We've changed our name — alarm-clock.org is now timeandspace.science. Same tools, same pages, new address.
Set how far out a planet sits and how fast it is moving sideways, and watch what gravity does with it — a circle, a long ellipse, an escape, or a fall into the sun. The two arrows are the whole story: where it is going, and where it is being pulled.
Green: the way it is movingAmber: the sun's pull
Stable circle
Falling exactly as fast as the curve of the orbit carries it away.
×1.00 of circular
Set it to a real planet:
Each tap of a planet sets that planet's distance and the speed that distance actually requires — the two always move together, which is the whole point. The sun is drawn far larger than scale (at this size its true disc would be a fraction of a pixel, and you could not see whether an orbit hits it); the rings are one AU apart, and the arrows are indicative in length — the exact figures are the numbers beside them.
It is falling in. Constantly. That is what an orbit is — a fall that keeps missing. Mercury is pulled toward the sun 6.7× stronger than Earth is, and it does exactly what that pull demands: it accelerates sunward the whole time. What saves it is that it is also travelling sideways at 47.9 km/s, so by the time it has fallen, it has also moved along — and the sun is no longer where it was falling toward.
Stronger pull needs faster sideways motion to keep missing, and that is the entire relationship: the speed for a circle is the square root of the pull times the distance. Mercury feels 6.7× Earth's pull and needs 1.6× Earth's speed. Neptune feels 904 times less pull and coasts at 5.4 km/s — slower than a rifle bullet is fast, and plenty.
The surprise is how hard it is to actually fall in. Slowing a planet down does not drop it into the sun; it drops it onto a longer, more lopsided ellipse that swings close and comes straight back out. From Earth's distance you would have to shed almost all of your 29.8 km/s — down to about 2.9 km/s — before the near end of that ellipse actually reached the sun's surface. Try it on the slider above.
The amber arrow is the sun's pull. It always points straight at the sun, and its strength is GM/r² — nothing else. Not the planet's mass, not its speed, not what it is made of. Move twice as far out and it drops to a quarter.
The green arrow is where the planet is already going. Gravity never points along it; at a circular orbit the two are exactly at right angles, which is why the pull changes the planet's direction continuously and its speed not at all. Bend the path enough and it closes into a circle.
The planet's own mass is absent from all of this, and that is not an approximation. A heavier planet is pulled harder — but it also takes proportionally more force to turn, and the two cancel exactly. A grain of dust at Mercury's distance orbits at Mercury's speed. This is the same fact as Galileo's two balls hitting the ground together, and it is why the simulator above never asks you for a mass: there is nowhere to put one.
Scale check on that pull: at Earth's distance the sun tugs each kilogram with about 0.0059 newtons — roughly 1/1654 of what the ground under your feet does right now. It is a weak pull that has simply been applied, without interruption, for four and a half billion years.
This is the comparison the whole page is about. The third column is the sun's pull on one kilogram at that planet's distance — the same kilogram, moved further out each row. It collapses as the square of the distance: Mercury's kilogram is pulled 6.7× stronger than Earth's and 181× stronger than Jupiter's. The speed columns are what each planet does about it.
| Planet | Distance (AU) | Sun's pull (N per kg) | vs Earth | Circular speed (km/s) | Mean actual speed (km/s) | Year (Earth years) |
|---|---|---|---|---|---|---|
| Mercury | 0.39 | 0.0396 | 6.7× | 47.9 | 47.4 | 0.2 |
| Venus | 0.72 | 0.0113 | 1.9× | 35.0 | 35.0 | 0.6 |
| Earth | 1.00 | 0.0059 | 1/1 | 29.8 | 29.8 | 1.0 |
| Mars | 1.52 | 0.0026 | 1/2 | 24.1 | 24.1 | 1.9 |
| Jupiter | 5.20 | 0.00022 | 1/27 | 13.1 | 13.1 | 11.9 |
| Saturn | 9.54 | 0.00007 | 1/91 | 9.6 | 9.6 | 29.5 |
| Uranus | 19.19 | 0.00002 | 1/368 | 6.8 | 6.8 | 84.1 |
| Neptune | 30.07 | 0.00001 | 1/904 | 5.4 | 5.4 | 164.9 |
Every figure is computed from two things only: the sun's gravitational parameter and each planet's semi-major axis. Nothing here is typed in, so nothing can drift from the simulator above.
Why two speed columns. "Circular speed" is what a perfect circle at that distance needs — the number the simulator uses. "Mean actual speed" is the average around the real, slightly squashed orbit, and it is the figure reference books print. They agree for the near-circular orbits and part company for Mercury (47.9 against 47.4), whose orbit is the most eccentric of the eight: it actually runs 59.0 km/s at its closest and 38.9 km/s at its furthest. That swing inside one orbit is the same law again — closer means faster.
Why doesn't the sun's gravity pull the planets into it? It does pull them — every planet is falling toward the sun at every moment. They miss because they are also moving sideways fast enough that the sun is no longer directly ahead by the time they have fallen. An orbit is a continuous fall that keeps missing, not a balance between gravity and some outward force.
Does Mercury have to travel faster than the other planets? Yes. The sun's pull on each kilogram at Mercury's distance is about 6.7 times what it is at Earth and about 181 times what it is at Jupiter, because gravity falls off as the square of distance. To keep missing a pull that strong, Mercury must move sideways at about 47.9 km/s, against Earth's 29.8 and Jupiter's 13.1. Closer in means pulled harder and moving faster — the speed goes as one over the square root of the distance.
Does a heavier planet orbit differently from a lighter one? No. The planet's mass cancels out completely: it is pulled harder in exact proportion to how much harder it is to turn. At a given distance every object needs the same orbital speed, whether it is Jupiter, a satellite or a speck of dust. That is why the simulator has no mass control.
What would actually happen if a planet slowed down? It would not spiral in. It would drop onto a more elongated ellipse — swinging closer to the sun, speeding up as it fell, then climbing back out to where it started. To actually hit the sun from Earth's distance you would have to cut the speed from 29.8 km/s to roughly 2.9 km/s, because anything faster still has enough sideways motion to miss.
What if a planet sped up instead? It swings further out and slows down as it climbs, then falls back — a longer ellipse. Past 42.1 km/s at Earth's distance (the circular speed times the square root of two) it never comes back at all: that is escape velocity, and the orbit stops being a closed loop.
Why don't the planets gradually slow down and fall in? Because there is nothing to slow them. Space has no meaningful air resistance, and gravity — being always at right angles to the motion on a circular orbit — does no work on them. With no friction there is nothing to bleed away the sideways speed, so the fall keeps missing indefinitely.
Where did the sideways motion come from in the first place? From the cloud of gas and dust the solar system condensed out of, which was already turning slightly. As it collapsed it spun faster, for the same reason a skater speeds up when they pull their arms in, and it flattened into a disc. The planets formed inside that already-orbiting disc, and inherited its motion.
Is this simulator accurate? The physics is exact for the case it models: one body orbiting a much heavier one, with the sun's real gravitational parameter and no other planets pulling. Closed orbits are solved rather than stepped, so they do not drift. What it does not include is the pull of the other planets on each other, or the tiny relativistic effect that shifts Mercury's orbit; the drawing's sun is also far larger than scale, which the caption states.
Why planets don't fall into the sun The whole solar system, moving Earth, sun & moon together Launch windows to Mars