Both orbits are treated as coplanar circles (Earth at 1 AU, asteroid at the chosen distance) and the transfer between them is a real Hohmann ellipse — the minimum-energy two-burn path between two circular orbits:
a = (r1+r2)/2
Δv1 = |√(μ/r1)·(√(2r2/(r1+r2)) − 1)| (Earth departure)
Δv2 = |√(μ/r2)·(1 − √(2r1/(r1+r2)))| (asteroid rendezvous)
Transfer time = π·√(a³/μ) (half the transfer ellipse's period)
The ship's position each frame is the real two-body solution: solve Kepler's equation M = E − e·sin(E) for the eccentric anomaly E, then place it at (a(cosE−e), a√(1−e²)·sinE) — the same math that plots any real elliptical orbit, run all the way around so the same ellipse also carries the ship home.
Propellant burned per leg comes straight from the rocket equation, applied twice each way (departure + rendezvous, then rendezvous + capture on the way back — the two burns share the same total Δv by the symmetry of a Hohmann transfer):
m_after = m_before / exp(Δv·1000 / (Isp·g0))
Max cargo the return burns can still carry:
c_max = propellant_at_asteroid / (exp(Δv_out·1000/(Isp·g0)) − 1) − dry_mass
That last line is the real tension the sliders expose: extracting more ore than your remaining propellant can lift home is not a resource problem, it's a fuel problem — the hold is capped by whichever is smaller, the ore actually present, the hold's physical size, or what the return burns can afford.
Total extractable resource comes from the asteroid's own geometry and composition — volume from diameter, mass from bulk density, extractable mass from ore grade — and mission economics is a plain ledger: launch cost per kilogram of wet mass plus fixed overhead, against extracted mass times market price, updated live as the hold fills.
- Heliocentric-transfer Δv only (spacecraft assumed already free of Earth's gravity well, as after launch-vehicle separation) — real launch-to-orbit cost is folded into the launch-cost-per-kg dial instead.
- High specific impulse defaults model electric (ion) propulsion, the same choice real missions like Hayabusa2 and Dawn made for exactly this Δv-hungry, low-thrust regime.