Power-Limited Transfer Calculator

This version uses the more accurate variable-mass result for a symmetric accelerate/decelerate transfer with equal delta-v halves, constant jet power and constant exhaust velocity. For dated transfers it solves the geometry self-consistently (the destination moves during the flight) and adds the orbital velocity-matching budget, so the ship no longer starts and ends at a standstill relative to the Sun. Enter initial mass, final mass, and power, then either type a transfer distance manually or solve a planet-to-planet transfer for a departure date.

Inputs

Transfer distance from planet positions

Departure

Destination

Departure date

Uses a Keplerian heliocentric position and velocity model with elliptical, inclined orbits and J2000-style mean elements. The transfer is solved self-consistently: the destination is propagated forward by the flight time, and the engine must also make up the difference between the two planets' orbital velocities. This is still an approximation, not a JPL ephemeris.

Initial mass

Spacecraft initial mass m0

Unit

Final mass

Spacecraft final mass mf

Unit

Jet power

Useful power delivered to exhaust

Unit

Transfer distance

Idealized transfer distance D (editing here clears velocity matching)

Unit

Results

Ready

Enter values and press Calculate.

Trip time vs. mass ratio

This holds the dry/payload mass (mf) fixed at the value you entered and adds propellant, so the mass ratio R = m0/mf rises by making the ship heavier. Trip time trades two effects: a higher mass ratio is more efficient, but hauling more propellant costs time (trip time grows with the mass that must be carried). The result is an interior minimum at exactly R = 4 — its location does not depend on power, payload, distance, or geometry, because R enters trip time only through (R − 1)/(√R − 1)^(4/3), which is minimized at R = 4 for any mission. What changes between missions is the trip time at that optimum, not the optimum itself. The green dot marks it; the accent line marks your entered R.

Press Calculate to generate the sweep.

Variable-mass equations used

R = m0 / mf

m_mid = √(m0 · mf) (switch point: equal Δv each phase)

D = ve³ / (2P) × (m0 + mf − 2√(m0·mf))

ve = ( 2 P D / (m0 + mf − 2√(m0·mf)) )^(1/3)

t = ve² (m0 − mf) / (2P)

Δv_crossing = ln(R) × ve

Isp = ve / g0

T = 2P / ve

v_max = Δv_crossing / 2 (speed at the switch point)

v_match = | v_dest(t_arrive) − v_origin(t_depart) |

diagnostic combined Δv ≈ 2 × √( v_max² + (v_match/2)² )

spiral gate: T/m0 ≥ 0.5 × (μ☉ / r_mean²)

This uses the full variable-mass transfer distance, not an accelerate-segment formula mirrored across the midpoint. Thrust stays constant while mass falls, so acceleration rises; initial, midpoint, and final acceleration are reported separately. The vehicle accelerates until its mass reaches the geometric mean √(m0·mf), then decelerates. The two phases have equal Δv but unequal distance and time — the switch is not at the halfway point of the trip (for R = 5 the acceleration phase covers ≈63% of the distance).

For dated planet-to-planet transfers the destination is propagated forward by the flight time and the geometry is re-solved until D and t are self-consistent. The crossing itself is computed in the Sun-rest frame: the engine is charged with the full chord between the two planet positions, starting and ending at rest relative to the Sun. The orbital velocity difference v_match = |v_dest − v_origin| is then reported as a separate diagnostic of the additional velocity change a real mission would need. These are not combined into a self-consistent trajectory — the "diagnostic combined Δv" is only a rough scalar estimate, and the exhaust velocity, time, and mass ratio are solved from the crossing alone. A co-moving treatment that let the ship inherit the origin's velocity would require integrating the Sun's gravity over the flight (the inherited velocity is orbital, not inertial, so it curves), which this straight-line model deliberately does not do.

A spiral gate (a crude straight-line-model validity check, not a hard physical law) rejects vehicles too weakly powered for a direct crossing: if thrust acceleration is below ~50% of local solar gravity, the Sun dominates and the ship would have to spiral outward over many orbits, which this model cannot represent. Because ve ∝ P^(1/3) and thrust acceleration ∝ P^(2/3), the power needed to clear the gate scales as (a_target / a_current)^(3/2).

Interpretation notes

This is still an idealized deep-space model. The crossing is treated as a straight line in the Sun-rest frame and ignores the Sun's gravity during flight. Changing geometry, a velocity-matching diagnostic, and a spiral-regime feasibility gate are included; full gravity-aware trajectory integration is not.
The crossing charges the engine for the full chord between the planet positions (start and end at rest relative to the Sun). The orbital velocity difference is reported only as a separate diagnostic — it is not subtracted from the crossing as inherited drift, because that inherited velocity is orbital and would curve under solar gravity, which this model omits. So the displayed numbers are crossing-only; a self-consistent mission accounting for inherited velocity needs the full trajectory.
The planet positions and velocities use approximate linear mean Keplerian elements, good for scale-setting near J2000 but degrading for dates far from 2000, especially for the outer planets.
The spiral gate means very low-power ships are rejected by design. Such ships can reach the destination, but only by spiraling — a fundamentally different and much longer trajectory than the direct brachistochrone modeled here.
Mass ratio must exceed 1. For very large mass ratios, the equations remain mathematically valid, but real vehicle and operational limits become increasingly important.

Standard gravity used: g0 = 9.80665 m/s². One AU = 149,597,870,700 m.