Exomoon Tidal Heating Detection Map (2D)

Exomoon Orbit

Orbital eccentricity e 0.030

Moon–planet distance 420,000 km

Tidal dissipation k₂/Q 0.0200

Planet–star distance 5.20 AU

Detection Readouts

Tidal heat power

— W

vs Io (1.5×10¹⁴ W)

—×

T (insolation only)

— K

T (with tidal heat)

— K

—

excess IR luminosity ÷ assumed noise floor (3σ)

How it works

A moon on an eccentric orbit is squeezed and stretched every revolution; internal friction converts that flexing into heat (Peale & Cassen 1979). The orbit-averaged power is:

H = (21/2) · (k₂/Q) · R⁵n⁵ · e² / G
n = √(GM_planet / a³)   (mean motion)

This 2D view plots that formula directly as a field: the top panel is a heatmap over the two variables that matter most physically — eccentricity (horizontal) and orbital distance (vertical) — with brightness showing tidal heating power (log scale) at your current k₂/Q. The white contour line is the detection boundary: everywhere above/right of it, H exceeds the assumed 3σ photometric noise floor. The orange dot marks your current slider position on that map — drag the sliders and watch it move across the field instead of watching a body orbit in perspective.

The bottom panel is the physical mechanism behind the H formula: a strip-chart of the periapsis-weighted flexing rate over one orbit, replayed as the small deforming ellipse changes shape in sync — most elongated right at periapsis (closest approach, strongest tidal stretch), nearly circular at apoapsis.

4πR²σT_ins⁴ = F(1-A)·πR²         (insolation only)
4πR²σT_tot⁴ = F(1-A)·πR² + H     (insolation + tides)
F = L_star / (4πa_planet²)

Eccentricity / distance — the two axes of the heatmap; heating grows as e² (moving right brightens the map) and falls off steeply with distance (n⁵ ∝ a⁻⁷·⁵, moving up dims it fast).
k₂/Q — rescales the whole heatmap and its contour; icy or partially molten interiors dissipate far more than rigid rock.
Planet–star distance — sets the insolation-only baseline temperature the tidal excess must be measured against; it does not move the heatmap because detection significance here depends only on H versus the noise floor.

Current (e, distance) Detection contour (3σ) Tidal flex waveform