[Leejohnston]

## Orbital Velocity — Why Satellites Keep Missing Earth

### 1. The Equation

Orbital velocity:

v = √(GM ÷ r)

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### 2. What Each Symbol Means

- v = orbital velocity
- G = gravitational constant
- M = mass of the planet
- r = distance from the planet’s centre

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### 3. What the Equation Is Telling Us

An orbit is **continuous free fall** where forward speed causes the ground to curve away.

Satellites don’t avoid falling — they miss the planet.

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

Gravity pulls inward while velocity carries the satellite forward.

At the right speed, these balance perfectly.

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### 5. Worked Example

For low Earth orbit:
v ≈ **7.8 km/s**

That’s fast enough to circle Earth every ~90 minutes.

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### 6. Real-World Applications

- Satellites
- Space stations
- Planetary motion
- Orbital mechanics

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### 7. Common Misconceptions

- Orbit means no gravity → false
- Higher orbits need more speed → false
- Rockets keep firing in orbit → false

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### Try It Yourself

Why do higher orbits actually move more slowly?