Elliptical Orbit Calculator
Explore period, apsis distances and speeds for a bound two-body orbit around a supplied central mass.
Calculate locally
No account, API or uploaded inputs. All calculations run in this browser.
Worked example
With μ = 400000 km³/s² (mass ≈ 5.993137857 × 10²⁴ kg), a = 10000 km and e = 0.6, distances are 4000 and 16000 km. Speeds are about 12.649111 and 3.162278 km/s, and period about 165.576471 minutes.
Method and units
Let μ = GM in km³/s². Periapsis rp = a(1−e); apoapsis ra = a(1+e); period P = 2π√(a³/μ). Vis-viva gives v = √[μ(2/r−1/a)]. At the apsides the implementation uses equivalent ratios of (1+e) and (1−e).
What this result means
The orbiting mass is assumed negligible. Distances are from the central body centre, not surface heights; no body radius is supplied, so a computed path may pass inside the body and be physically impossible. No drag, perturbations, relativity or collision screening is included. Eccentricity 1 or greater is outside this bound-ellipse model.