[Leejohnston]

## Escape Velocity — How Fast You Need to Leave a Planet

### 1. The Equation

v = √(2GM ÷ r)

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### 2. What Each Symbol Means

- v = escape velocity
- G = gravitational constant
- M = mass of the planet
- r = radius from the centre

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### 3. What the Equation Is Telling Us

Escape velocity is the **minimum speed needed to never fall back**.

It does not depend on:
- mass of the object
- direction (ignoring atmosphere)

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### 4. Where It Comes From (Intuition)

You must give an object enough energy to overcome gravity completely.

This equation compares:
- gravitational energy
- kinetic energy

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### 5. Worked Example

For Earth:
Escape velocity ≈ **11.2 km/s**

That’s:
- ~40,000 km/h
- fast enough to cross continents in minutes

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### 6. Real-World Applications

- Rocket launches
- Space missions
- Planetary science
- Black hole physics

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### 7. Common Misconceptions

- Rockets must keep firing forever → false
- Escape velocity is a speed limit → false
- Gravity stops at space → false

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### Try It Yourself

Which planet would be hardest to escape:
- Earth?
- Mars?
- Jupiter?