🧮 Tritech Predictive Transit Formula — Question

A traveler moves from Planet A to Planet B along a spatial corridor that is perfectly aligned but subject to orbital rotation. The traveler begins with an initial velocity v₀, but experiences linear velocity decay due to inertial drag. The corridor rotates at angular velocity ω, introducing a correction factor α = 1 + sin(ωt) to the transit time. The total distance between the planets is D.

Given:

D = 4.5 × 10⁸ km

v₀ = 25,000 km/h

Decay rate r = 500 km/h²

Angular velocity ω = 0.002 rad/h

Correction factor α = 1 + sin(ωt)

Find:

Time t such that:

t = [D / (v₀ − r·t)] · (1 + sin(ωt))