State at true anomaly

r(ν) and v on an ellipse from a, e, ν.

SIDUS educational calculator. Category orbital. Tags: GNC, orbital. Pure SI. Not flight software.

Formula

r = a(1−e²)/(1+e cos ν)

Radius at true anomaly

Primary sources

• Fundamentals of Astrodynamics and Applications (David A. Vallado): Standard reference for two-body, Lambert, maneuvers, and J2. Equations implemented independently in SIDUS.
• Orbital Mechanics for Engineering Students (Howard D. Curtis): Textbook derivations for Hohmann, vis-viva, rocket equation, elements.

How do AI agents use this tool?

Read /llms.txt or call https://sidus.tools/api/mcp. Open the interactive page for live SI inputs.