Standing still among falling paths

This optional article uses moving reference points to explore standing, falling and orbiting. Read Putting gravity together first for the complete main explanation.

Start with an ideal spherical Earth, with no atmosphere. Imagine small objects falling straight towards it from rest at an extremely large distance. They approach the surface at about 11.2 kilometres per second.

Now place a stream of these objects along every direction towards Earth’s centre. The visualisation uses them as moving reference points. They help us describe other motions, much as passing scenery helps us describe the motion of a train.

Why this particular speed?

The reference objects have the local escape speed at each height. Reverse their motion and they follow an outward journey that gradually slows, approaching zero speed at an infinite distance.

Other starting conditions give other paths. A stone dropped from a tower has not fallen as far and reaches the surface much more slowly. A sideways launch can produce an orbit. The reference stream is one chosen example of free fall, not the motion every object must have.

Holding and releasing a stone

Hold a stone still above the ground. Relative to you, its speed is zero. Relative to a reference object passing downwards, the stone is moving upwards. These are two measurements of the same situation from different viewpoints.

Your hand supplies the support that holds the stone at one height. A scale would measure that supporting force, rather than either of those relative speeds.

When you release the stone, it starts with zero speed relative to the ground and then gains downward speed. It does not immediately match the fast-moving reference stream. The visualisation lets you follow both measurements as the fall continues.

Giving it sideways motion

Release the stone with sideways speed and its path changes. At a suitable height and speed, it can orbit Earth while remaining in free fall throughout the journey.

You can also compare neighbouring falling objects. Two released side by side tend to draw together; two released one above the other tend to separate. This is the tidal stretching and squeezing introduced in How free-fall paths reveal curvature.

Compare a held stone, a drop and a sideways launch. Watch which viewpoint each speed reading uses: the ground or the falling reference objects.

The model leaves out air resistance, Earth’s rotation and the gravity of other bodies. Paths stop at the surface. The moving reference points are a way to describe the motion; they do not represent a substance flowing through space and carrying the stone with it.