Shadowhunter is an interactive browser-based tool for computing and visualizing Permanently Shadowed Regions (PSRs) on planetary bodies. Given a set of orbital and physical parameters, the tool calculates the critical latitude above which crater floors or sloped terrain can remain in permanent shadow throughout a full orbital period, and estimates whether those regions are cold enough to trap and preserve water ice.
The tool runs entirely in the browser, requires no installation and updates in real time as parameters are adjusted. It includes presets for Mercury, the Moon, Mars, Ceres and Europa, and supports fully custom planetary configurations.
A Permanently Shadowed Region is a surface location that never receives direct sunlight over a complete orbital period. On airless or thin-atmosphere bodies, these regions can remain extraordinarily cold; cold enough to act as cold traps for volatiles such as water ice, CO₂, SO₂ and other compounds that would otherwise sublimate.
The fundamental quantity governing PSR formation is the topographic horizon angle α — the angular height of any obstruction as seen from the shadowed location, measured from the local horizontal in the direction of the Sun. Shadowhunter computes α from two contributions:
α = arctan(2 × d/D) + β
where d/D is the crater depth-to-diameter ratio and β is an additional pole-facing slope angle. If only one term is known, set the other to zero.
The maximum elevation of the center of the solar disk at latitude φ on a body with axial tilt ε occurs at summer solstice:
el_max(φ) = 90° − |φ| + ε
Permanent shadow, however, requires that even the upper limb of the Sun never clears the horizon obstruction. The solar disk has an apparent angular radius θ☉ that is largest at perihelion, so the worst case over a full orbit is:
θ☉ = arcsin( R☉ / [a(1 − e)] )
Setting el_max + θ☉ = α and solving for φ gives the critical PSR latitude:
φ_PSR = 90° + ε + θ☉ − α
All surface locations with |φ| ≥ φ_PSR can host PSRs if they have the appropriate topography.
Eccentricity enters the model through two channels:
Note: the θ☉ term is evaluated at perihelion, i.e. assuming polar summer solstice can coincide with perihelion. Over precession cycles this alignment recurs, so it is the correct conservative choice for permanent shadow.
Equilibrium temperature (fast-rotator model, orbit-averaged insolation):
T_eq = 278.5 × (1 − A)^0.25 / √a × (1 − e²)^(−1/8) [K]
PSR temperature (empirical, calibrated against Mercury and Moon observations):
T_PSR ≈ T_eq × 0.25 × (1 − α / 90°)^0.40
Water ice is considered stable below 110 K, marginal between 110–180 K, and unstable above 180 K.
| Parameter | Symbol | Description |
|---|---|---|
| Obliquity | ε | Axial tilt (degrees). Most important factor controlling PSR extent. |
| Eccentricity | e | Orbital eccentricity. Sets perihelion distance, which controls the solar disk size θ☉ (raises φ_PSR), the orbit-averaged T_eq, and the peri/aph flux range. |
| Crater d/D ratio | d/D | Depth-to-diameter ratio. Typical: 0.10–0.20 for fresh craters. |
| Slope angle | β | Additional pole-facing terrain slope (degrees). Set to 0 if unknown. |
| Body radius | R | Mean radius in km. Used for PSR area calculation. |
| Distance from star | d | Semi-major axis in AU. Affects temperature estimates. |
| Bond albedo | A | Fraction of incident solar radiation reflected by the body. |
| Body | ε (°) | d/D | Distance (AU) | Notes |
|---|---|---|---|---|
| Mercury | 0.034 | 0.15 | 0.387 | PSRs confirmed by MESSENGER; water ice detected |
| Moon | 1.54 | 0.15 | 1.000 | PSRs confirmed by LCROSS, LRO; water ice detected |
| Mars | 25.19 | 0.20 | 1.524 | High obliquity limits PSRs; very deep craters required |
| Ceres | 4.0 | 0.15 | 2.770 | PSRs confirmed by Dawn; water ice detected (2016–17) |
| Europa | 0.1 | 0.08 | 5.204 | Global ice shell present; PSRs relevant for exotic volatile trapping |
PSRs were first proposed as potential cold traps for lunar volatiles by Kenneth Watson, Bruce Murray, and Harrison Brown in 1961. Their existence on the Moon was confirmed by the LCROSS impact experiment (2009) and subsequently characterized by the Lunar Reconnaissance Orbiter. MESSENGER confirmed water ice in Mercury's PSRs in 2012. The Dawn mission detected water ice in Ceres' permanently shadowed north polar craters in 2016/2017.
This tool implements a first-principles geometric model and is currently intended for exploration and teaching rather than mission-level analysis. Key simplifications include that the equilibrium temperature formula assumes a fast rotator. Slowly rotating bodies (e.g. Mercury with its 3:2 spin-orbit resonance) have a more complex thermal environment. Also, the PSR temperature estimate is empirical and does not account for conduction, internal heat sources (relevant for tidal heating), or regolith thermal inertia. The model also assumes a spherical body, but real topography can create PSRs at latitudes below the theoretical critical latitude on bodies with rugged polar terrain. Linear slope addition assumes a 2D worst-case geometry. In a true 3D environment, the solar azimuth rotates relative to the slope direction throughout the day. Orbital eccentricity now enters the model through the solar disk size at perihelion (geometric, raises φ_PSR) and the orbit-averaged insolation (thermal, scales T_eq); the θ☉ term conservatively assumes that polar summer solstice can coincide with perihelion, which is the correct worst case for permanence over precession cycles but may overstate the effect for a fixed present-day orbital configuration. Kepler timing asymmetries (more time spent near aphelion) and spin–orbit resonances such as Mercury's longitude-dependent "hot poles" are not modeled.