Gravity · N-body · JPL Horizons
The Sun and planets from NASA JPL's own positions, run forward and back in time with Einstein's correction switched on, so you can watch relativity move Mercury's orbit by its famous 43 arcseconds a century.
Positions to scale; sizes are not.
The Sun, the eight planets and Pluto begin exactly where NASA's Jet Propulsion Laboratory puts them at midnight on 1 January 2026: positions and velocities from JPL's Horizons system, which spacecraft navigators use, and the masses from its DE440 ephemeris. From there nothing is looked up. Every body pulls on every other by Newton's law, and the page works out the rest, forward or backward in time.
Each planet carries its moons, so “Earth” is really the Earth–Moon pair's centre of mass and Jupiter weighs as much as Jupiter and its moons together. Asteroids and the Moon's own orbit are left out.
The integrator is a fourth-order symplectic method (Yoshida 1990), which keeps the system's energy from creeping up or down over millions of steps, stepping a tenth of a day at a time. Checked against Horizons a century later, in 2126, Mercury's direction from the Sun is off by about 1.6 arcseconds (the width of a coin seen from three kilometres), Venus and Mars by less than a tenth of one, and the outer planets by hundredths. Earth is about 15″ off, because the Earth–Moon pair does not move quite like a single point.
Without relativity, Mercury ends up 15″ off instead, which is where the story gets good.
Mercury's orbit is an ellipse whose closest point to the Sun, the perihelion, slowly turns. The other planets' tugs account for about 532″ a century of that turning. By the late 1800s astronomers knew the observed total was about 43″ more, and nothing in Newton's physics explained it. In 1915 Einstein showed that general relativity, which treats gravity as curved spacetime, predicts exactly that extra 43″. It was the theory's first success.
This page runs two copies of the solar system side by side: one with relativity's correction to the Sun's pull, one without. Everything else is identical, so the difference between their two Mercurys is relativity's share alone. Run it a few decades and the readout settles at about 42.85″ per century, against the 42.98″ general relativity predicts.
Kepler found in 1619 that a planet's orbital period squared is proportional to its distance cubed. The table works that law backwards: from each planet's position and speed right now it finds the ellipse it is on, and from the ellipse's size, the period. Compare it with NASA's measured periods. They agree to a fraction of a percent, and the small, wandering differences are the planets disturbing each other, which is exactly what Kepler's single-planet law leaves out.
Then break it. Make Jupiter ten, a hundred or a thousand times heavier. At a thousand it is nearly a second Sun, the Sun visibly swings around their shared centre, and the inner planets' orbits come apart.