An orbit is just falling. The trick is moving sideways fast enough that you keep missing the ground.
In 1687, Isaac Newton published a thought experiment that, more than three centuries later, is still the cleanest explanation of what an orbit actually is. He asked the reader to picture a cannon mounted on top of a very tall mountain, firing horizontally. With a small charge of gunpowder, the cannonball arcs through the air and falls back to the ground a short distance away. Pack in more powder and it travels farther. With enough powder, Newton claimed, something strange would happen.
The body projected with a less velocity, describes the lesser arc; with a greater velocity, the greater arc; and, augmenting the velocity, it goes farther and farther, and at last, going beyond the circumference of the Earth, should pass quite by without touching it. Newton, A Treatise of the System of the World, 1728
The cannonball never lands. It falls toward the Earth at every moment, but the Earth's surface curves away beneath it just as fast. That is what an orbit is — a permanent state of falling in which you keep missing what you're falling toward.
Newton's other contribution was working out why. He proposed that every massive object in the universe attracts every other, with a force that grows with mass and weakens with distance. The full statement is Newton's law of universal gravitation:
$$ F = \frac{G M m}{r^2} $$Here $F$ is the gravitational force between two objects of mass $M$ and $m$, separated by distance $r$. The constant $G \approx 6.674 \times 10^{-11}\ \mathrm{N\,m^2/kg^2}$ — small, because gravity is by far the weakest of the fundamental forces. Two bowling balls a meter apart attract each other with a force of about a billionth of a newton. You'd never notice. But pile up enough mass and the effect adds up: the Earth is six trillion trillion kilograms, and the result is the steady tug we live in.
The form of the equation contains two ideas worth pausing on. First, $F$ scales with the product of both masses — not the sum, not the larger one, but the product. Heavy objects pull on each other harder than light ones do. Second, $F$ falls off as $1/r^2$. Double the distance and the force drops by a factor of four. Move ten times farther away and gravity is one percent of what it was. This inverse-square law is what makes orbits possible. With a different power — say $1/r$ or $1/r^3$ — the math works out completely differently and you don't get the closed elliptical orbits we'll explore in later modules.
If you've taken introductory physics, you've used $g = 9.8\ \mathrm{m/s^2}$ — the acceleration of falling objects near Earth's surface. That number isn't fundamental. It's just what Newton's law gives you when you plug in Earth's mass and radius:
$$ g = \frac{G M_\oplus}{R_\oplus^2} \approx 9.8\ \mathrm{m/s^2} $$where $M_\oplus = 5.97 \times 10^{24}\ \mathrm{kg}$ and $R_\oplus = 6{,}371\ \mathrm{km}$. The acceleration only feels constant because we don't usually move far enough up or down to notice $r$ changing. Climb a tall mountain and $g$ drops by about 0.3%. Get to the altitude of the International Space Station, 400 km up, and $g$ is around $8.7\ \mathrm{m/s^2}$ — still 89% of the surface value.
The simulator below puts a cannon on top of a tall mountain — adjustable from 200 km to 2000 km — and lets you set the firing speed. Real Newtonian gravity, real numerical integration, no flat-Earth approximation. Drag the speed slider through the suborbital range and watch the cannonball arc back down. Past orbital velocity at your launch altitude, the cannonball stops coming back. Past escape velocity, it leaves Earth forever.
Try varying the launch altitude. The orbital and escape speeds aren't fixed numbers — they depend on how far you start out from Earth's center. The often-quoted figures of 7.9 km/s and 11.2 km/s apply to a launch right at Earth's surface; from higher up, the numbers come down, because gravity is a little weaker there. The "orbital" and "escape" preset buttons retag themselves as you change altitude. We'll work out exactly how the numbers depend on altitude in the next module.
A few things to play with. With the altitude fixed, fire one shot at 6 km/s and another at 9 km/s — both are partial ellipses, but the slow one comes back to Earth and the fast one carries far around. Walk the speed up gradually and find the point where the trail just barely closes into a complete loop: that's the boundary between suborbital and orbital. Now change the launch altitude and find the boundary again. The exact value depends on where you started from. The math behind why is the subject of module 2.
Newton's cannonball stayed a thought experiment for 270 years. There was no way to give an object 7.9 km/s of horizontal speed. Cannons couldn't do it; rifles couldn't either. The fastest projectile humans had built before the 20th century was the Paris Gun of World War I, which managed about 1.6 km/s — fast enough to lob shells 130 km but nowhere near orbit.
What changed was rockets. Unlike a cannon, which gives a projectile its full speed in one shove, a rocket accelerates continuously, building up velocity over minutes. The first object to reach orbital velocity was Sputnik 1 in October 1957 — a 58-cm aluminum sphere, fired horizontally at the right speed from the right altitude, doing exactly what Newton had described.
And every satellite since then has been doing the same thing. Satview shows thousands of them at once, each one a permanent free-fall trajectory tuned to keep missing the planet they're falling toward.
The next module turns Newton's qualitative picture into a quantitative one. By setting the gravitational force equal to the centripetal force needed to follow a circle, we can derive the exact speed required for a circular orbit at any altitude — including whatever values the simulator above told you for the heights you tried.