Diagrams.ink / Orbital mechanics

Launch speed decides the orbit.

Gravity always pulls the planet toward the star. A sideways push decides whether it falls in, loops round on a circle or an ellipse, or escapes for good. Drag the violet launch arrow, then watch the trail.

Fig. 1 — One star, one planet, one launchReady
gravity (length compressed) velocity predicted path trail: circle · ellipse · escape · crash Top-down view, tilted · 1 AU = Earth–Sun distance
Time
Try

Distance

1.00 AU

Speed

Gravity here

Orbit type

Period

Integrator check

What you are seeing

Speed set by the slider is measured against the circular speed at 1 AU (29.8 km/s). Escape speed is always √2 times the circular speed at the same distance, which is why the track changes colour at 1.00 and 1.41.

Simplified two-body model
  • One star fixed at the centre and one planet of negligible mass, pulled only by the star's inverse-square gravity. No other planets, drag, relativity or star spin.
  • Consistent units: distance in AU, time in years, GM = 4π² AU³/yr², so a circular orbit at 1 AU lasts exactly 1 year. The launch is tangential, counter-clockwise.
  • The star is drawn 0.05 AU in radius (about 11× the Sun's, so you can see it). If the path reaches that radius, the planet collides and the run stops.
  • Stepping uses a symplectic leapfrog with steps of 1% of the local orbital time, so orbits don't spiral; the check above shows the leftover energy error.