Assumptions

This section simplifies the original problem and helps in developing the theoretical models by filling in the missing information for the physical system. The assumptions refine the scope by providing more detail.

twoBody: The system consists of exactly two stars with masses \({m_{1}}\) and \({m_{2}}\) . Perturbations from third-body gravity are ignored. (RefBy: IM:accelY2, IM:accelY1, IM:accelX2, IM:accelX1, and LC:Derived-Output-Quantities.)

isolated: Non-gravitational forces (e.g., drag, thrust, radiation pressure) are neglected; the only interaction modeled is mutual gravity between the two stars (from A:newtonianGravity). (RefBy: IM:accelY2, IM:accelY1, IM:accelX2, IM:accelX1, and LC:Derived-Output-Quantities.)

newtonianGravity: The gravitational interaction between the stars is modeled using Newton’s law of universal gravitation, with the gravitational constant \(G\) provided in Values of Auxiliary Constants. (RefBy: TM:UniversalGravLaw, IM:accelY2, IM:accelY1, IM:accelX2, IM:accelX1, UC:Newtonian-Gravity-Model, A:nonzeroSeparation, LC:Derived-Output-Quantities, and A:isolated.)

nonRelativistic: The motion is modeled using classical (non-relativistic) mechanics; relativistic effects are neglected. (RefBy: IM:accelY2, IM:accelY1, IM:accelX2, IM:accelX1, and LC:Derived-Output-Quantities.)

pointMass: Each star (\({m_{1}}\), \({m_{2}}\)) is modeled as a point mass, and effects due to stellar size, deformation, or rotation are neglected. (RefBy: IM:accelY2, IM:accelY1, IM:accelX2, IM:accelX1, A:nonzeroSeparation, and LC:Derived-Output-Quantities.)

constantMass: The masses \({m_{1}}\) and \({m_{2}}\) remain constant over time. (RefBy: IM:accelY2, IM:accelY1, IM:accelX2, IM:accelX1, and LC:Derived-Output-Quantities.)

inertialFrame: The simulation is performed in an inertial reference frame. (RefBy: TM:centerOfMass, IM:accelY2, IM:accelY1, IM:accelX2, IM:accelX1, and LC:Derived-Output-Quantities.)

planar: The motion of the binary star system is confined to a two-dimensional plane. (RefBy: TM:relPosAndSep, IM:accelY2, IM:accelY1, IM:accelX2, IM:accelX1, and LC:Derived-Output-Quantities.)

nonzeroSeparation: Collisions are out of scope: the separation distance \({r_{12}}\) is positive for all simulated times, so the gravitational force model remains well-defined (from A:newtonianGravity and A:pointMass). (RefBy: TM:UniversalGravLaw, IM:accelY2, IM:accelY1, IM:accelX2, IM:accelX1, and LC:Derived-Output-Quantities.)