figures.py     # rebuild the figures in this page

• parallax_fix.py: line-of-position least squares, inputs with their sources
• results.json: every computed value
• plan_experiment.py: predict the accuracy of your own experiment
• build_figures.py and svgchart.py: figure generation
• LICENSE: the scripts are MIT-licensed. Use them freely, keep the notice; they come with no warranty

Changelog

• 2026-06-05Rev 1. First publication. The datasheet check in §8 led us to split YS·NAV 7's "position fix" into a live fix (±0.01 au) and a course hold (±0.02 ly).
• 2026-10-03Rev 2. Gaia DR3 and Horizons values re-queried; references re-checked.