Solar System in Motion

One rule, eight orbits

Every planet here obeys a single rule, Newton’s law of gravity: each body pulls every other body with a force proportional to their masses and falling off with the square of the distance between them. Nothing in the simulation tells Mercury to go round in 88 days or Neptune in 165 years. Those periods come out of the maths on their own.

The simulation adds up the pull of the Sun and of every planet on every other planet, then nudges each one forward by a tiny step of time, over and over. It uses a method called leapfrog (also known as velocity Verlet), which half-updates the speeds, moves the positions, then finishes the speeds. It is a favourite of astronomers because it keeps the total energy of an orbit from drifting, so planets stay on their tracks for thousands of years instead of slowly spiralling away.

Where the planets start

Each planet begins at the position NASA’s Jet Propulsion Laboratory formulas give for the day you open the page, using their published orbital elements. We checked these against known dates when Mars, Jupiter and Saturn lined up opposite the Sun as seen from Earth, and they agree to within about a degree. From then on, gravity takes over.

Why the outer planets are so slow

Distant planets feel a weaker pull, so they move more slowly, and they also have a longer way to go. Johannes Kepler found the exact relationship in 1619: the square of a planet’s year is proportional to the cube of its distance from the Sun. Jupiter is about 5.2 times farther out than Earth, and 5.2 cubed is about 140, whose square root is about 11.9. Jupiter’s year is indeed almost 12 Earth years.

A squeezed map

Space is mostly empty. If Neptune were drawn at the edge of your screen, Mercury would sit almost on top of the Sun and every planet would be smaller than a pixel. So this view squeezes distances: the drawing uses a logarithmic scale, so the inner planets get more room and the outer ones are pulled in. The planets are also drawn far larger than they really are. The physics underneath always uses the true distances, masses and speeds.

For the curious

Units are astronomical units (the Earth–Sun distance), years and solar masses, which makes the gravitational constant exactly 4π². The acceleration of each planet is the sum of G·m/r² towards every other body, and a tiny softening length keeps close encounters smooth. Kepler’s third law follows: P² = a³/(M + m) with P in years and a in AU. The faint rings are each planet’s starting orbit. The Kirkwood gaps in the asteroid belt mark distances where an asteroid’s year would be a simple fraction of Jupiter’s, so Jupiter’s regular tugs clear them out over millions of years.