Lagrange Points

The view spins with the Sun and Earth, so both stand still. A probe that sits still in this spinning view feels three things: the Sun's pull, Earth's pull, and the spin push (the centrifugal effect of riding along), always pointing straight away from the centre of mass (CM).

The arrows are drawn tip to tail. The white leftover runs from the probe to the end of the chain. When the chain closes back on the probe, nothing is left over: the probe can ride along with Earth, engine off. That spot is a Lagrange point.

Arrows use the frame's natural scale, where the spin push is an exact copy of the dashed line from the CM to the probe. So balance means one thing you can see: gravity lands on the target ring at the CM. When arrows would get too long they all shrink together, and the target slides along the dashed line by the same factor.

"Sun" and "Earth" are just names for a heavier and a lighter body. The default mass (25% of the Sun) is exaggerated so every effect is easy to see; the Earth tick on the slider is the real ratio.

Keys

←↑→↓

Move the probe (Shift: faster, Alt: finer)

1–5

Jump to L1–L5 (once found)

[ ]

Change the mass (Shift: next preset)

S

Sweep the mass

Space

Let go / catch the probe (chapter "Let go")

F

Chain or fan arrows

Z / 0

Zoom to Earth / fit view

R

Reset probe and mass

PgUp PgDn

Previous / next chapter

Esc

Stop an animation, close this

Mouse and touch

Press or tap anywhere to put the probe there, then drag. On touch screens the drag is relative, like a trackpad, so your finger never covers the arrows. Scroll or pinch to zoom; Shift-drag to pan. Hold Alt to turn off snapping.