---
title: "Gravitational Potential and Escape Speed"
description: "Gravitational potential is the work per kilogram needed to bring a mass in from infinity, which makes it negative everywhere near a source. Escape speed is the speed whose kinetic energy exactly fills"
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: 2026-09-12
---

> **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 work per kilogram needed to bring a mass in from infinity, which makes it negative everywhere near a source. Escape speed is the speed whose kinetic energy exactly fills that well.

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 is the work per kilogram needed to bring a mass in from infinity. Infinity is set as zero, so the value is negative everywhere near the source.

**Example.** Lifting a 9000 kg craft from Earth's surface to 400 km up needs positive work against gravity. The gain is about 3.32 times 10 to the 10 joules, roughly ten months of one home's energy use.

Potential energy is potential times the small mass: U equals minus G M m over r. Escape speed comes from setting kinetic energy equal to the depth of the well, giving v equals root 2 G M over R. From Earth it is about 11.2 km/s ignoring air.

**Tip.** Negative total energy means bound and orbiting, while zero or more means escaping. Falling inward drops to lower, more negative energy, and separating needs positive work.

**Recap.** Potential is negative work per kilogram from infinity, and escape speed just fills that well.

## 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)