Binary mass function: Difference between revisions

Revision as of 23:52, 17 February 2017

Revision as of 00:01, 18 February 2017

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<math>f = \frac{M_{2}^{3}\ \mathrm{sin}^{3}i }{(M_{1} + M_{2})^{2}} = \frac{P_\mathrm{orb}\ K^{3}}{2 \pi G}.</math>

For an estimated or assumed mass <math>M_{1}</math> of the observed object 1, a [[minimum mass]] <math>M_\mathrm{2, min}</math> can be determined for the unseen object 2 by assuming <math>i = 90^{\circ}</math>. The true mass <math>M_{2}</math> depends on the orbital inclination. The inclination is typically not known, but to some extent it can be determined from observed [[Transit (astronomy)|eclipses]],<ref name="podsiadlowski" /> orbe constrained from the non-observation of eclipses.,<ref name="bailes" /><ref name="kerkwijk" /> or be modelled using ellipsoidal variations (the non-spherical shape of a star in binary system leads to variations in brightness over the course of an orbit that depend on the system's inclination).<ref>{{cite web |url=http://cmi2.yale.edu/bh/week4/pages/page5.html |title=The Orbital Inclination |publisher=[[Yale University]] |access-date=February 17, 2017 }}</ref>

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