{"success":true,"version":"v1","request":{"tool":"get_calculator_schema","calculator_id":"gravitational-force"},"result":{"entity_type":"calculator","id":"gravitational-force","calculator_id":"gravitational-force","canonical_url":"https://tttkmbb.com/physics/gravitational-force","name":"Gravitational Force Calculator","title":"Gravitational Force Calculator – Newton's Law of Universal Gravitation F = G·m₁·m₂ / r²","category":"physics","category_name":"Physics","tool_name":"calculate_gravitational_force","featured_mcp_tool":false,"description":"Computes the attractive gravitational force between two point or spherically symmetric masses at a given centre-to-centre distance with Newton's law and the CODATA 2018 value of G, plus the acceleration each mass experiences.","use_when":"You need the gravitational pull between two bodies (planet and satellite, star and planet, two laboratory masses) or the surface gravity of a body from its mass and radius.","do_not_use_when":"You only need weight near Earth's surface (use force with 9.80665 m/s²), or relativistic effects matter (near black holes, precision orbits).","inputs":[{"name":"mass1_kg","label":"Mass 1","type":"number","unit":"kg","required":true,"exclusive_min":0,"description":"First mass in kilograms (Earth = 5.972e24, Sun = 1.989e30).","example":5.972e+24},{"name":"mass2_kg","label":"Mass 2","type":"number","unit":"kg","required":true,"exclusive_min":0,"description":"Second mass in kilograms (Moon = 7.342e22).","example":1},{"name":"distance_m","label":"Distance between centres","type":"number","unit":"m","required":true,"exclusive_min":0,"description":"Centre-to-centre separation in metres (Earth's mean radius = 6.371e6, Earth–Moon = 3.844e8).","example":6371000}],"outputs":[{"name":"force_n","label":"Gravitational force","type":"number","unit":"N","decimals":15,"description":"F = G × m1 × m2 / r², attractive along the line joining the centres (rounded to 1e-15 N)."},{"name":"force_micronewton","label":"Gravitational force","type":"number","unit":"µN","decimals":6,"description":"Same force in micronewtons, convenient for laboratory-scale masses."},{"name":"acceleration_of_mass2_m_s2","label":"Acceleration of mass 2","type":"number","unit":"m/s²","decimals":15,"description":"F / m2 = G × m1 / r²: the gravitational field of mass 1 at that distance (surface gravity when r is the radius)."},{"name":"acceleration_of_mass1_m_s2","label":"Acceleration of mass 1","type":"number","unit":"m/s²","decimals":15,"description":"F / m1 = G × m2 / r² (rounded to 1e-15 m/s²; negligible for planet-sized mass 1)."}],"input_schema":{"type":"object","properties":{"mass1_kg":{"description":"First mass in kilograms (Earth = 5.972e24, Sun = 1.989e30). Unit: kg.","type":"number","exclusiveMinimum":0,"examples":[5.972e+24],"x-unit":"kg"},"mass2_kg":{"description":"Second mass in kilograms (Moon = 7.342e22). Unit: kg.","type":"number","exclusiveMinimum":0,"examples":[1],"x-unit":"kg"},"distance_m":{"description":"Centre-to-centre separation in metres (Earth's mean radius = 6.371e6, Earth–Moon = 3.844e8). Unit: m.","type":"number","exclusiveMinimum":0,"examples":[6371000],"x-unit":"m"}},"additionalProperties":false,"required":["mass1_kg","mass2_kg","distance_m"]},"output_schema":{"type":"object","properties":{"force_n":{"description":"F = G × m1 × m2 / r², attractive along the line joining the centres (rounded to 1e-15 N). Unit: N.","type":"number","x-unit":"N"},"force_micronewton":{"description":"Same force in micronewtons, convenient for laboratory-scale masses. Unit: µN.","type":"number","x-unit":"µN"},"acceleration_of_mass2_m_s2":{"description":"F / m2 = G × m1 / r²: the gravitational field of mass 1 at that distance (surface gravity when r is the radius). Unit: m/s².","type":"number","x-unit":"m/s²"},"acceleration_of_mass1_m_s2":{"description":"F / m1 = G × m2 / r² (rounded to 1e-15 m/s²; negligible for planet-sized mass 1). Unit: m/s².","type":"number","x-unit":"m/s²"}}},"formula":"force_n = G × mass1_kg × mass2_kg / distance_m² with G = 6.67430e-11 m³ kg⁻¹ s⁻²; acceleration_of_mass2 = force_n / mass2_kg; acceleration_of_mass1 = force_n / mass1_kg","method":"Point masses or uniform spheres (shell theorem); inside a body or for irregular shapes the inverse-square law does not apply directly.","sources":[{"name":"NIST CODATA 2018 – Newtonian constant of gravitation G","url":"https://physics.nist.gov/cgi-bin/cuu/Value?bg","type":"standard","retrieved_at":"2026-09-23"},{"name":"HyperPhysics – Gravity","url":"http://hyperphysics.phy-astr.gsu.edu/hbase/grav.html","type":"reference","retrieved_at":"2026-09-23"},{"name":"Wikipedia – Newton's law of universal gravitation","url":"https://en.wikipedia.org/wiki/Newton%27s_law_of_universal_gravitation","type":"reference","retrieved_at":"2026-09-23"}],"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 and 1 kg at Earth's mean radius","inputs":{"mass1_kg":5.972e+24,"mass2_kg":1,"distance_m":6371000},"expected":{"force_n":9.82,"force_micronewton":9819973,"acceleration_of_mass2_m_s2":9.82},"url":"https://tttkmbb.com/api/v1/calculate/gravitational-force?mass1_kg=5.972e%2B24&mass2_kg=1&distance_m=6371000"},{"name":"Two 1000 kg masses 1 m apart","inputs":{"mass1_kg":1000,"mass2_kg":1000,"distance_m":1},"expected":{"force_n":0.000066743,"force_micronewton":66.743,"acceleration_of_mass1_m_s2":6.6743e-8},"url":"https://tttkmbb.com/api/v1/calculate/gravitational-force?mass1_kg=1000&mass2_kg=1000&distance_m=1"}],"faq":[{"q":"Why is the result 9.82 and not 9.81 m/s² for Earth?","a":"The mean radius and mass give the field of a non-rotating uniform sphere; the measured surface value (about 9.80 average) is lowered by Earth's rotation and flattening."},{"q":"Which distance do I use for planets?","a":"The distance between the centres of mass, not between the surfaces: for surface gravity use the planet's radius."}],"tags":["gravitational force","universal gravitation","newton's law of gravity","gravitational constant","surface gravity"],"related":[{"calculator_id":"newtons-second-law","reason":"Weight from mass and local g."},{"calculator_id":"potential-energy","reason":"Energy of a mass at a height near the surface."},{"calculator_id":"centripetal-force","reason":"Force required to keep a satellite in circular orbit."}],"links":{"html":"https://tttkmbb.com/physics/gravitational-force","markdown":"https://tttkmbb.com/physics/gravitational-force.md","json":"https://tttkmbb.com/physics/gravitational-force.json","api":"https://tttkmbb.com/api/v1/calculate/gravitational-force","schema":"https://tttkmbb.com/api/v1/calculators/gravitational-force","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp"},"version":"v1","updated_at":"2026-09-23"},"timestamp":"2026-09-23T23:30:17Z","next_actions":[{"tool":"run_calculator","calculator_id":"gravitational-force","reason":"Run Gravitational Force Calculator with the inputs above."}],"links":{"markdown":"https://tttkmbb.com/physics/gravitational-force.md"}}