Escape Velocity
The minimum speed to escape a planet's gravity.
About this topic
Escape velocity is the minimum speed needed to leave a planet's gravity without further propulsion: v = √(2GM/r). For Earth it is about 11.2 km/s, for the Moon 2.4 km/s. It comes from setting kinetic energy equal to the gravitational potential energy to be overcome.
It doesn't depend on the mass of the escaping object, only on the planet's mass and the starting distance, so a bullet and a rocket would need the same speed if they were fired in a single burst. It also doesn't depend on direction, as long as the path doesn't hit anything. It is exactly the square root of 2 times the circular orbit speed at the same height.
Worked example: for Earth, M = 6.0 × 10²⁴ kg and r = 6.4 × 10⁶ m, giving v = √(2 × 6.67 × 10⁻¹¹ × 6.0 × 10²⁴ / 6.4 × 10⁶) ≈ 11,200 m/s, or about 40,000 km/h. Real rockets do not need this speed at launch because they keep burning fuel and climb gradually.
Escape velocity explains why the Moon has almost no atmosphere: its gravity is weak enough that gas molecules can leak away, while Earth holds on to nitrogen and oxygen but loses light hydrogen and helium. A black hole is an object whose escape velocity exceeds the speed of light. Remember that reaching escape speed means you coast away with zero speed at infinity.
Key ideas
- v = √(2GM/r)
- About 11.2 km/s for Earth
- Independent of the mass of the projectile
Quick check
Use cases: where Escape Velocity helps
- Homework: review the key idea behind Escape Velocity before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Escape Velocity without notes.
- Visual learning: play with the interactive lab to see how Escape Velocity changes when you adjust its inputs.
- Teaching a friend: explain Escape Velocity in your own words, then compare your version with the key ideas.
The same laws describe car crashes, sports, satellites and everyday machines.
Frequently asked questions
What is Escape Velocity?
The minimum speed to escape a planet's gravity.
What will I learn in Escape Velocity?
v = √(2GM/r). About 11.2 km/s for Earth. Independent of the mass of the projectile.
Is Escape Velocity part of Physics?
Yes. It is one of 150 Physics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Escape Velocity lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Escape Velocity?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.