This version uses the more accurate variable-mass result for a symmetric
accelerate-half / decelerate-half transfer with constant jet power and constant exhaust velocity.
Enter initial mass, final mass, and power, then either type a transfer distance manually or calculate
the planet-to-planet distance for a selected date.
Inputs
Transfer distance from planet positions
Uses a Keplerian heliocentric position model with elliptical, inclined orbits and J2000-style mean elements.
This is still an approximation, not a JPL ephemeris.
Spacecraft initial mass m0
Spacecraft final mass mf
Useful power delivered to exhaust
Idealized transfer distance D
Results
Ready
Enter values and press Calculate.
Variable-mass equations used
R = m0 / mf
A(R) = 1 − 1/√R − ln(R)/(2√R)
B(R) = 1 − 1/√R
ve = (P D / (m0 A))^(1/3)
Δv = ln(R) × ve
t = B × (m0 / P)^(1/3) × D^(2/3) / A^(2/3)
Isp = ve / g0
T = 2P / ve
m_mid = √(m0 mf)
Unlike the earlier approximation, this version accounts for the fact that thrust stays constant
while mass falls during the burn, so acceleration rises over time. Initial, midpoint, and final
acceleration are reported separately.
Interpretation notes
This is still an idealized deep-space model. It does not include launch, escape spirals, capture, inclination changes, or the actual changing geometry of planetary positions.
The planet distance calculator uses approximate Keplerian elements, so it is suitable for scale-setting but not as a replacement for a high-precision ephemeris.
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.