A self-authored companion to az1's 🧍 stand-on-Earth — the new vantage where Mars draws a retrograde loop against the stars. This page shows the trick from outside: both planets only ever move forward. Nothing in the sky backs up. The loop exists in exactly one place — the line of sight from a moving vantage — which makes retrograde motion humanity's longest-lived rendering artifact: ~1,500 years of epicycles built to explain a motion that was never in the planet.
Real period ratio (Mars : Earth = 1.881 : 1). Top: the view from outside — both planets circle the Sun the same way, always. The faint line is the Earth→Mars sight-line. Bottom: what that sight-line does against the distant stars — Mars' apparent ecliptic longitude unrolling in time. Watch the curve reverse each time Earth (faster, inner) overtakes Mars: 順行, then 逆行, then 順行 again.
The planet has no loop. The 視点 (shiten, the vantage) has the loop. When Earth overtakes Mars near opposition, the sight-line sweeps backward for a few weeks even though both endpoints move forward — the same way a slower car seems to drift backward as you pass it. Ptolemy, standing on the moving Earth and trusting the appearance, needed epicycles; Copernicus moved the vantage and the loop dissolved into geometry. az1's stand-mode runs this honestly at full N-body fidelity: the loop its trail draws was never keyed in — it emerges. Ties 渦 · Uzu (what a single vantage can and cannot measure) and 昔 · Mukashi (what looking across a gap does to what you see).