{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"escape-velocity"},"result":{"entity_type":"calculator","id":"escape-velocity","calculator_id":"escape-velocity","canonical_url":"https://tttkmbb.com/science/escape-velocity","name":"Escape Velocity Calculator","title":"Escape Velocity Calculator – Escape Speed, Circular Orbital Speed and Surface Gravity of Planets or a Custom Body","category":"science","category_name":"Biology, Earth & Space","tool_name":"calculate_escape_velocity","featured_mcp_tool":false,"description":"Computes the escape velocity √(2GM/r) and the circular orbital velocity √(GM/r) at the surface (or a given altitude) of Earth, the Moon, Mars, Jupiter, the Sun or a custom body defined by mass and radius, plus its surface gravity GM/R².","use_when":"You need the speed required to escape a planet or moon without further propulsion, the speed of a low circular orbit, or the surface gravity of a body from its mass and radius.","do_not_use_when":"You need the period of an orbit of a given size (use orbital-period), the rocket delta-v including gravity and drag losses, or the weight of an object on a planet (use planet-weight).","inputs":[{"name":"body","label":"Body","type":"enum","required":true,"values":[{"value":"earth","label":"Earth"},{"value":"moon","label":"Moon"},{"value":"mars","label":"Mars"},{"value":"jupiter","label":"Jupiter"},{"value":"sun","label":"Sun"},{"value":"custom","label":"Custom body (give mass_kg and radius_m)"}],"description":"Body to escape from; GM and mean radius are taken from the JPL/NASA constants.","example":"earth"},{"name":"mass_kg","label":"Mass (custom body)","type":"number","unit":"kg","required":false,"max":1e+42,"exclusive_min":0,"description":"Mass of a custom body; only used when body is custom.","example":5.972e+24},{"name":"radius_m","label":"Radius (custom body)","type":"number","unit":"m","required":false,"max":1000000000000000,"exclusive_min":0,"description":"Radius of a custom body in metres; only used when body is custom.","example":6371000},{"name":"altitude_m","label":"Altitude","type":"number","unit":"m","required":false,"default":0,"min":0,"max":1000000000000000,"description":"Height above the surface at which the speeds are evaluated (0 = surface).","example":0}],"outputs":[{"name":"escape_velocity_m_s","label":"Escape velocity","type":"number","unit":"m/s","decimals":1,"description":"√(2GM / r) with r = radius + altitude."},{"name":"escape_velocity_km_s","label":"Escape velocity (km/s)","type":"number","unit":"km/s","decimals":3,"description":"Escape velocity / 1000."},{"name":"escape_velocity_km_h","label":"Escape velocity (km/h)","type":"number","unit":"km/h","decimals":0,"description":"Escape velocity × 3.6."},{"name":"circular_orbital_velocity_km_s","label":"Circular orbital velocity","type":"number","unit":"km/s","decimals":3,"description":"√(GM / r): escape velocity / √2."},{"name":"surface_gravity_m_s2","label":"Surface gravity","type":"number","unit":"m/s²","decimals":3,"description":"GM / R² at the surface (altitude 0)."},{"name":"radius_used_km","label":"Distance from centre used","type":"number","unit":"km","decimals":1,"description":"Radius + altitude."},{"name":"gm_m3_s2","label":"GM used","type":"number","unit":"m³/s²","decimals":0,"description":"Standard gravitational parameter of the body."}],"input_schema":{"type":"object","properties":{"body":{"description":"Body to escape from; GM and mean radius are taken from the JPL/NASA constants.","type":"string","enum":["earth","moon","mars","jupiter","sun","custom"],"examples":["earth"]},"mass_kg":{"description":"Mass of a custom body; only used when body is custom. Unit: kg.","type":"number","maximum":1e+42,"exclusiveMinimum":0,"examples":[5.972e+24],"x-unit":"kg"},"radius_m":{"description":"Radius of a custom body in metres; only used when body is custom. Unit: m.","type":"number","maximum":1000000000000000,"exclusiveMinimum":0,"examples":[6371000],"x-unit":"m"},"altitude_m":{"description":"Height above the surface at which the speeds are evaluated (0 = surface). Unit: m.","type":"number","minimum":0,"maximum":1000000000000000,"default":0,"examples":[0],"x-unit":"m"}},"additionalProperties":false,"required":["body"]},"output_schema":{"type":"object","properties":{"escape_velocity_m_s":{"description":"√(2GM / r) with r = radius + altitude. Unit: m/s.","type":"number","x-unit":"m/s"},"escape_velocity_km_s":{"description":"Escape velocity / 1000. Unit: km/s.","type":"number","x-unit":"km/s"},"escape_velocity_km_h":{"description":"Escape velocity × 3.6. Unit: km/h.","type":"number","x-unit":"km/h"},"circular_orbital_velocity_km_s":{"description":"√(GM / r): escape velocity / √2. Unit: km/s.","type":"number","x-unit":"km/s"},"surface_gravity_m_s2":{"description":"GM / R² at the surface (altitude 0). Unit: m/s².","type":"number","x-unit":"m/s²"},"radius_used_km":{"description":"Radius + altitude. Unit: km.","type":"number","x-unit":"km"},"gm_m3_s2":{"description":"Standard gravitational parameter of the body. Unit: m³/s².","type":"number","x-unit":"m³/s²"}}},"formula":"v_escape = √(2 × GM / r); v_orbit = √(GM / r); g = GM / R²; r = R + altitude_m; GM(custom) = 6.67430 × 10⁻¹¹ × mass_kg","method":"Energy conservation for a non-rotating, airless body (kinetic energy equals the gravitational binding energy). Constants: GM in m³/s² Earth 3.986004418 × 10¹⁴, Moon 4.9048695 × 10¹², Mars 4.282837 × 10¹³, Jupiter 1.26686534 × 10¹⁷, Sun 1.32712440018 × 10²⁰; mean radii 6,371 / 1,737.4 / 3,389.5 / 69,911 / 695,700 km. Real launches need extra speed for drag and gravity losses and gain from the body's rotation.","sources":[{"name":"Wikipedia – Escape velocity","url":"https://en.wikipedia.org/wiki/Escape_velocity","type":"reference","retrieved_at":"2026-09-24"},{"name":"NASA NSSDCA – Planetary Fact Sheet","url":"https://nssdc.gsfc.nasa.gov/planetary/factsheet/","type":"government","retrieved_at":"2026-09-24"},{"name":"NASA JPL Solar System Dynamics – Astrodynamic parameters (GM of the Sun and planets)","url":"https://ssd.jpl.nasa.gov/astro_par.html","type":"government","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"examples":[{"name":"Earth, surface","inputs":{"body":"earth"},"expected":{"escape_velocity_m_s":11186.1,"escape_velocity_km_s":11.186,"escape_velocity_km_h":40270,"circular_orbital_velocity_km_s":7.91,"surface_gravity_m_s2":9.82},"url":"https://tttkmbb.com/api/v1/calculate/escape-velocity?body=earth"},{"name":"Moon, surface","inputs":{"body":"moon"},"expected":{"escape_velocity_km_s":2.376,"circular_orbital_velocity_km_s":1.68,"surface_gravity_m_s2":1.625},"url":"https://tttkmbb.com/api/v1/calculate/escape-velocity?body=moon"}],"faq":[{"q":"Why is 11.2 km/s different from the speed rockets reach?","a":"Escape velocity is the speed needed at the surface with no further thrust and no atmosphere; rockets accelerate gradually, lose speed to drag and gravity, and usually enter orbit (7.9 km/s at low altitude) rather than escaping."},{"q":"Why does the value change with altitude?","a":"Both speeds fall with distance from the centre as 1/√r: at 400 km above Earth the escape velocity is about 10.85 km/s and the orbital speed 7.67 km/s."},{"q":"How does surface gravity relate to escape velocity?","a":"v_escape = √(2 g R): two bodies with the same g but different radii have different escape speeds, which is why the Moon's small radius gives only 2.38 km/s."}],"tags":["escape velocity","orbital velocity","surface gravity","gravitational parameter","escape speed","planet"],"related":[{"calculator_id":"orbital-period","reason":"Period and speed of an orbit of any size around the same bodies."},{"calculator_id":"planet-weight","reason":"Weight of an object under each body's surface gravity."},{"calculator_id":"kinetic-energy","reason":"Kinetic energy needed at escape speed for a given mass."}],"links":{"html":"https://tttkmbb.com/science/escape-velocity","markdown":"https://tttkmbb.com/science/escape-velocity.md","json":"https://tttkmbb.com/science/escape-velocity.json","api":"https://tttkmbb.com/api/v1/calculate/escape-velocity","schema":"https://tttkmbb.com/api/v1/calculators/escape-velocity","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-24"},"timestamp":"2026-09-24T03:44:31Z"}