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<p>For the Sun-Planet system, Lagrange points are locations around the planet’s orbits in space where the combined gravitational forces of the Sun and the planet balance the centrifugal force experienced by a much smaller satellite ‘parked’ there. Recently, the news of the successful injection of Aditya-Ll, the first space-based Indian observatory to study the Sun, into its final destination orbit, some 1.5 million kilometers from the Earth, has brought to the limelight the vital significance of these points. In this article, we present a brief history of the ‘three-body problem’ and discuss its simplified variant, the ‘circular restricted three-body problem’ (CR3BP). Taking the Sun-Earth system as an example of CR3BP, the location of its five Lagrangian equilibrium points is determined using a code written in Python. The stability of these equilibrium points is discussed. Finally, the significance of Lagrangian equilibrium points for space mission design and satellite position is also briefly discussed.</p>

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Lagrangian Equilibrium Points

  • 期刊论文

  • 发表日期：

    2025年4月16日

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  • Pankaj Hurkat,
  • Nisha Patel,
  • Pruthul Desai

摘要

For the Sun-Planet system, Lagrange points are locations around the planet’s orbits in space where the combined gravitational forces of the Sun and the planet balance the centrifugal force experienced by a much smaller satellite ‘parked’ there. Recently, the news of the successful injection of Aditya-Ll, the first space-based Indian observatory to study the Sun, into its final destination orbit, some 1.5 million kilometers from the Earth, has brought to the limelight the vital significance of these points. In this article, we present a brief history of the ‘three-body problem’ and discuss its simplified variant, the ‘circular restricted three-body problem’ (CR3BP). Taking the Sun-Earth system as an example of CR3BP, the location of its five Lagrangian equilibrium points is determined using a code written in Python. The stability of these equilibrium points is discussed. Finally, the significance of Lagrangian equilibrium points for space mission design and satellite position is also briefly discussed.