Lagrange Points

A Sun-Earth co-rotating reference frame is used, in which the Sun and Earth are stationary. Move the white point and inspect force vectors.

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Note: for easier visual interpretation, the default Earth mass is intentionally increased to 25% of the Sun mass.

Point Diagnostics

Reference framerotating with Sun-Earth
Sun-Earth distance (m)n/a
Rotation rate ω (rad/s)n/a
Distance to CM (m)n/a
Co-rotation speed (m/s)n/a
Gravity from Sun (m/s2)n/a
Gravity from Earth (m/s2)n/a
Centrifugal acceleration (m/s2)n/a
Total acceleration (m/s2)n/a
Nearest L-point distance (m)n/a
g_sun
g_earth
centrifugal
sum
Sun-Earth orbit (dotted)
CM-Earth orbit (dashed)

Hotkeys

  • 1Toggle g from Sun
  • 2Toggle g from Earth
  • 3Toggle centrifugal
  • 4Toggle vector sum
  • LToggle Lagrange points
  • GToggle grid
  • SpaceLock/unlock particle
  • OToggle Sun-Earth orbit
  • CToggle CM-Earth orbit
  • RReset state

Tap/click canvas to lock/unlock the particle.
This scene is shown in a rotating frame co-rotating with the Sun-Earth pair around CM (center of mass), so Sun and Earth stay fixed in this view; the centrifugal term is therefore included and points away from CM.
The vectors are a local snapshot for a particle instantaneously at rest in this rotating frame.
Sun/Earth labels are intuitive names for two rotating bodies, one more massive than the other.