Orbital Velocity Simulator

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.

What this is, and how it works

This is a working model of one planet around the Sun. The green arrow is the way it is already moving. The amber arrow is the Sun’s pull, always straight inward. Set the distance and the sideways speed, then watch: a circle, a long ellipse, an escape, or a fall into the Sun.

Distance is how far out. Sideways speed is a percentage of the speed a circle at that distance needs. Make it circular sets the two together, which is the whole point. Planet chips set a real planet’s distance and the speed that distance actually requires.

A heavier planet is pulled harder, and is harder to turn, in exact proportion — so mass never appears on the sliders. The table below is the comparison the page exists for: the pull per kilogram at each planet, and the speed that answers it.

Things to try

• Break the circle, gently. Press Make it circular, then drag the speed down to about 90%. The point where you slowed it stays put, and the far side of the orbit drops closer to the sun. Slowing down doesn't make a planet spiral in — it reshapes the loop.
• Raise an orbit by pushing forwards. Back to circular, then up to about 110%. Now the far side lifts away. This is how real spacecraft climb: they don't point up, they speed up.
• Find escape. Keep adding speed and watch the ellipse stretch — somewhere around 141% of circular it stops being a loop at all and the planet leaves. That number is no accident: escape speed is always the circular speed times the square root of two.
• Try to hit the sun. Drag the speed as low as it goes. Even at a crawl, the planet whips around the sun and comes back — to actually fall straight in you would have to shed nearly all of it. Falling into the sun is one of the hardest trips in the solar system.
• Move house. Use the presets to jump to Mercury's distance, then Neptune's, and watch two read-outs together: the sun's pull per kilogram, and the speed a circle needs. Closer means pulled harder means faster — the race the solar system simulator shows, explained by two numbers.

Every planet: the pull it feels, and the speed that answers it

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.

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.

Keep going

The glossary of every term Newton's cannonball, with the tables The whole solar system, moving Earth, sun & moon together Every planet, a page each Launch windows to Mars