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  • Introduction Two or more stars that are located close together in space interact gravitationally, causing deviations from linear motion as each star is accelerated. If we consider the case of two stars with a physical separation of many times the radius of either star (but still close enough to generate significant accelerations), it is sufficient to consider the stars as point masses. The equations of motion for such a system can be solved by assuming the inverse-square law of gravity and applying Newton's laws of motion. Newton's solution elegantly explained Kepler's laws of planetary motion, since one of the general solutions of motion is an ellipse with the more massive body (the Sun, in the case of the Solar System) at one focus. Kepler's third law of planetary motion (i.e. the harmonic law) as applied to the binary-star situation can be written where m1 and m2 are the masses of the two stars in solar units, a is the semi-major axis of the relative orbital ellipse in astronomical units, and P is the orbital period of the system in years. If you can only apply this formula, then it is not possible to obtain individual masses from the observables on the right-hand side, nor is the mass sum possible without an estimate of the parallax of the system (which allows for the conversion of a from an angular measure to astronomical units). Furthermore, while it is usually possible to measure the orbital period to high precision, the application of the formula is complicated by the fact that the semi-major axis, and implicitly the parallax, is raised to the third power. © Cambridge University Press 2013.

Last update from database: 3/13/26, 4:15 PM (UTC)

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