How can a spacecraft keep falling without reaching the ground?

Astronauts can float inside a spacecraft while gravity continues pulling the spacecraft toward Earth. The apparent contradiction disappears when we follow both motions together. The spacecraft is falling, and the astronauts are falling with it. What keeps them from reaching the ground is not the absence of gravity, but the sideways motion that carries their path around the curved planet.

A thrown object moves forward while gravity bends its path downward. An orbit extends that idea: with a suitable starting position and velocity, the surface curves away beneath the falling object. In an ideal orbit above the atmosphere, no continual rocket push is needed to hold the spacecraft up. A launch supplies the position and motion; gravity keeps changing the direction of travel afterward.

A circular orbit makes the geometry especially clear. At each instant, the velocity is tangent to the circle, while gravitational acceleration points toward the center. Without that inward acceleration, the spacecraft would continue along a straight tangent. With it, the direction of velocity changes continually even when the speed remains constant. Gravity is the force providing centripetal acceleration; it is not canceled by a second outward force in this description from an inertial frame.

For an approximately spherical Earth, gravitational acceleration is μ/r², where μ = GM combines the gravitational constant and Earth's mass. Circular motion at speed v requires inward acceleration v²/r. Equating them gives v = √(μ/r). The spacecraft's mass cancels, so a more massive spacecraft does not need a higher circular speed at the same radius. The radius r is measured from Earth's center, not from the ground beneath the spacecraft.

Using the rounded values μ = 400,000 km³/s² and r = 16,000 km gives v = √25 = 5 km/s. The inward acceleration is 400,000 divided by 16,000², or 0.0015625 km/s²: 1.5625 m/s². These are an ideal example, not a particular mission. A larger circular orbit has a lower speed because gravity is weaker there. It also has a longer path around Earth, so completing a revolution takes longer.

Inside the cabin, nearby freely moving objects have almost the same gravitational acceleration as the spacecraft. The floor does not need to keep pushing them up as a floor on Earth does, so they appear weightless relative to their surroundings. Small differences in gravity, air motion and contact forces still affect their relative motion; floating is not proof that all forces have disappeared.

Many real orbits are elliptical, and atmospheric drag and other gravitational influences gradually change trajectories. Maintaining a particular orbit can therefore require corrections. The central idea remains extraordinary: an orbit is a continuous fall whose changing direction can carry a spacecraft around a world, while everything freely floating inside shares nearly the same journey.