--- title: "Gravitational Potential and Escape Speed" description: "Gravitational potential is the signed external work per kilogram to move a small mass slowly from infinity to a point. With zero at infinity it is negative. Escape speed is the minimum outward launch " canonical: https://lightmysky.com/learn/science/gravitational-potential-and-escape-speed-mt_drqTwCD9W8 source: https://lightmysky.com/learn/science/gravitational-potential-and-escape-speed-mt_drqTwCD9W8.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Gravitational Potential and Escape Speed Gravitational potential is the signed external work per kilogram to move a small mass slowly from infinity to a point. With zero at infinity it is negative. Escape speed is the minimum outward launch speed that reaches infinity under gravity alone, without drag or collision. Subject: Science · Area: Forces & Motion · Ages 16 to 18 Page: https://lightmysky.com/learn/science/gravitational-potential-and-escape-speed-mt_drqTwCD9W8 ## Ready when they can - Calculates potential as minus GM over r and potential energy as minus GMm over r at a stated position - Explains the negative sign by naming infinity as the zero of the scale - Gets escape speed by setting kinetic energy equal to the depth of the well ## Lesson: Negative potential wells and escape speed Gravitational potential V is the work per kilogram done by an external force to move a small mass slowly from infinity to a point. With zero at infinity, V = -GM/r outside a spherical source of mass M. G is the gravitational constant and r is distance from its centre. V is in J/kg and is negative: gravity does positive work inward, so the external work is negative. **Example.** Lifting a 9000 kg craft from Earth's surface to 400 km up raises U by about 3.32 x 10^10 J. Use change in U = GMm(1/r1 - 1/r2), with r1 = 6.37 x 10^6 m, r2 = r1 + 4.00 x 10^5 m, M = 5.96 x 10^24 kg and G = 6.67 x 10^-11 N m^2/kg^2. This excludes the kinetic energy needed for orbit. This is about ten months' energy for a household using 909 kWh per month. Potential energy U = mV = -GMm/r, in joules. Kinetic energy K = m v^2 / 2. At starting distance R, GMm/R is the depth of the potential-energy well below zero. Escape speed is the minimum outward launch speed to reach infinity under this source's gravity alone, without drag, further thrust or collision. At this threshold K + U = 0, so m v^2 / 2 = GMm/R and v = sqrt(2GM/R). Measure R from the source's centre. From Earth's surface it is about 11.2 km/s. Total mechanical energy is E = K + U. With gravity alone, an inward fall lowers U and raises K by the same amount, so E stays constant. Negative E means gravitationally bound, not necessarily in orbit. E of zero or more means unbound, not necessarily moving outward. An unbound object can escape if its path avoids collision. Separating masses raises U and needs positive work against gravity. For a spherical planet of mass M and radius R, surface escape speed is v = sqrt(2GM/R), under the gravity-only launch assumptions. Compare planets with the same mass by keeping 2GM fixed. A smaller radius gives a larger 2GM/R and therefore a greater escape speed. Its surface potential energy U = -GMm/R is more negative, so its potential-energy well is deeper. **Recap.** With zero at infinity, V = -GM/r. Escape speed supplies enough kinetic energy to approach infinity with zero speed under gravity alone. *Includes a lifting example adapted from OpenStax, University Physics Volume 1, section 13.3, Gravitational Potential Energy and Total Energy. The inward-fall question was written for this dataset.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Calculating work done and power](https://lightmysky.com/learn/science/calculating-work-done-and-power-mt_udulQxseg1) - [Newton's Law of Gravitation and Gravitational Field Strength](https://lightmysky.com/learn/science/newtons-law-of-gravitation-and-gravitational-field-strength-mt_uUYXl3L0oW) ## Opens up - [General Relativity: Curved Spacetime and Its Tests](https://lightmysky.com/learn/science/general-relativity-curved-spacetime-and-its-tests-mt_-rZZxZwU2L) - [Curvature and the Einstein field equation](https://lightmysky.com/learn/science/curvature-and-the-einstein-field-equation-mt_1CxE6kRDt_) - [The Two-Body Problem, Orbital Energy and Kepler's First Two Laws](https://lightmysky.com/learn/science/the-two-body-problem-orbital-energy-and-keplers-first-two-laws-mt_CjHFftkB6M) - [Electric Potential and the Uniform Field Between Plates](https://lightmysky.com/learn/science/electric-potential-and-the-uniform-field-between-plates-mt_LKTfeYxNde)