Orbital speed at altitude calculator

This orbital speed at altitude calculator forms the total path radius r equals R plus h, evaluates v equals the square root of μ over r, and returns structured JSON that homework checkers and lightweight pipelines can pin in continuous integration. Non-positive total radius is rejected with a clear invalid_input error because the formula divides by r and a vanishing or inverted geometry is not a physical circular orbit.

What orbital speed at altitude means and which inputs to send

Send required field body_radius as a finite number or numeric string for the mean or equatorial radius of the body—for Earth about 6.371 times ten to the sixth metres—and required field altitude as the height above that surface in the same length units. Aliases R, radius, and planet_radius map to body_radius; h, height, and altitude_m map to altitude; gravitational_parameter, GM, and mu_body map to mu. Units are your responsibility: with metres and SI μ, orbital_speed is in metres per second. The path is pure floating-point arithmetic with no network, no random seed, and no wall clock, so identical inputs always produce identical JSON.

Reading the response fields, errors, and unit consistency

On success the response echoes body_radius, altitude, and mu, then reports total_radius as R plus h and orbital_speed as the circular speed magnitude. The formula field is always the string v equals sqrt of mu over open parenthesis R plus h close parenthesis, and method is always circular_orbital_speed_at_altitude so clients can branch without sniffing shapes. Missing body_radius, missing altitude, missing mu, non-finite values, non-positive mu, and non-positive total radius all fail with invalid_input and are not charged after the engine rejects the request. The product contract for this capability is explicit: when R plus h is not strictly positive, the solve aborts with a message that names total_radius and the sum that failed. That covers zero radius, inverted geometry from a large negative altitude, and other non-physical paths. Use orbital_speed alone when a dashboard only needs the speed number; keep total_radius and formula when documenting the step for students or when logging which algorithm produced a mission sketch. Pair this endpoint with orbital period tools when the next question is how long one revolution takes at the same altitude, remembering that period scales with r to the three-halves power while speed falls as one over the square root of r.

API usage, pricing, classroom workflows, and practical limits

Send a JSON body with required body_radius, altitude, and mu. 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_speed into tables that compare circular speeds across altitudes, teaching how speed falls as altitude grows while period lengthens—a companion concept you may compute separately when building multi-step lesson flows.