The Cannonball Concept
Learning Objectives
- Identify the difference between scalar velocity and vector velocity.
- Understand Isaac Newton's famous "Cannonball on a Mountain" thought experiment.
- Formally define an "orbit" as a state of perpetual, continuous free-fall.
- Conclude why satellites do not need engines firing continuously to stay in space.
What does it actually mean to be "in orbit"? It is a common misconception that rockets break free from gravity. In reality, they are completely surrendering to it.
1.3.1 Newton's Thought Experiment
Imagine standing on top of an impossibly tall mountain whose peak reaches far above the atmosphere ($100\text{ km}+$ altitude). You set up a heavy iron cannon perfectly level to the horizon.
If you drop a cannonball directly out of your hand, it falls straight down and hits the base of the mountain.
If you pack a small amount of gunpowder into the cannon and fire it horizontally, the ball flies forward, traces a graceful parabola, and eventually crashes into the ground far away.
But the Earth is a sphere, not an infinite flat plane. If you pack an absurd amount of gunpowder into the cannon, firing the ball at an extremely high horizontal velocity, something magical happens. The ball falls downward due to gravity, just like before. However, the ball is moving horizontally so incredibly fast, that the physical surface of the Earth curves away beneath it at the exact same rate the ball is falling.
FIGURE 3.1: PERPETUAL FREE-FALL
The International Space Station does not hover. Its engines are turned off. It is essentially a steel cannonball falling toward the Earth at 9.81 m/s², while simultaneously flying sideways at 7.6 km/s, allowing the planet to perpetually curve away beneath it.
1.3.2 The Definition of an Orbit
Therefore, we can formally define an orbit. An orbit is not "being weightless." An orbit is a trajectory where the horizontal vector velocity of the object mathematically matches the geometric curvature of the gravitational body.
The Engine-Off Truth
Because space is a perfect vacuum, there is exactly zero drag. Once a rocket turns off its engines and achieves this "orbital velocity," it will stay in free-fall forever without burning a single extra drop of fuel. The only force acting upon it is gravity, pulling it into a continuous circle.