This is an independent 2D companion, not a flattened 3D scene: it solves the same orbital-distance and bandwidth equations and draws the result as two purpose-built 2D views — a top-down orbit map and a message-exchange timeline — instead of a rendered 3D solar system. Two additive delays govern any deep-space medical link:
Earth-Mars distance (coplanar circular approx):
d = sqrt(rE² + rM² − 2·rE·rM·cos(θE − θM))
rE = 1.000 AU, rM = 1.524 AU
θE = 2π·day/365.25, θM = 2π·day/686.98
Propagation delay (speed of light, fixed by distance):
t_prop(one-way) = d / c, c = 299,792.458 km/s
Transmission delay (bandwidth-limited, independent of distance):
t_xfer = payload_bits / data_rate
Total one-way delivery: t_total = t_prop + t_xfer
- Mission day moves Earth and Mars along their orbits, so distance — and therefore delay — genuinely varies between ≈54.6M km (opposition) and ≈401M km (conjunction), giving a one-way light delay of roughly 3 to 22 minutes for Mars. The Moon is modelled at its near-constant ≈384,400 km, a ~1.28 s one-way delay.
- Payload + data rate model the second, independent bottleneck: even with zero propagation delay, pushing a 300 MB imaging batch down a Deep Space Network downlink measured in kilobits per second takes real time. NASA's actual DSN links to Mars run from a few kbps up to a few Mbps depending on distance, antenna and mission priority — the slider spans that realistic range.
- Send consult message animates one round trip on the timeline at a compressed (log-scaled) visual speed so a multi-minute Mars round trip is still watchable, while every number shown is the real, uncompressed physical time.
- Recommended mode is a simplified round-trip-delay heuristic mirroring real mission-medicine guidance: under ~3 s the crew can hold a live conversational video call; under ~4 min a delayed video/audio exchange is still watchable; up to ~40 min, store-and-forward telemetry (ECG, labs, imaging) with asynchronous physician review is the working model; beyond that, onboard AI must render an autonomous first-pass diagnosis and only notify Earth afterward, because no round-trip consultation can happen in clinically useful time.