This report investigates a question prompted by curiosity: as the Solar System moves through the Milky Way, could our changing viewpoint help us observe different planetary systems? It describes what the simulation calculates, what the current results mean, and what evidence would be needed for a stronger conclusion. Neighbouring stars move too, so relative motion is central to the question. This project asks how their relative motion changes distances, directions and opportunities to observe exoplanets. We distinguish three questions: how far we move from a fixed spatial reference; how far we move relative to a particular star; and whether the resulting geometry improves a specified detection method. These are different calculations. The demonstration combines a 250-million-year illustrative Galactic orbit model, a published-input Proxima Centauri case study, and a simple transit-geometry experiment. It does not forecast a number of newly discovered or habitable planets. A new Gaia DR3 experiment adds 1,387 selected sources, correlated astrometric errors and a four-scenario comparison of century motion and instrument thresholds. It finds a small, threshold-dependent motion contribution in a standardised planet-injection experiment. This is single-visit accessibility, not a mission discovery forecast.

Original conceptual illustration reproduced from the supplied discussion note. Named arms, arrows and A/B/C epochs explain the question; they are not a measured future map or an external photograph. Its underlying image provenance is not independently established here. Quantitative trajectories use the separately documented model.

Are stars moving with us? Many nearby disk stars share broadly similar Galactic rotation, but not the same three-dimensional velocity. Their relative positions change. A star's own mass does not set its acceleration in the smooth Galactic potential: gravitational and inertial mass cancel in the test-particle equation. Location, velocity, orbit history and the Galaxy's mass distribution matter. Mutual gravity matters for bound systems and close encounters.

Will 250 million years give us a different sky? Yes, but not because we travel through stationary stars. Both observer and targets move. With our assumed 8.2 kpc radius and 233 km/s circular speed, one nominal Galactic period is about 216 million years. After roughly one revolution the Sun is again near the starting azimuth; its neighbours need not be the same. A travelled path length alone cannot tell us which target becomes closer.

Could that help us detect planets? It can change apparent brightness, angular separation and transit alignment. Whether that helps depends on the instrument, observing schedule and system geometry. We can already point telescopes in different directions without waiting for Galactic travel. NASA's exoplanet archive displayed 6,451 confirmed planets, dated 15 October 2026, when checked on 24 October 2026. This is a dated catalogue count, not an estimate of all planets that exist. Kepler's concentrated fields and TESS's much broader sky survey also make it incorrect to treat the catalogue as one fully explored patch of space. [1–3]

Is Proxima approaching? Yes. In our historical-input calculation it is approaching along the line of sight at about 22.2 km/s, while also moving sideways. Its full relative speed is about 32.5 km/s. It does not share exactly the Sun's velocity. The interactive case below shows the distinction.

Would getting closer make a planet habitable? It could improve observations of that planet; it would not by itself establish habitability. A planet's environment depends primarily on its host star, orbit, atmosphere and other physical properties. A habitable-zone classification is not evidence of a habitable surface or life. [4]

Let the Galaxy-centred coordinates be non-rotating within the adopted Newtonian model. Subscript S denotes the Sun, E the Earth proxy, and j a target star. Bold symbols are vectors.

The main Galactic view cannot resolve Earth's AU-scale orbit inside a kiloparsec-scale scene, so the observer there is the Solar System marker. The close-up uses the Earth–Moon barycentre approximation documented in the model notes.

Negative radial velocity means decreasing distance; positive means increasing distance. The transverse component changes the direction on the sky:

For a small angular change and nearly constant distance, the scale is:

This expression must use relative transverse speed. Substituting the Sun's 233 km/s Galactic speed would wrongly treat the target as stationary. The original discussion note's example, 30 km/s transverse relative speed at 100 light-years over 100 years, gives approximately 20.64 arcseconds.

Why a common Galactic velocity cancels

If we add the same constant velocity to both target and observer, their relative velocity stays unchanged:

That is why a large absolute path length need not give a large change in the exoplanet sky. Equal initial velocities at different Galactic positions do not guarantee constant separation forever: their accelerations can differ.

We use the historical astrometry and corrected radial velocity tabulated by Kervella, Thévenin & Lovis (2017), Table 2. This input set is reproducible; it is not presented as the latest astrometric solution. [5]

We construct orthonormal ICRS basis vectors along the line of sight, increasing right ascension and increasing declination. With parallax and proper motions expressed in the same angular units:

The factor 4.74047046 converts one AU per Julian year to km/s. The initial vector is propagated from 1991.25 to the model year 2026, then the interactive calculation holds its relative velocity constant. Time and velocity are converted consistently to years and pc/year:

These closest-approach equations describe an unconstrained straight-line trajectory. A negative minimum time would mean a past encounter; the Proxima result is positive.

The last two rows hold luminosity and a projected physical separation fixed. They are geometric factors, not a prediction of telescope signal-to-noise or planetary phase. A roughly 1.87-fold flux increase is modest compared with an arbitrary future improvement in instrumentation; this calculation supplies no reason to postpone observations.

Limits: Proxima is bound to Alpha Centauri AB. The linear illustration omits that orbital acceleration, Galactic tides and solar/stellar mutual deflection. Its input uncertainties are recorded but not propagated, so the table is not a confidence interval or a precision encounter forecast. We restrict the interactive illustration to −50,000 through +100,000 years, and do not extend it to 250 Myr. The projected plot lies in the plane spanned by the initial relative position and velocity. Adding the Sun's common Galactic translation would move both tracks without changing their separation in this linear approximation.

The Sun and three synthetic, explicitly illustrative targets follow the same smooth axisymmetric potential. The targets are not Proxima, named catalogue stars, or confirmed planetary systems. Their initial offsets and velocity assumptions are supplied in stellar-motion.cjs and data/synthetic-tracers.json.

The disk is Miyamoto–Nagai, the bulge Plummer, and the halo spherical logarithmic:

Here the logarithm's reference scale is 1 kpc and only changes the zero of potential. We adopt disk mass 6.8×10¹⁰ solar masses, a=3 kpc, b=0.28 kpc, bulge mass 5×10⁹ solar masses, c=0.5 kpc and halo core radius 12 kpc. The halo amplitude is calibrated to circular speed 233 km/s at 8.2 kpc. The Sun starts at (0, −8.2, +0.020) kpc with velocity (−233, 0, +7) km/s. These are illustrative assumptions, not a Gaia fit. Coordinates and sign conventions are in MODEL_NOTES.md.

We integrate with a kick–drift–kick leapfrog at 0.01 Myr steps. The exact initial state is shared with the century model. Gold traces the Sun; coloured labelled markers show separately integrated synthetic targets. The sidebar reports separation and relative speed for the selected example. The star's own mass is absent from this external-potential equation. The Galaxy's distributed gravitational field matters; orbiting the Galactic centre is not the same as orbiting a lone central point mass.

This particular example set separates over the full interval. It is not a representative sample and cannot establish a Galactic encounter rate, a future nearest-neighbour catalogue or a discovery yield. Their motion nevertheless demonstrates why the observer alone is insufficient. The visible Galaxy uses the ESA/Gaia artist’s reconstruction, with illustrative depth and warp; the separate cyan layer contains measured VLBI positions at catalogue epochs. Optional pattern rotation is schematic. The visual reconstruction is not a set of integrated individual stars. See section 16 for data provenance and limits; [6] documents the artwork.

The Sun travels about 59.57 kpc over 250 Myr but ends about 7.70 kpc from the 2026 fixed reference. At the nominal 216.21 Myr circular period it has travelled about 51.52 kpc and is about 0.062 kpc from that reference. Path length, displacement and star–observer distance must remain separate quantities.

Direct imaging and brightness

For fixed luminosity L and projected planet–star separation a_perp:

A closer star usually gives more photons and a larger angular planetary separation. It does not automatically improve planet/star flux contrast, since the two fluxes share essentially the same observer distance. A practical model needs instrument throughput, inner working angle, contrast performance, backgrounds, stellar variability and planetary phase.

Transits

Let the planet's orbital angular-momentum unit vector be h and the host-to-observer direction be n. For a circular orbit of radius a, stellar radius R_star and planetary radius R_p:

This is a conjunction geometry test, not a transit light curve or a claim that a transit occurs at the slider's exact time. Orbital phase and an observing window are also needed. For eccentric systems the usual conjunction-distance correction depends on eccentricity and argument of periastron. The toy control uses a circular 1 AU orbit, a Sun-sized host and an Earth-sized planet; it is not a Proxima b orientation model. Its angular half-width is about 0.269°. A change of sightline can move a system into or out of that band. Getting closer alone does not guarantee a transit, and fractional transit depth remains approximately (R_p/R_star)².

Radial velocity and other methods

The Keplerian stellar reflex amplitude is:

It has no direct observer-distance term. Brightness affects measurement precision, while viewing inclination affects the projected velocity. Astrometric reflex angles scale inversely with distance; microlensing instead requires a suitable changing alignment with a background source. A selection function must be specific to the detection method.

Habitability is a separate inference

No control here turns a geometrically accessible planet into a demonstrated habitable world. Proxima b already exists as an observationally detected exoplanet; its habitability cannot be established from our changing distance. It has been independently confirmed with ESPRESSO measurements, and atmospheric survival and stellar activity remain relevant scientific questions. [4,7] This project makes no claim that Proxima b has an atmosphere, liquid water or life.

The broad idea that stellar motion changes transit viewing opportunities is already established in the literature. Kaltenegger & Faherty (2021) propagated nearby stars through a 10,000-year interval to identify changing opportunities to see Earth transit the Sun. That is a reciprocal viewing-geometry study, not a prediction of how many exoplanets our future observers will discover. It is directly relevant precedent. [8]

Bailer-Jones and colleagues (2018) studied stellar encounters with the Sun using six-dimensional Gaia DR2 data, integrating Galactic orbits and propagating correlated measurement uncertainties. That workflow illustrates what a scientifically defensible encounter calculation needs. It is not evidence that our three synthetic targets are actual predicted encounters. [9]

The project began as a transparent educational implementation and a focused community discussion question, originating in Biswajit Jana's supplied note. It connects fixed-reference displacement, relative stellar motion and detection geometry in one inspectable demonstration. No priority claim is made for the general physical principle, and the present code has not established a new planet or a new detection opportunity for a particular real planetary orbit.

1. Select a dated stellar catalogue and documented quality cuts. Obtain positions, parallaxes, proper motions, radial velocities, covariance matrices and binary-system information. Missing radial velocities must not silently become zero.
2. Transform all stars and the Sun into a consistent frame and epoch. Integrate full systems where required, including Proxima–Alpha Centauri binding. Sample uncertainties and alternative Galactic parameters.
3. Model evolving Galactic structure, encounters and stellar evolution when the timescale demands them. A static smooth potential can be numerically accurate while physically inadequate over 250 Myr. Do not infer a universal prediction horizon from a small integration error.
4. Supply planetary orbital orientations, eccentricities and evolution, or an explicitly statistical distribution when those are unmeasured. A sky-direction change alone is insufficient to predict transit entry for an unknown orbital plane.
5. Define actual instruments and observing schedules. Separate pure geometric gains from improvements in technology, survey coverage, extinction, target availability and selection bias.
6. Validate against independent astrometry/orbit software and published encounter cases. Report posterior distributions, sample completeness and sensitivity to model choices, not just a single future animation.

Section 11 now implements a first catalogue experiment: a dated nearby-source selection, full five-parameter covariance plus independent RV errors, century propagation, a specified threshold model and paired instrument comparisons. The requirements above remain relevant to a full mission forecast; binary dynamics, observatory scheduling and realistic planetary demographics are not solved by this first experiment. The 250 Myr scene supplies Galactic context; it is not the appropriate precision forecast for Proxima's next encounter.

The cyan 2026 marker is a fixed coordinate, initially at the Earth proxy, in the chosen Galactic frame:

A passive spacecraft inherits its release velocity and accelerates under gravity. Holding it at a fixed coordinate would require cancellation of inherited velocity and continued force compensation. The simulation does not demonstrate that such a mission is feasible. There is no universal absolute-rest location. A useful spacecraft need not remain fixed: New Horizons and Earth measured stellar parallax from separated observing locations. A future probe extension should compare a feasible trajectory and measured baseline against existing astrometry; this project does not supply a propulsion or navigation design.

The reference is a place, not a preserved moment in time. Looking toward it does not show the year 2026 indefinitely. The century view's distance/c readout is an instantaneous geometric light-time scale, not a solution of retarded emission times. Earth plus Solar motion gives a winding spatial path in some frames; it is not a universal helix through spacetime.

Run npm ci, npm run build and npm test using Node.js 22.12 or newer. Build output embeds application assets and pre-rendered mathematical markup; no online library is needed to use the downloaded HTML. data/proxima-input.json preserves the cited input set. stellar-motion.cjs defines its unit conversions, rectilinear propagation, synthetic tracers and transit geometry. stellar-results.json and the exported CSV preserve derived values.

The new research tests also check all catalogue covariance decompositions, source identifier integrity, phase-integrated accessibility, paired epoch-zero controls, threshold monotonicity, warp velocities and exact reproduction of the saved experiment. Tests check astrometric basis reconstruction, radial/transverse decomposition, closest-approach stationarity, common-velocity cancellation, transit boundaries, Galactic integration conservation/convergence and data exports. Existing tests also compare approximate planetary states with archived JPL Horizons samples. These checks establish limited implementation consistency; they do not validate omitted physics or the long-term future of named stars. Detailed historical checks and current results are supplied in AUDIT.md and the validation JSON files.

• Which parts of this question are already answered by existing transit-zone, encounter, astrometric or direct-imaging studies? Which references should be added?
• Which measurable detection opportunity could change appreciably because of relative motion, with today's instrument capabilities held fixed?
• Which selection biases and unresolved binaries most affect the supplied Gaia DR3 sample? Does the source ranking survive a more complete nearby-star catalogue?
• What uncertainty treatment and comparison case would make the Proxima example scientifically useful?
• Over what timespan does a deterministic calculation stop being informative for the chosen observable?
• What findings would show that this proposed observing advantage is negligible?

Please distinguish corrections to the implementation, corrections to the physics, and possible research extensions. Reports of errors and relevant published answers are especially welcome. Feedback can be submitted through the repository's issue templates. This report does not imply endorsement by any scientist or institution.

A. Start with the Galactic view

1. Open the website or downloaded Moving_Observer_2026.html. The initial scene is Milky Way, paused at the 2026 origin. The long clock covers 250 million years; Myr means one million years.
2. Click Play Galactic journey or Play. Gold marks the Sun and its elapsed path. The cyan reference stays at its 2026 Galactic coordinate. The timeline slider selects an epoch; 2026 resets the active clock. Playback speed changes how many model years pass per real second; it does not change the equations.
3. Compare Distance travelled with Sun → fixed 2026 reference. The first is accumulated path length; the second is straight-line separation. Jump to ≈ one Galactic orbit illustrates why they differ: the Sun can return near its starting location after travelling a long distance.
4. Use Plane view for the disk from above, Edge-on for thickness, or Reset camera for the initial perspective. Drag to rotate and scroll or use Zoom + / − to change magnification. Plane guides and Object labels can be switched off.
5. Evolving outer-disk warp controls a sourced-scale kinematic surface. Use Edge-on to inspect it; the Solar-height plot separately reveals vertical oscillation. Animate disk pattern controls schematic rotation of the illustrated Galaxy. It does not control the integrated Solar orbit. Enhance arm contrast changes display brightness and haze; it does not change stellar density or the gravity model.

B. Compare the Sun with moving stars

1. In the right-hand controls, scroll to Moving stars. On a narrow screen first open Controls.
2. Keep Show illustrative stars enabled. Select Illustrative A, B or C under Compare with the Sun. Each coloured marker has an independent integrated orbit.
3. Move the Galactic timeline and read Star–Sun separation, Relative speed and Radial speed. Negative radial speed means approaching; positive means separating. Total relative speed is a magnitude and is never negative.
4. Compare the target separation with the Sun-to-reference readout. A changing distance to a moving star cannot be inferred from the fixed-reference baseline alone. These three examples are invented initial states, not a real-star catalogue or a planet-discovery prediction.

C. Explore the Proxima question

1. Click Research report, then Proxima lab in the report contents, or click Is Proxima approaching? in the Galactic sidebar. The report is a separate reading view within the website; Return to simulation brings you back.
2. In the lab click 2026. The distance is about 4.240 light-years, radial velocity about −22.19 km/s, and total relative speed about 32.51 km/s. Read Approaching alongside the signed radial value.
3. Click Closest approach. In this linear approximation the minimum is about 3.099 light-years, roughly 26,700 years after 2026. Radial speed reaches zero at the minimum, while sideways motion and total speed remain nonzero.
4. Click +100,000 years. The star is receding. Scrub the slider to compare the encounter-plane diagram with the distance-versus-time curve. The graph removes the Sun's shared Galactic motion; it is not the Milky Way map.
5. Read the flux and angular-separation ratios. They assume constant luminosity and constant projected physical separation. They are not detection probabilities or estimates of habitability.
6. Use Export Proxima CSV to download the full −50,000 to +100,000-year calculation at 100-year intervals. The source measurements, epoch conversion and omitted physics are documented in this report and data/proxima-input.json.

D. Test transit alignment

1. In the Proxima lab expand Test a transit viewing angle. This control is a separate invented Earth–Sun analogue, not an orbital orientation measurement for Proxima b.
2. Move the angle toward 0°, meaning the observer lies in the orbit's plane. The control reports that transit geometry is possible.
3. Move beyond about ±0.269°. The observer leaves this example's transit band. The displayed impact parameter and threshold explain the change.
4. Remember that this is a geometry test. A real observation also needs the correct planetary phase, observing time and sufficient measurement precision.

E. Inspect the century experiment and Earth's path

1. Select 100 years in the Galactic view to see how tiny a century's motion is at whole-galaxy scale. Select 2026 reference to resolve that same baseline in AU.
2. Move the century clock to 2126. The Earth-to-reference separation is about 4,917 AU in this assumed model. The cyan marker is a hypothetical fixed coordinate, not a passive spacecraft.
3. Select Compare a passively released probe to display the separate simplified tracer that inherits Earth's initial motion. It remains near the Solar System rather than staying at the starting coordinate.
4. Select Earth & Sun to resolve the inner orbits. Entry selects 0.1 yr / s. Faster playback can visually undersample planetary orbits.
5. Enable Show Earth’s path through Galaxy to see the sum of Earth's orbit and Solar translation. If the clock is earlier than 2029, enabling this control advances it to 2029 so a three-year trail is available. Blue is Earth's spatial path; gold is the Sun's. The distances are not stretched into a decorative helix. Turn the option off to return to the Earth-orbit framing.
6. The century and Galactic clocks retain their own times. Changing views pauses playback. They do not turn a million-year epoch into a planetary ephemeris millions of years beyond its valid range.

F. Export and request review

• Export CSV in the main simulation downloads either 501 Galactic samples or 101 century samples, according to the active clock. This main export describes the observer/reference model; the three synthetic target initial states and endpoint results are in data/synthetic-tracers.json. The report lab has its own Proxima CSV export.
• Save image downloads the current 3D scene with epoch, units and attribution. Labels and enlarged markers are display annotations.
• Print / save PDF in this report opens the browser's print dialogue. Choose its PDF destination if you want a document copy. The interactive controls become a static snapshot at their selected state.
• Use GitHub & feedback to inspect source, data and tests, or open a scientific-feedback issue. When requesting review, state which claim or result you mean, its frame, units and epoch, and whether you are asking about geometry, measurement capability or habitability.

Question and contribution

For a fixed nearby-source sample, how does century-scale relative motion change single-visit direct-imaging accessibility, and does that change survive a different instrument threshold? We test this question with a frozen Gaia DR3 sample and paired calculations, instead of converting the Sun's Galactic travel into a discovery count. The deliverable is a reproducible, source-by-source sensitivity experiment, including cases that become less accessible. This is an exploratory contribution, not an established priority claim or a new exoplanet detection.

Data and scope

The ESA Gaia Archive query on 24 October 2026 returned 1,387 sources with parallax at least 50 mas, parallax signal-to-noise greater than 20, a measured radial velocity, RUWE below 1.4 and at least ten visibility periods. The frozen CSV, exact ADQL, retrieval script and checksum are distributed with the code. Identifiers retain their full integer precision. See Gaia DR3 and the data provenance.

The sample is selected, not volume-complete: RV availability and quality cuts exclude many stars and can favour particular stellar types. RUWE filtering does not eliminate all binaries. A Gaia source is not necessarily an independent planetary system. Sources outside the original cut do not enter this fixed-sample experiment. We do not treat the artwork's rendered particles as catalogue data.

We propagate barycentric Cartesian positions at constant relative velocity from J2016.0 to 2026.0 and 2126.0. Radial motion, transverse motion and perspective geometry are retained. This is an instantaneous geometric calculation, not a light-cone or relativistic astrometry solution. Annual Earth parallax, Galactic differential acceleration, binary orbits and stellar variability are omitted. Century-scale application is deliberate; it must not be extrapolated to 250 Myr.

A deliberately controlled planet and instrument model

Each source is assigned the same hypothetical circular 1 AU orbit, Earth radius and geometric albedo 0.3. Orbital orientations and phases are isotropic/random. This standardised injection isolates geometry; it is neither a list of actual planets nor a habitable-zone prescription for different stellar types. It assumes no occurrence rate. For phase angle $\alpha$, Lambert reflection and angular separation are:

The baseline thresholds are 60 mas inner working angle, a contrast floor of $10^{-10}$, and limiting planet G magnitude 30. The improved scenario uses 40 mas, 5 × $10^{-11}$ and G = 31. These are chosen sensitivity settings, not specifications or forecasts for an approved telescope. We assume grey reflection in Gaia's G band. For constant stellar luminosity, stellar magnitude changes by $5\log_{10}(d_{\rm future}/d_{\rm initial})$, and planet magnitude is stellar magnitude minus $2.5\log_{10}c$.

With isotropically distributed planet positions, $\cos\alpha$ is uniform. We solve the simultaneous angular-separation, contrast and magnitude inequalities to obtain the allowed phase interval $[\alpha_{\min},\alpha_{\max}]$. The resulting single-visit accessibility is:

This marginalisation removes dependence on the absolute sky direction for an isotropic population. It therefore measures distance/brightness and separation-threshold effects, not entry into transit bands for known orbital planes. The two epochs use the same population distribution; we do not claim to follow the orbital phase of an individually known planet.

Paired experiment and uncertainty

Let $S$ be the sum of $C$ over the fixed sample. The first index below denotes present/future geometry; the second denotes baseline/improved thresholds:

All four evaluations share the same star and astrometric draw. We use 1,024 draws per source, with a fixed random seed, the full five-parameter Gaia covariance and an independently sampled RV error. The positional RA uncertainty is treated as a tangent-plane quantity, with its cos(dec) factor handled explicitly. The published intervals are the 2.5th and 97.5th percentiles of summed paired differences. They reflect formal input errors under Gaussian assumptions, not total scientific uncertainty. Cross-source correlations, parallax systematics, unresolved binaries, planet-population uncertainty and instrument-model uncertainty are absent. Reproduction is exact for the saved seed; 1,024 draws do not warrant precision in the interval tails.

Results

The baseline motion change is approximately 0.031% of the initial accessibility sum. Forty-two sources gain and 45 lose accessibility (absolute changes greater than $10^{-12}$); the remainder are unchanged under these thresholds. This is not a claim that 42 planets become detectable or that 45 planets disappear. The largest nominal absolute change belongs to Gaia DR3 762815470562110464, with +0.00350 in accessibility and a model distance change from 2.54526 to 2.53656 pc. It is a screening result, not a validated observing recommendation or confirmation of a planet around that source.

The result is threshold-sensitive: keeping contrast and magnitude cuts fixed, a 70 mas IWA produces a net motion contribution of −0.00145, whereas 60 mas produces +0.00911. This counterexample rejects the simple assertion that waiting always improves aggregate accessibility. The negative interaction means the improved thresholds reduce the marginal benefit of motion in this chosen example; it is not evidence that improved instruments perform worse overall.

What this result can and cannot establish

This experiment supplies a real catalogue, explicit selection, consistent short-time propagation, correlated astrometric uncertainty, a specified geometric detection proxy, paired controls, a sensitivity sweep and source-level outputs. An independent numerical integration over phase checks the analytic accessibility formula. Astropy 8.0.2 independently reconstructs the catalogue positions and velocities; propagated distances agree within 7.11 × 10^-15 pc at both epochs. This checks coordinates and units, not the omitted physics. The optional compare-astropy.py benchmark requires Astropy and writes data/astropy-comparison.json. The existing physics tests and a non-default integration-cadence regression test run alongside these checks.

It does not supply a mission yield. Exposure times, throughput, backgrounds, exozodiacal light, scheduling, observatory sky access, repeated visits, planet occurrence, known-planet exclusion and confirmations are not modelled. Applying an arbitrary occurrence factor to S would not solve those omissions. A future mission calculation should use a validated tool such as EXOSIMS, and compare with the instrument-dependent methods of Stark et al..

Research status and the question for the community

The literature search found established studies of proper-motion effects on transits, changing Earth-transit viewpoints, Gaia stellar encounters, and direct-imaging completeness/yields. The sources examined did not establish an identical 2026–2126, Gaia-covariance, four-scenario threshold comparison. This limited search does not prove that none exists. The methods themselves are established; the specific reproducible comparison and source ranking are this project's current contribution. See LITERATURE_SEARCH.md for the dated search scope.

Open question: after modelling binaries, realistic planets, observability and a fixed observing-time budget, does any nearby system retain a scientifically useful century-scale accessibility gain attributable to relative motion, rather than to changed instrument capability—and which prior study already answers this most directly?

Tutorial: reproduce and explore this experiment

1. Read the four scenario scores above. They use the same frozen source sample and injected planet distribution.
2. Change the IWA selector. Compare 60 and 70 mas to see the sign reversal; this control leaves the contrast and magnitude limits fixed.
3. Expand the source table to inspect the strongest absolute changes and formal uncertainty intervals. Download the CSV for all 1,387 sources.
4. In the repository run npm ci, npm run research, npm run build, then npm test. The calculation uses the local snapshot and does not need a network connection.
5. Only to refresh input data, run python fetch-gaia.py. Review the changed snapshot and regenerate results before drawing conclusions. Refreshing data is not part of the ordinary build.
6. Test an alternative instrument or injected planet in research.cjs; regenerate results and update the report's interpretation. The report table is generated from the results during the build, so the displayed numbers remain consistent.

The Galactic disk is not perfectly flat. Poggio et al. (2020) inferred a precessing warp with a model-dependent rate near 10.86 km/s/kpc. Poggio et al. (2025) report an outer-disk corrugation in stellar positions and velocities, in addition to the warp. These are evidence for vertical Galactic structure; they do not prescribe a universal corkscrew trajectory for the Sun or every planetary system.

The updated display uses an optional kinematic warp illustration, with a 700 pc height scale at radius 14 kpc and an adopted onset at 8.4 kpc. The onset, radial quadratic profile and initial phase are display assumptions. The surface precesses independently of the spiral artwork. It does not add a new gravitational force to the integrated Solar orbit. The 2025 travelling corrugation is discussed but not fitted or animated as though it were a measured future evolution.

where R is in kpc, t in Myr, and the signed precession rate in this coordinate convention is −10.86 × 0.001022712 $\mathrm{Myr}^{-1}$. A material tracer following this surface would require:

The implementation supplies and tests this derivative. It remains a kinematic description, not a self-consistent evolving gravitational model. Artwork points indicate structure, not integrated physical stars. A dynamically coupled warp requires a different potential and validation against data before being used for predictions.

The Sun already undergoes vertical oscillation in the smooth axisymmetric potential. A new height-versus-time plot makes this motion visible at its true parsec scale without artificially stretching the 3D Galaxy. Select Edge-on, enable Evolving outer-disk warp, and play the million-year clock to distinguish the two motions. Disabling the warp does not change the Solar integration.

In Sun & all planets, all eight planets can be viewed in Solar System coordinates or with Galactic translation included. A separate Solar-wobble close-up resolves the small barycentric reflex motion. Earth & Sun retains a simpler two-body viewing option. The ecliptic is oblique to the Galactic plane. The paths can look winding in Galactic coordinates, while the Sun also has a smaller, non-circular barycentric wobble caused by the planets, and the planets do not trail behind it in a single plane perpendicular to its velocity. A trajectory's appearance depends on the chosen frame. The separate Space & Time view explains weak-field gravity and clock rates using a labelled potential-grid analogy; it does not solve the Einstein field equations.

The Sun is not fixed at the centre of the Solar System. Its planets pull on it, and it moves around the system's barycentre. This is an established effect, explained by NASA's barycentre introduction. The motion is generally a changing loop, not a perfect circular helix. It is also different from the Sun's vertical oscillation around the Galactic midplane.

The new view computes heliocentric positions for all eight planets. Jupiter, Saturn, Uranus and Neptune use saved NASA/JPL Horizons positions and velocities, sampled every quarter Julian year over 2026–2126 and interpolated with cubic Hermite polynomials. The inner four planets retain JPL's approximate Table 2a elements. Thin orbit guides for all planets use approximate elements (including Table 2b corrections for the outer planets); they indicate orbital scale rather than an exact ephemeris track. The Earth marker represents the Earth–Moon barycentre, and giant-planet positions and masses represent their planetary systems. The Solar reflex position is reconstructed using gravitational mass parameters from JPL's DE440/DE441 work:

Here $\mu=GM$, B denotes the barycentric frame, and the sum includes the eight planetary systems. Pluto, asteroids and other small bodies are omitted. This construction preserves the centre-of-mass identity for the included bodies; it does not make the approximate orbital elements a full N-body ephemeris.

Independent numerical check: at six between-node dates per outer planet, the largest differences from separate Horizons requests were 611.1 km for Jupiter, 59.1 km for Saturn, 42.6 km for Uranus and 41.7 km for Neptune. These are sampled interpolation errors, not a proven bound at every date. At six further dates, the reconstructed Sun differed from the Horizons Solar barycentric position by at most 161.8 km (0.024% of a Solar radius). The omitted small bodies and approximate inner-planet inputs remain limitations. Saved requests, values and comparison code are supplied with the project; ordinary use works offline.

How to see it: open Sun & all planets. The overview shows all eight orbits. Choose Paths through the Galaxy for the sum of planetary orbits, Solar reflex motion and common Galactic translation. Choose Sun's barycentric wobble for a 30-year close-up, with the Sun's radius shown to scale. The other planets lie outside that close-up; the cyan marker is the barycentre. Path histories of 3, 12 and 84 years serve different planets, while the overall clock remains 2026–2126. Neptune needs approximately 165 years for a full orbit, so its century path does not complete a revolution.

On the Galactic view, Reveal Galactic wobble selects an edge-on camera, starts the long clock and magnifies every vertical coordinate by a labelled factor of five. The numerical distances retain their true values. Return to True proportions (1×) for an undistorted view. This exposes the integrated Solar oscillation without inventing an annual Galactic helix. The warp remains a separate kinematic illustration.

A body does not sit in a literal downward dent in space. The grid in this simulation is an explanatory picture of gravitational potential, drawn as height so that variations are visible. A real relativistic description involves spacetime geometry, with both spatial and temporal components. The connection between gravity and clock rates is experimentally established; see NIST's explanation of atomic-clock tests and Einstein Online.

Outside slowly moving bodies in a weak field, the Newtonian potential and the leading clock-rate terms are:

The displayed numerical readouts deliberately use one isolated spherical body and a stationary clock, so $v=0$. The comparison is to a clock at rest infinitely far from that body, with the potential chosen to vanish at infinity. The approximate clock lag per day is therefore:

This does not give the total rate of a real clock on Earth or a moving spacecraft. Those comparisons require the Sun's field, other bodies, rotation, orbital speed, a defined reference clock and propagation effects. Planetary masses and mean radii are sourced from JPL/NASA; the isolated Earth calculation uses Earth's mass alone, excluding the Moon. The giant-planet mass parameters include their moons, an approximation for these educational surface estimates.

The drawn wells use softened distances and a logarithmic height transform to remain visible and finite. That plotted depth has arbitrary units. Changing Visual depth only changes the drawing, never gravity or the clock calculation. The overview projects the moving Solar System into the ecliptic plane; selecting a body opens a normalized local well with horizontal distances in that body's radii. Neither the mesh nor the prescribed trajectories solve Einstein's field equations, light bending or gravitational-wave emission.

Tutorial: select Space & Time, then choose the Sun or a planet. Move Test-clock radius from one to ten body radii. Gravity falls by a factor of 100 and the isolated gravitational clock lag by a factor of ten. Compare Earth and Jupiter at the same radius multiple. Use the overview to see where the moving bodies contribute to the potential diagram. Export CSV to obtain the numerical comparisons for every body.

Same sample, different waiting times

Isolated-body surface clock comparison

The sampled Solar barycentric offset spans 93,704–1,273,966 km over 2026–2126 (1,001 samples). The smooth Galactic model travels 4917.34 AU in that century and departs from its initial straight tangent by 0.00714 AU. Its long-clock vertical oscillation spans approximately ±99 pc. These are distinct physical scales. At 1 AU from an isolated Sun, a stationary clock has a predicted lag of 852.82 microseconds/day relative to infinity.

The 10- and 100-year comparisons use the same nominal catalogue experiment as section 11. The 1,000-year row is a sensitivity extrapolation, with no new uncertainty propagation or binary integration. It must not be treated as a reliable millennium forecast. The sample remains frozen, so the table does not count newly entering stars. These values describe one hypothetical injected planet distribution and instrument setting, not the actual planets present around the selected sources.

The physical scale comparison explains why the Sun can look straight in a short trail. Its century motion spans thousands of AU, while barycentric deviations and the departure from a straight tangent are tiny fractions of an AU. Making those small motions visible requires a close-up or a clearly labelled scale change. All planets inherit the common Solar translation, while retaining different orbital periods and orientations.

Questions the community can answer without an email

1. Is the model's question well posed? What prior work most directly addresses century-scale changes in accessibility for a fixed nearby sample?
2. Which targets deserve closer study? Do the strongest changes survive binary modelling, parallax systematics and a realistic observing budget?
3. Is the effect useful? What minimum gain in observing efficiency or information would justify waiting or using a second observer?
4. Which simplification matters most? Is the first priority the planet population, instrument noise, orbit uncertainty or scheduling?
5. What would change the conclusion? Supply a target, assumptions and a reproducible counterexample where motion has a substantial advantage.

Feedback and corrections can be recorded in the public project discussion through GitHub issues. No email or outreach is required. These questions invite scrutiny of the calculation; they do not assert that a new physical principle or a previously unstudied problem has been discovered.

Display revisions: making motion legible

The Show the bend control looks along the warp line of nodes, so the vertical bend lies across the image instead of along the line of sight. Gold shows the maximum-bend section, grey its flat-plane reference, and blue rings follow the same height function as the artwork. The 5× view is labelled; 1× restores equal spatial proportions. The 2025 corrugation is distinct from this warp and has not been fitted or forecast.

Sun & all planets opens with all bodies in the winding-path view. Two presets resolve inner-planet motion over three years and all-planet tracks over 84 years. Gold marks forward Solar motion. Reference lines at 2 AU (inner) or 20 AU (all bodies) are fixed in the selected translating frame; they move past the camera that follows the Sun. The 98% co-moving frame leaves about 0.98 AU/year of residual Solar travel. Switching to the Galactic frame restores approximately 49 AU/year. These are coordinate changes, not a modification of planetary orbits.

Space & Time defaults to a circular test clock. Earth orbit presets start playback. The separate 1PN lab starts from saved JPL initial states, shows all planets by default, and begins playback after integration. Its barycentric/Sun-centred orbital views remove common Galactic translation; use the planetary winding-path view to see that separate effect.

The heliosphere is the solar-wind plasma and magnetic environment surrounding the planets. It is distinct from a gravitational sphere of influence and from Earth's magnetosphere. Solar wind and magnetic turbulence modulate Galactic cosmic rays; the amount depends on particle energy, species and solar conditions. High-energy particles still enter, and the Sun itself produces energetic particles. There is no universal shielding percentage in this simulation.

NASA describes competing global-shape models rather than an established rigid spherical boundary. Voyager 1 crossed the heliopause near 122 AU in 2012 and Voyager 2 near 119 AU in 2018, at different directions and times. These two samples do not determine the entire surface. NASA: heliosphere shape, Voyager observations and cosmic-ray modulation review.

What the envelope actually calculates

Sun & all planets → Show the heliosphere fits a Sun-centred 120 AU spherical reference surface around the system. The dashed 90 AU termination shock is another adopted scale, not a fit to either Voyager crossing. Solar-wind dots move radially at an assumed constant 400 km/s and stop at that shock. Dots recycled at the inner boundary are tracers, not a particle-density model. Beyond the shock, the wind slows and the simple radial model no longer applies. The sphere follows the Sun as a reference geometry; it does not simulate the flow response to a changing interstellar medium.

At that assumed speed the kinematic travel time to 1 AU is 4.33 days, to 30 AU 129.9 days, and to 90 AU 389.6 days. These are constant-speed estimates, not measured parcel arrival times. The reference heliopause radius is four times Neptune's approximately 30 AU orbit. Magnetic-field geometry, shocks, charge exchange, radiation doses and cosmic-ray transport are not solved. The demonstration does not insert a fictional protective force into planetary dynamics. NASA's solar-wind explanation and IMAP mission provide the observational context.

Forward travel and readable trajectories

The physical trajectory in the adopted local Galactic coordinates is the barycentric Solar-System trajectory plus common Galactic translation. The translating display frame subtracts a velocity, not a distance scale:

For 233 km/s and $f=0.98$, the residual forward speed is 4.66 km/s, approximately 0.983 AU/year. All simultaneous relative positions are unchanged: $\mathbf x'_i-\mathbf x'_j=\mathbf r_i-\mathbf r_j$. Thus winding paths become legible without stretching orbits. Earth & Sun uses this 98% frame for its forward-path option; Sun & all planets also offers the full Galactic frame. The camera stays fixed at its entry epoch unless Follow Sun with camera is enabled. Reset camera re-centres it. Over long playback objects can naturally leave a fixed camera's field of view.

The gold Solar trail includes mass-weighted planetary reflex motion in Sun & all planets. Earth & Sun uses the smooth Solar reference trajectory. Planetary trails are limited to two revolutions by default to reduce overplotting; uncheck that option for the selected full history. This truncates displayed history, never orbital coordinates. The Moon uses an illustrative circular orbit; select its close-up to resolve it. Body sizes are enlarged outside that close-up and the Solar-wobble view.

Entire Solar System in Space & Time

The default view contains the Sun, eight planets and an illustrative Moon at their three-dimensional barycentric positions, rotated into ecliptic axes. Its years clock advances all bodies. Selecting an individual body switches to the separate one-day clock. The optional potential sheet is an analogy with arbitrary depth; bodies remain at their physical positions and do not sink into that sheet.

At the displayed test point, fixed at $(0,0,1)$ AU in barycentric ecliptic coordinates, all ten masses contribute:

The readout is the instantaneous weak-field rate of a clock held at that coordinate point, relative to the isolated-system asymptotic coordinate clock. It is not a clock attached to Earth or a free-falling spacecraft. For comparison, an isolated Sun at 1 AU contributes approximately 0.00593 m/s² and 853 microseconds/day of gravitational lag. The full readout varies with the actual summed field; no arbitrary diagram depth enters it. The Galactic external potential and time-coordinate scale conventions of precision ephemerides are omitted. Single-body experiments retain their isolated Schwarzschild formulas, and the separate coupled 1PN lab provides a higher-order dynamical comparison. This is not a numerical solution of the full Einstein equations.

Finding Earth 2.0: related work and dated plots

Finding Earth 2.0 observatory · source and methods · author perspective.

Historical screenshot reproduced from the original discussion note. It is a catalogue view, not a predicted future sky; its precise catalogue version and image-generation provenance are not independently established here.

Saved analysis dated 28 August 2026. The related project's summary contains 6,354 confirmed planets and 4,764 host systems, plus five Solar-System controls. This plot uses 5,767 planets with temperature and incident-flux data, including 1,659 with radius below two Earth radii. The Earth-2.0 index is a similarity/evidence score, not a probability of life. Habitable-zone placement does not demonstrate surface habitability. Figure provenance and hashes are saved in output/figures/provenance.json. This dataset and the Moving Observer's 1,387-source injection experiment are different samples.

Two different distances matter. Galactic radius R is the distance from the centre measured in the disk; z is height above its midplane. Moving outward in R generally reduces disk star density. Moving farther from the plane also reduces it, while changing the mixture of thin-disk, thick-disk and halo populations. Neither coordinate alone specifies an individual star's velocity. The displayed synthetic examples A, B and C are invented orbit comparisons, not catalogue stars. They are off by default; only a selected example appears when enabled.

A transparent density scenario

The new panel uses a smooth double-exponential number-density profile, with thin/thick radial lengths 2.6/3.6 kpc, heights 0.3/0.9 kpc and midplane thick/thin ratio 0.12. These structural choices come from the M-dwarf analysis of Jurić et al. (2008). We adopt the project's radius 8.2 kpc and initial height 0.020 kpc, and normalize the profile there:

Reylé et al. (2021) listed 373 stars within 10 pc, including white dwarfs, separately from brown dwarfs and planets. This historical count supplies an illustrative normalization of 0.0890 stars per cubic parsec. It is not a newly measured 2026 census. Applying one tracer population's spatial profile to the whole stellar count is an explicit simplification; the count display is a scenario with no calibrated uncertainty interval.

Along the current 250 Myr Solar integration, sampled every 0.5 Myr, R stays between approximately 8.1996 and 8.2047 kpc. The Sun does not approach the bulge. Its vertical oscillation changes this smooth density to approximately 0.784–1.063 times the starting value, or 292–397 scenario stars in an instantaneous 10 pc sphere. At the screenshot epoch of +34.9 Myr, the model gives about 0.949 times the starting density. These values do not count new arrivals, discovered planets, or distinct stars encountered over the full journey.

This profile is independent of the force model and the artwork. It omits spiral-arm enhancements, clusters, the bar, halo, warp-relative density changes, stellar evolution and migration. It cannot identify a reliable future arm-crossing date. A denser patch in the picture is not a measured star-count map. The 3–16 kpc comparison range is educational; extrapolation into the bulge is deliberately excluded.

How many stars might enter a neighbourhood?

For a uniform, stationary statistical population, the approximate incoming crossing rate of a sphere of radius b is:

Using the historical normalization, b = 10 pc and an assumed mean relative speed of 30 km/s gives an expectation of approximately 0.086 incoming crossings in 100 years. Similar outgoing flux balances it in this stationary approximation. This is not a prediction of a particular arrival, independent unique targets or new discoveries. The relevant speed is relative to nearby stars; inserting the Sun's 233 km/s Galactic speed would treat those stars as stationary and answer the wrong question.

Speed depends on the potential and the stellar population

The circular speed is a property of an adopted potential, not a universal speed for every star:

A limitation exposed by this comparison: the existing illustrative force model rises outward. It is not a current fit to the observed rotation curve. Põder et al. (2023) inferred 233 ± 7 km/s near the Sun and a curve consistent with flatness across their 5–14 kpc fit. A 2026 Cepheid study reports roughly 236 km/s near the Sun and 230 km/s around 16 kpc, with radial structure. These tracer-dependent results must not be replaced by the model values in the table. Future orbit predictions require a better constrained potential and uncertainty propagation.

Farther out, stars can take longer to go around even when their speeds in km/s are similar: the circumference is larger. Farther above the plane, older populations typically have larger random motions and can rotate more slowly on average. There is no single speed-height law. Our height slider therefore changes density, while the speed readout explicitly remains the midplane circular-speed reference, not the velocity of a star at that height. See the population analysis in APOGEE orbit-superposition work.

Tutorial: in Milky Way, scroll to Stellar environment · model. Play the Galactic clock and follow the density history. Expand Compare radius, height & speed to change R and z independently. Export CSV on the Galactic clock to obtain the density scenario alongside positions. The model-versus-observation distinction is part of the result, not an uncertainty to hide.

The one-click Show winding paths · 3D tour starts a three-year inner-system trajectory in a frame translating at 98% of the Sun's initial velocity. This resolves winding motion while retaining equal AU scales on all axes. It is a change of reference frame, not a slower Sun or a stretched orbit. Select Galactic frame · full Solar travel to restore the full displacement. The other planets can be restored with Bodies to show. Manual dragging stops the 30-second camera tour.

The optional lunar example adds one Moon to the eight planets and Sun, for ten displayed bodies. It uses a circular 384,400 km orbit, 27.321661-day period and 5.145° inclination; the phase is illustrative. These scales are documented in NASA's Moon fact sheet. Earth and Moon offsets preserve the model Earth–Moon barycentre. Eccentricity, precession, perturbations and other moons are omitted. The Earth & Moon close-up resolves a lunar path that is nearly indistinguishable from Earth's on the all-planet Galactic scale.

Exterior spherical spacetime, with explicit clock references

Space & Time now offers a textured 3D Earth/body, an inverse-square field display, and an exterior Schwarzschild spatial slice. The circular-clock mode includes gravity and ideal orbital motion. Let $\mu=GM$, $r_s=2\mu/c^2$, and r be the areal radius outside the body's surface. For an isolated nonrotating spherical body:

Here t is the Schwarzschild time referenced to infinity; a held clock needs support. A circular geodesic clock is in free fall even though the displayed Newtonian field magnitude is nonzero. Rates relative to a stationary surface clock use the ratio of the two lapse factors, not the difference of potentials alone. The local animation clock spans 24 hours; its acceleration setting specifies physical seconds per playback second. It is separate from the Galactic and century clocks.

For a spherical, nonrotating Earth, the 400 km circular preset has an approximately 92.4-minute period and −24.7 microseconds/day relative to the stationary surface clock. The 20,200 km preset gives +38.5 microseconds/day. This reproduces the scale and sign of the familiar GNSS result described by NIST; it is not a navigation-grade GPS correction. Earth's rotation, oblateness, other bodies, eccentricity and signal propagation are omitted. See Ashby (2003) for the fuller relativistic timekeeping problem.

The spatial-slice option embeds the constant-time equatorial exterior geometry in Euclidean 3D:

Only radii outside the physical body are drawn. The embedding height is magnified by the factor shown on screen; the unscaled geometry obeys the radial metric identity. Z is an embedding coordinate, not a physical downward direction. This depicts a spatial slice, not all of spacetime, and marbles rolling on it would not reproduce geodesics. The older softened potential diagram remains a separately labelled analogy. See the derivation in University of Bath relativity notes.

Tutorial: open Space & Time, select Earth, and choose 3D body, field & clock. Select Earth · 400 km, then Play to follow the ideal circular clock. Compare Earth · 20,200 km and the sign of Gain vs stationary surface. Switch to Schwarzschild spatial slice and read the magnification label. Diagram height only never changes the numerical clock rates. Orbit the 3D view changes the camera, not the physics.

Share the question

Download the two-page project brief and 24-second scientific model animation. The animation is generated from the numerical modules, not recorded from the website. It labels its reference frames, scale changes between shots and illustrative lunar assumptions.

The original question and the 100-light-year preview

The revised two-page brief restores the A-to-B-to-C sightline question, transit-boundary geometry and longer timescales from the original discussion note, which is preserved in full. The original's A, B and C denote observer epochs, unlike the optional synthetic comparison stars in the simulation. The present direct-imaging score experiment does not settle transit-zone crossings for known orbital planes.

100 light-years is a distance, not 100 years. At a constant 233 km/s it takes about 128,666 years. The integrated Solar path includes its 7 km/s initial vertical component and reaches that path length in about 128,608 years. These are model-dependent estimates, not target-encounter forecasts. The idealized orbit is nearly circular in a static smooth axisymmetric potential. Evolution of the Galactic plane is omitted; the animated warp is not coupled to the force model.

Record from the website: click 100 light-years · preview & record, then Preview 10 seconds or Record 10 seconds. The local 3D scene uses equal light-year scales and 10 ly grid spacing; the path covers only about 0.2 degrees around the Galactic centre, so it appears almost straight. Planetary ephemerides are not extrapolated over 129,000 years. The browser records the live scene with its labels and assumptions at 1280 × 720. It saves MP4 where supported, otherwise WebM. Keep the tab visible; hiding it cancels the capture. No audio or external screen content is captured. The earlier 24-second model-rendered animation remains a separate resource.

Illustrated report

The six-page illustrated discussion report follows the original note's visual style, with seven numbered figures, rendered equations, quantitative results, a simulation tutorial and references. It is separate from the two-page brief. Its diagrams and scientific plots are model renderings, not browser screenshots.

The new lab integrates the Sun, eight planetary point masses and the Moon together. Each included body acts on every other included body. A paired Newtonian integration starts from exactly the same state. The relativistic branch uses the order-reduced Einstein–Infeld–Hoffmann first post-Newtonian (1PN) equations, rather than adding only a Solar precession term to prescribed Keplerian orbits. These equations retain corrections of order $v^2/c^2$ and $GM/(rc^2)$ in weak fields and slow motion.

This is a coupled relativistic approximation appropriate to this educational Solar System lab. It is not a numerical solution of the full Einstein field equations, a replacement for JPL ephemerides or a spacecraft-navigation product. The GR clock diagrams elsewhere in the project and this dynamical integration have different purposes and assumptions.

Starting data, coordinates and represented bodies

The frozen JPL Horizons queries return geometric barycentric positions and velocities at JD 2461041.5 TDB, labelled 2026.0, with independent comparison states 30 days, one Julian year and ten Julian years later. Coordinates use the J2000 ecliptic orientation with the Solar System barycentre as origin; vectors are uncorrected for light time. Units are AU and AU/day; one AU is 149,597,870.7 km. The input files preserve the request URLs, returned headers, body identifiers and response hashes. The returned planetary states identify DE441 as their source; the model does not claim to reproduce DE441's full force model.

Earth and Moon are separate bodies with separate mass parameters. Mars and the outer planets are represented by their system barycentres and total system mass parameters; their individual satellites are not integrated. Planetary parameters follow the table in Park et al. (2021). Pluto, asteroids and Kuiper-belt objects are omitted. This lab uses Solar System barycentric coordinates; Galactic translation and Galactic tidal forces are not added to these equations or clock rates.

Equations implemented

Let $\mu_i=GM_i$, $\mathbf d_{ij}=\mathbf r_i-\mathbf r_j$, $r_{ij}=|\mathbf d_{ij}|$, and define the external positive potential and Newtonian acceleration:

For GR parameters $\beta=\gamma=1$, the order-reduced equation used here is:

Replacing accelerations inside the $1/c^2$ terms by their Newtonian values discards terms beyond the retained 1PN order. This is an explicit order reduction, not an iterative exact-GR solution. The equations follow the published point-mass PPN formulation summarized in Park et al., section 3.1. Tamayo et al. and the REBOUNDx documentation distinguish all-body 1PN dynamics from dominant-central-body approximations. The project's implementation is independently written from the equations; it does not embed REBOUNDx source code.

Fixed-step classical RK4 integrates the velocity-dependent equations. The standard step is 0.0625 day, with 0.03125 day available for refinement. RK4 is not symplectic. The browser computes in a background worker, saves paired states every two days and retains the exact end epoch. Displayed saved states are not precision dense-output ephemerides. The lab accepts spans of 1, 5, 10 or 20 Julian years; the frozen external comparisons extend only to ten years. A longer display span does not imply a validated long-term prediction.

What the checks actually show

The isolated test-particle limit recovers the Schwarzschild weak-field acceleration. A ten-year two-body Mercury test fits the difference of relativistic and Newtonian apsidal angles and returns 42.9798 arcseconds per century, compared with 42.9807 from the analytic 1PN prediction:

This is an isolated dynamical benchmark; it is not the full Solar System's total observed precession. At 30 days in the ten-body model, Mercury's heliocentric relativistic/Newtonian position difference is approximately 8.825 km, while halving the integration step changes its relativistic position by 0.000085 km. For the Moon, the same refinement changes the heliocentric position by about 0.00239 km. These are numerical consistency checks, not physical uncertainty bounds.

Errors are instantaneous heliocentric 3D position discrepancies at the saved epochs, using identical initial states. They do not bound every epoch or every observable. The growing lunar discrepancy reflects omitted physics as well as integration error. Complete results, including all bodies and step-refinement checks, are in data/relativity-validation.json. Additional tests check Newtonian force balance, rotational covariance, $1/c^2$ scaling, finite outputs, worker completion and rejection of unsupported settings. No fresh browser rendering or browser-worker execution has been verified in this environment; the worker algorithm is executed directly under Node for validation.

Relative clock rates

The lab gives a separate leading weak-field estimate for ideal nonrotating spherical surface clocks, using each body's centre velocity and external potential, plus its spherical self-potential:

The instantaneous readout is microseconds per coordinate day relative to the model Earth clock. The cumulative difference is integrated using trapezoidal quadrature at each dynamics step. It is not a UTC/TT time-transfer solution. Surface rotation, location, tidal potential, atmospheric effects and non-spherical self-gravity are omitted. The Sun's clock, for example, uses its adopted photospheric radius; these readings are not clocks located at singular point-mass centres. The approximation is lower order than a complete relativistic ephemeris/time-transfer treatment; see Ashby (2003).

Light propagation: a limited Solar Shapiro term

For non-occulted Earth-to-body geometry, the optional readout computes the leading one-way delay in the field of a static spherical Sun:

Here the endpoints are instantaneous body-centre positions; $R$ is their geometric separation and $r_E,r_T$ are their distances from the Sun. Rays whose straight segment intersects the adopted Solar radius are excluded. This readout is a diagnostic approximation: it omits moving endpoints, retarded positions, light deflection, other bodies' delays and full null-geodesic ray tracing. It does not turn the spatial display into an apparent sky image.

Tutorial and limitations

Open Space & Time → Relativistic Solar System · coupled 1PN lab. Choose a span and integration step, then Calculate both models. When the calculation finishes, press Play or scrub the saved epochs. Use the inner-system, all-planet or Earth–Moon view; drag to orbit and scroll to zoom. Select a readout body to inspect the positional difference, relative surface-clock rate and accumulated clock offset. Export the paired CSV for numerical inspection. The coordinate origin is Sun-centred in the planetary views, at the Solar System barycentre in the all-body barycentric view, and Earth-centred in the lunar view; the integrator itself remains barycentric.

Body markers are enlarged; coordinates use equal AU scales. Grey tracks show the Newtonian comparison. At true scale the relativistic and Newtonian paths mostly overlap: the numerical difference is the useful observable. No artificial precession or difference magnification is silently applied.

The model omits spin/frame dragging, Solar and planetary quadrupoles, other satellites as separate bodies, lunar rotation and tides, asteroids, Pluto, Kuiper-belt perturbations, 2PN and higher corrections, gravitational radiation, a self-consistent evolving spacetime metric and full photon ray tracing. It uses pre-fitted starting data without refitting parameters to observations. These omissions prevent calling it a complete relativistic ephemeris or a full numerical-relativity Solar System. The delivered capability is a reproducible, coupled all-included-body 1PN lab, with measured limits and a Newtonian control.

The default Galaxy view uses the detailed ESA/Gaia artist’s reconstruction by Stefan Payne-Wardenaar, geometrically mapped onto a warped 3D disk. A shallow emissive volume supplies thickness at grazing angles. This is an illustrated reconstruction, not an external photograph or a fitted three-dimensional density survey. Published VLBI measurements remain a separate, selectable evidence layer. The appearance does not determine any orbit, density readout or exoplanet result.

Static measurement and synthetic-model comparison retained from the structural experiment; not the current browser appearance. The measured catalogue samples only part of the Galaxy.

Measured layer. The frozen Reid et al. (2019) VLBI catalogue supplies 199 parallax entries, with 198 distinct rounded Galactic names. Two entries share G123.06−06.30 and have different aliases and measurements; both are retained. These are high-mass star-forming regions, not a representative census of ordinary stars. Nominal distance is $d=1/\varpi$ kpc for parallax in mas. The transformation uses the ICRS–Galactic rotation and this project's Sun position $(0,-8.2,0.020)$ kpc. The raw catalogue, references, importer and SHA-256 checksum are included. Positions retain their catalogue epochs; they are not propagated to 2026.

The 168 entries with parallax signal-to-noise at least 5 can show endpoints $1/(\varpi+\sigma_\varpi)$ and $1/(\varpi-\sigma_\varpi)$. These are transformed measurement-error endpoints, not Bayesian distance intervals. No selection-function or covariance correction is made. This overlay and the published arm segments disappear during future playback rather than masquerading as future observations.

Modelled structure. Six kinked logarithmic arm segments use Table 2 of Reid et al.:

The gold fit overlay stops at the published azimuth intervals. The fainter stellar-light continuation extends those fits by 65° at either end (15° for the Local arm): that extension is an illustration, not an observed or uniquely determined arm map. The bar adopts 30° orientation and 5 kpc half-length, consistent with Wegg, Gerhard & Portail (2015), without refitting their data.

The archived structural sampler contains 190,000 synthetic light samples, not measured individual stars. Its deterministic disk/bar/arm experiment and tests remain available, but that point distribution no longer supplies the default visible Galaxy. The current appearance uses the ESA reconstruction with a 40 kpc image span, an outer fade, and a 256 × 256 tessellated disk. Its scale registration is approximate; it must not be read as a precise arm-boundary catalogue. A 144-step grazing-angle renderer uses an illustrative vertical emissivity proportional to exp(−|z−z_w|/h), with h = 0.14 + 0.40 exp(−R²/12) kpc for R in kpc. The height, transfer coefficients and blend between surface and volume are presentation choices, not calibrated radiative transfer or measured extinction. This rendering does not replace the explicitly assumed environment-density model.

The kinematic warp retains its sourced 700 pc scale at 14 kpc. It is not a fit to the 2025 corrugation. Default vertical scale is 1×; Show warped disk selects labelled 5× and a suitable camera. Rotation of the reconstruction is schematic and cannot predict the Galaxy’s appearance millions of years from now.

Planetary appearance and close-ups. Sun, Mercury, Venus, Mars, Jupiter, Saturn, Uranus, Neptune and Moon textures come from Solar System Scope / INOVE, CC BY 4.0. The source combines imagery with enhanced colours and filled mapping gaps. Earth retains its previously credited map. Mapped surface orientation, atmospheric limb glow and ring bands are illustrative; there is no surface/cloud ephemeris, calibrated exposure or scattering calculation. These materials are shared by Earth & Sun, Sun & all planets, Space & Time and the coupled 1PN lab. In Sun & all planets → Inspect a planet, the camera follows that body and uses physical body radii; the whole-system overview retains enlarged markers. Spin axes are a presentation approximation, so the ring orientation is not suitable for predicting occultations. Orbit positions and numerical clock/field readouts are unchanged by these appearance options.

A real, limited hydrodynamics experiment

Gas hydrodynamics lab solves the two-dimensional, isothermal Euler equations in a prescribed potential. The 3D surface height represents gas surface density, not the vertical shape of a three-dimensional gas disk:

Here $r_c=1$ kpc, $b=5$ kpc, $v_c=233$ km/s, $c_s=10$ km/s, $\epsilon=0.1$, and $\alpha=-\Omega_b t$ with $\Omega_b=40$ km/s/kpc. The bar and initial gas rotate in the same clockwise direction in the displayed coordinates. The initial surface density is proportional to $\exp(-R/4\,{\rm kpc})$, with circular speed including its radial pressure gradient in the axisymmetric potential. The bar perturbation is present from the start; the initial state is not an equilibrium with the bar.

Implementation: 64×64 cells over 32×32 kpc, first-order finite-volume Rusanov flux, gravity kicks bracketing the flux update, Courant factor 0.3, and zero-gradient open boundaries. The boundary flux is included in the mass budget. Density is never silently clipped. The independent gas clock runs to 100 Myr; Export gas grid supplies positions, density and velocities. Top view and 3D density view change the camera only.

The isothermal closure exchanges heat implicitly and does not evolve an energy equation; compare the standard hydrodynamics equations documented for Athena. This project uses its own much simpler implementation, not Athena. It omits magnetic fields, self-gravity, cooling physics, feedback, star formation and an observational gas fit. It is numerically diffusive and is not a validated hydrodynamic reconstruction of the Milky Way. The stellar orbits, Solar System and heliosphere are not driven by this gas experiment. A credible heliosphere flow calculation would additionally require magnetohydrodynamics and interstellar-plasma boundary data.

Tests preserve uniform gas exactly, conserve periodic mass, account for open-boundary mass flux, compare acceleration with the potential gradient, and recover a small-amplitude travelling acoustic wave with decreasing error on grid refinement. These verify limited numerical behaviour, not astrophysical realism. Stars and planets continue to use gravitational trajectories; fluid equations are not used to produce attractive but unphysical corkscrews.

Scores use the same hypothetical 1 AU, Earth-radius planet distribution and baseline 60 mas / 10⁻¹⁰ contrast / G=30 thresholds. They are not discovery counts.

The Solar path column assumes constant tangential speed 233 km/s on a locally circular Galactic path. Over 10,000 years it covers about 7.77 light-years and 0.01665° around the centre: still the local Galactic neighbourhood, not a journey into a different spiral arm. The gas clock and the 250 Myr context view answer different questions.

Sightline angles come from the relative three-dimensional motion of the same 1,387 selected Gaia DR3 sources, propagated from their catalogue epochs to 2026 and then to the comparison year:

This is a nominal screening calculation, not a certified 10,000-year ephemeris. Constant velocity omits Galactic differential acceleration, binary dynamics and observer orbital parallax. Uncertainties are not newly propagated for the 1,000- and 10,000-year rows; the earlier century experiment separately provides formal astrometric uncertainty. Gaia quality cuts, available radial velocities and the fixed sample introduce selection effects. Sources not in this sample are not counted as future entrants.

Changing sightlines can open or close a transit window. But the isotropic planet population in this direct-imaging calculation marginalises over orbital orientation: its score changes through distance, brightness and angular-separation thresholds, not through the plotted sky angle itself. Identifying new transits requires orbital planes and their uncertainties for individual systems. Kaltenegger & Faherty (2021) already demonstrated time-dependent membership of Earth's transit zone. This project does not claim that changing viewpoints are an undiscovered idea.

Closer systems can make imaging and spectroscopy easier; they can also have less favourable orbital phase or obscuring dust. Nothing in these calculations establishes life, a new habitable planet or a future discovery count. A useful next experiment would rank individual targets at fixed exposure time and instrument performance, propagate binary and astrometric uncertainties, and test whether any gains survive. A second observer needs a feasible spacecraft trajectory: a released probe retains its initial velocity and does not remain at a fixed Galactic location.

How to inspect the new layers

1. Open Milky Way → Inspect the measured evidence. Cyan points are catalogue entries, cyan segments show the selected distance-error endpoints, and gold curves show published arm segments. Rotate/zoom to inspect them.
2. Select Detailed Gaia reconstruction to restore the illustrated Galaxy; use Show warped disk for the bend and compare labelled 1×/5× vertical scales. Turn off Keep bend in view before choosing your own camera.
3. Open Gas hydrodynamics lab, play its independent clock, compare top and density views, and export the cell values. Density-height is a graph, not a warped Galactic surface.
4. In the report's 100 / 1,000 / 10,000 year comparison, select an interval. Read distance and sightline changes separately from the conditional accessibility score. The Solar System century clock is deliberately not extended beyond its ephemeris domain.

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2. NASA, Kepler / K2 mission overview. https://science.nasa.gov/mission/kepler/
3. NASA, TESS mission overview. https://science.nasa.gov/mission/tess/
4. NASA, The Habitable Zone, and An Earth-like Atmosphere May Not Survive Proxima b's Orbit (2017). https://science.nasa.gov/exoplanets/habitable-zone/ ; https://www.nasa.gov/science-research/heliophysics/an-earth-like-atmosphere-may-not-survive-proxima-bs-orbit/
5. Kervella, P., Thévenin, F. & Lovis, C. (2017). Proxima's orbit around α Centauri. A&A 598, L7. DOI: 10.1051/0004-6361/201629930. https://arxiv.org/html/1611.03495
6. ESA/Gaia/DPAC, Stefan Payne-Wardenaar (2025). The best Milky Way map by Gaia. Artist reconstruction, CC BY-SA 3.0 IGO. https://www.esa.int/ESA_Multimedia/Images/2025/01/The_best_Milky_Way_map_by_Gaia
7. Suárez Mascareño et al. (2020). Revisiting Proxima with ESPRESSO. A&A 639, A77. https://arxiv.org/abs/2005.12114
8. Kaltenegger, L. & Faherty, J. K. (2021). Past, present and future stars that can see Earth as a transiting exoplanet. Nature 594, 505–507. DOI: 10.1038/s41586-021-03596-y. https://arxiv.org/abs/2107.07936
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The current rendering maps the detailed ESA/Gaia reconstruction onto a bent three-dimensional disk, with illustrative thickness at grazing angles and an independently selectable VLBI layer (section 16). These depth parameters are not a fitted 3D stellar or dust catalogue. Multi-body planet illumination comes from the modeled Sun with dim ambient light; isolated-body experiments use a presentation light. Overview body markers remain enlarged. The new Sun & all planets inspection control follows a selected body at physical radius, using illustrative mapped surfaces; these do not alter the trajectory or field calculations.

Biswajit Jana originated the project question and supplied the original community discussion note, included unchanged as discussion-note.pdf. The project and this working report are attributed to him. Independent scientific review is welcome. Published measurements and prior research belong to their cited authors; the Gaia artwork carries its own attribution and licence. No institutional affiliation, peer review, discovery claim or outside endorsement is asserted.