Skip to main content

Aerospace operators

11 operators in the aerospace category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
HOHMANN_TRANSFERHohmann transfer orbit delta-v equation giving the velocity changes needed for a minimum-energy transfer between two circular orbits.\Delta v = \sqrt{\frac{GM}{r_1}}(\sqrt{\frac{2r_2}{r_1+r_2}}-1) + \sqrt{\frac{GM}{r_2}}(1-\sqrt{\frac{2r_1}{r_1+r_2}})
ORBIT_APOAPSISComputes the apoapsis (farthest orbital point) from the semi-major axis and eccentricity of an elliptical orbit.r_a = a(1+e)
ORBIT_ENERGYSpecific orbital energy relating a body's total mechanical energy to the semi-major axis of its orbit around a central mass.E = -\frac{GMm}{2a}
ORBIT_ESCAPEEscape velocity formula giving the minimum speed needed for an object to break free of a gravitational field without further propulsion.v_{esc} = \sqrt{\frac{2GM}{r}}
ORBIT_INCLINATIONDelta-v required for a simple plane-change maneuver, proportional to orbital velocity and the sine of half the inclination change.\Delta v = 2v\sin(\frac{\Delta i}{2})
ORBIT_PERIAPSISComputes the periapsis (closest orbital point) from the semi-major axis and eccentricity of an elliptical orbit.r_p = a(1-e)
ORBIT_PERIODKepler's Third Law giving the orbital period as a function of the semi-major axis and the central body's gravitational parameter.T = 2\pi\sqrt{\frac{a^3}{GM}}
ORBIT_VELOCITYCircular orbital velocity derived from balancing gravitational attraction against centripetal acceleration at radius r.v = \sqrt{\frac{GM}{r}}
THRUST_ACCELERATIONNewton's Second Law applied to rocket propulsion, relating net thrust force to the resulting acceleration of the vehicle mass.a = \frac{F}{m}
THRUST_SPECIFICSpecific impulse measuring rocket engine efficiency as thrust produced per unit weight flow rate of propellant.I_{sp} = \frac{F}{\dot{m} g_0}
THRUST_TSIOLKOVSKYTsiolkovsky rocket equation relating achievable delta-v to exhaust velocity and the natural log of initial-to-final mass ratio.\Delta v = I_{sp} g_0 \ln\frac{m_0}{m_f}

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["HOHMANN_TRANSFER"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​