Question

The bright red star Antares is actually a binary star system, its components are named a Scorpii A and a Scorpii B respectively. Assuming that the separation between the two stars are 529 AU, and they rotate around each other with a period ranging between 880 to 2562 years, calculate the range of the total mass for the Antares system in M. using the modified version of Kepler's Third Law. State what further observation is required to find the individual masses of the stars.

Answer 1

to know mass of individual stars of this binary system we need to know distance of any of them from barycentre(centre of rotation ).then we can find individual masses.

Given distance R3_52914. - 529X.1.196.X.0" en T = 880 Year n 880x3134x427 seconds T2=9562 Years - 2562X16 x 3.154 seconds. Keplay Law States TP 4x² R² GM luce .M= 422 183 & M₂ 4 2² R² T² G 722 . My 4x (3.14) ² x (529X1.496x104) 3 6.673x10 (880x3.154x167) 2 M4= 5.9 X101 x (1.914 X1013 13)3 (2.775X6on) 495.665 X 109 - Mi = 5.9x10" x 39 21.31 X1020 М. = 1.3685 Xlo 136.847X1630 soky अप 32kg M2. ܝ܂ 5.9x10" X 495.665X1039 0.3621 Xlo 8080.548X1020 M2 = 3.62x102 २१६ hangle of total mass is 3.62x16*M {_1:36.85X12 kg So mass