page_title: Roche lobe
section_title: Further analysis
hierarchical_section_title: Roche lobe / Further analysis
caption_attribution_description: 中文（简体）‎: Hill sphere and Horseshoe_orbit
context_page_description: The Roche lobe is the region around a star in a binary system within which orbiting material is gravitationally bound to that star. It is an approximately teardrop-shaped region bounded by a critical gravitational equipotential, with the apex of the teardrop pointing towards the other star.
  The Roche lobe is different from the Roche sphere, which approximates the gravitational sphere of influence of one astronomical body in the face of perturbations from a more massive body around which it orbits. It is different from the Roche limit, which is the distance at which an object held together only by gravity begins to break up due to tidal forces. The Roche lobe, Roche limit, and Roche sphere are named after the French astronomer Édouard Roche.
context_section_description: In the gravity potential graphics, L₁, L₂, L₃, L₄, L₅ are in synchronous rotation with the system. Regions of red, orange, yellow, green, light blue and blue are potential arrays from high to low. Red arrows are rotation of the system and black arrows are relative motions of the debris.
  Debris goes faster in the lower potential region and slower in the higher potential region. So, relative motions of the debris in the lower orbit are in the same direction with the system revolution while opposite in the higher orbit.
  L₁ is the gravitational capture equilibrium point. It is a gravity cut-off point of the binary star system. It is the minimum potential equilibrium among L₁, L₂, L₃, L₄ and L₅. It is the easiest way for the debris to commute between a Hill sphere (an inner circle of blue and light blue) and communal gravity regions (figure-eights of yellow and green in the inner side).
  L₂ and L₃ are gravitational perturbation equilibria points. Passing through these two equilibrium points, debris can commute between the external region (figure-eights of yellow and green in the outer side) and the communal gravity region of the binary system.
  L₄ and L₅ are the maximum potential points in the system. They are unstable equilibria. If the mass ratio of the two stars becomes larger, then the orange, yellow and green regions will become a horseshoe orbit.
  The red region will become the tadpole orbit.
caption: Hill sphere and horseshoe orbit
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