Saramsha

No. 051  ·  6 November 2026

Falling Fast Enough to Miss

An orbit isn't held up by anything — it's just falling, sideways fast enough that the ground curves away beneath you as quickly as you fall toward it. That's the whole idea Newton drew as a cannonball fired from an impossibly tall mountain: thrown fast enough, it never lands. Press anywhere on the sky, drag to aim and set the speed, then let go.

About this piece

Falling, and missing, forever

Isaac Newton made the point with a thought experiment: fire a cannonball from a mountain, and it falls in an arc and lands. Fire it faster, and it lands farther away, but it's still falling the whole time — gravity never stops pulling it down. Fire it fast enough, and something else happens: by the time it has fallen any noticeable distance, the curve of the Earth has dropped away by the same amount. The cannonball is still falling, continuously, forever — it just never gets any closer to the ground, because the ground keeps curving out from under it. That endless fall is an orbit. The International Space Station is not "above" the pull of gravity; astronauts aboard it feel weightless because they and the station are falling at exactly the same rate, sideways, together.

Reading the numbers

Whether a launch becomes a closed loop or a one-way trip comes down to a single number, the specific orbital energy: kinetic energy minus how deep in the gravity well you are, ε = v²/2 − GM/r. Launch slower than it takes to balance that well and ε is negative — the probe is bound, doomed to swing back no matter how far out it gets, tracing an ellipse with the star at one focus. Launch fast enough and ε crosses zero into positive territory: the probe is unbound, on a hyperbola, and it leaves with a specific "leftover" speed, v∞ = √(2ε), that it keeps forever once gravity can no longer slow it further. The panel's "path" reading is exactly this classification, and the eccentricity it reports is how stretched the ellipse is — 0 is a perfect circle, closer to 1 is a long thin cigar that just barely avoids crashing at one end.

Why a passing planet is free speed

In the Flyby scenario, a planet is quietly orbiting the star, and your probe can catch up with it. Seen from right next to the planet, gravity just bends the probe's path and hands its speed straight back on the way out — a close pass by a stationary body changes direction but never speed, the same way a ball bounces off a wall at the same speed it arrived. But the planet isn't stationary: it's moving through the star's frame, carrying momentum of its own. Catch it from behind and swing around its trailing side, and in the planet's own (moving) frame of reference the encounter is still speed-neutral — but translating that result back into the star's frame means the probe leaves carrying some of the planet's forward motion with it. It is exactly like a ball bouncing off the front of a moving truck: elastic in the truck's frame, a serious speedup in yours. NASA has used this for free, flying Voyager past four planets and New Horizons past Jupiter on the way to Pluto, without burning a drop of fuel for the boost itself. Time it wrong — catch the planet moving away from you — and the same trick steals speed instead, which is exactly how missions shed orbital energy to fall in toward the inner solar system.

What this model gets right, and what it skips

The gravity each probe feels is the real inverse-square law, integrated with a velocity-Verlet scheme that automatically takes smaller time steps during a close pass, which is what keeps a tight flyby from numerically exploding. What it skips, by design, is the full mutual problem: the star, the planet and the two binary stars move on paths fixed in advance — circles, worked out from the same gravity law — rather than being pulled back by the probes flying past them, which in reality have far too little mass to matter anyway. The Binary scenario is the one place that honesty matters most: two stars of equal mass pulling on a third small body is the classical three-body problem, famous for having no general closed-form solution at all. Almost every launch in there will eventually get flung out or swallowed; a loop that keeps closing on itself for more than a few orbits is luck, not an answer this simulation is hiding from you. The handful of exact closed three-body paths that do exist — including a genuine figure-eight — were only found by computer search in the 1990s and 2000s, centuries after Newton's cannonball.

Units throughout are arbitrary simulation units, not metres or seconds of real spaceflight — chosen only so an orbit takes a few comfortable seconds to watch. Drag distance sets launch speed directly (1 world-unit of drag ≈ 1 unit/s). The "path" reading for Flyby and Binary is a monopole approximation around the combined mass at the centre, marked accordingly — it is a good guide, not an exact conserved quantity, while a second body is actively pulling.