PhysSandbox

Lagrange Points L1–L5

This interactive simulator explores Lagrange Points L1–L5 in Gravity & Orbits. CRTBP effective potential; L1–L5; Coriolis test particle. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Gravity & Orbits.

Key terms

  • lagrange
  • points
  • lagrange points
  • gravity
  • orbits

How it works

In the rotating frame of two masses in circular orbit, five Lagrange points appear where gravitational and centrifugal effects balance in the corotating effective potential. L1–L3 are collinear; L4 and L5 form equilateral triangles with the primaries. Small bodies can librate near L4/L5; L1–L3 are saddle configurations.

Key equations

U_eff = −(1−μ)/r₁ − μ/r₂ − ½(x²+y²) (normalized)
ẍ = −∂U/∂x + 2ẏ , ÿ = −∂U/∂y − 2ẋ (Coriolis)

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