Orbital velocity calculator

This capability evaluates that expression deterministically from finite numeric inputs, rejects zero or non-positive radius with a clear invalid input error, and returns structured JSON that homework checkers, mission concept tools, and lightweight astrodynamics pipelines can pin in continuous integration without installing a full orbital mechanics stack.

What circular orbital velocity means and which inputs to send

Send the required field central_mass as a JSON number or numeric string for the body being orbited—for example Earth mass in kilograms—and the required field radius as the distance from the center of that body to the satellite, not merely the altitude above the surface. Aliases mass, M, and m are accepted for the central mass; aliases r and orbital_radius are accepted for the path radius. The optional field G, with aliases gravitational_constant and grav_const, lets you inject a textbook approximation or a non-SI constant; when omitted the engine uses the fixed value 6.6743 times ten to the minus eleven so every environment agrees. Radius must be strictly positive as well: zero radius is invalid_input because the formula divides by r and a vanishing orbit is not a physical circular path. Identical inputs always produce identical JSON because the path is pure floating-point arithmetic with no network, no random seed, and no wall clock.

Reading the response fields and unit consistency

If you switch to astronomical unit systems, supply a matching G; the calculator does not convert units for you. On success the response echoes central_mass, radius, and the G that was used, then reports orbital_velocity as the circular speed magnitude. The formula field is always the string v equals sqrt of G M over r, and method is always circular_orbital_velocity so downstream code can branch without sniffing shapes. Units are your responsibility and must be consistent: with SI mass in kilograms, radius in meters, and the default G, orbital_velocity is in meters per second. Missing central_mass, missing radius, zero radius, negative mass, non-positive G, and non-finite numbers all fail with invalid_input and are not charged after the engine rejects the request. Use orbital_velocity alone when a dashboard only needs the speed number; keep formula and method when documenting the physics step for students or when logging which algorithm produced a mission sketch. Pair this endpoint with centripetal force tools when the next question is the force magnitude for a given satellite mass, remembering that orbital velocity itself depends only on the central body and radius, not on the satellite mass under the two-body model.

API usage, pricing, classroom workflows, and practical limits

Call the free in-browser orbital velocity calculator for homework checks, lecture demos, and quick concept verification without installing Orekit, GMAT, or a local MATLAB toolbox. Typical classroom examples include low Earth orbit at roughly Earth radius plus a few hundred kilometers, geostationary radius near forty-two thousand kilometers, and simplified solar orbits with solar mass and astronomical-unit scales—always with matching G and consistent units. Extremely large or tiny magnitudes are bounded for isolate safety; stay within the published numeric range for reliable results. Send a JSON body with required positive central_mass and radius, and optional positive G when you need a non-default constant. Use the prepaid API when a tutoring platform, coding-assessment sandbox, curriculum generator, or early mission-design pipeline needs a stable contract under KIT balance at $0.002 per successful item; validation failures never consume balance after rejection. Authors shipping SDKs can map orbital_velocity into tables that compare circular speeds across altitudes, teaching how speed falls as the square root of one over r while period grows with r to the three-halves power—a companion concept you may compute separately when building multi-step lesson flows.