3. Determine orbital elements for a double-lined spectroscopic binanl spectrosco

Question

3. Determine orbital elements for a double-lined spectroscopic binanl spectroscopic binaries are generally short-period binaries with two stars that are ities of each star by Double-lined comparably bright. In this case, we are measure the radial of mass. In observing the Doppler shifts lines as they orbit their common center in their spectral this exercise, you radial velocities, orbital period, and orbital inclination of use the observed star masses. HD 220057 to determine other orbital elements, mass ratio, and individual Orbital period a 4.415 days e Orbital inclination 40 (MD), orbital phase, primary Input table 1 (obsRvs) containing date of observation radial velocity (v A, km/s), secondary velocity (v B, km/s) for 23 observations. Input table 2 (FitRvs) containing v A and v B Rv fit values for phase o 01-1.00 in o.01 Output: Plot of input data showing the radial velocities of the primary (filled circle) and secondary (open circle) for the observations as well as the Rv-fit curves for the primary and secondary systemic (Y). This is the radial velocity of the bina center of mass and can be velocity determined as the point of intersection of the two Rv-fit curves. This will require of interpolation or determining the point of intersection of two straight-line segments the velocity curves near the cross-over area. orbital elements w, using the graphical method using equations (1) and (2) Determine these elements independently for the primary and secondary fits, and then take the average for your final value. Velocity semi-amplitude of primary and secondary using equation (3) and orbital element a for primary and secondary using equation (4) and given inclination. Mass ratio, obtained using equation (5), mass sum using equation (6) and the given inclination value, and finally the individual masses of the two stars. RV plot for the double-lined spectroscopic binary, orbital elements e, w, au, aB, and stellar parameters MA Me (1) (2) at 42+41 (3) 86400 P (a+p) Vi-ez a sin i (4) (5) (MA MB) sins i (6)

Explanation / Answer

Solution:-

Figure is already drawn in the figure, so in this we have to first evaluate the average value.

To obtained the elements independently, for the primary and secondary fits:-

Values are defined below and sum & average is also shown below:-

Orbit Phase V_A(fit) (km/s) V_B(fit) (Km/s) 0.01 43.3022 -104.3415 0.02 10.0491 -69.801 0.03 -20.6735 -37.6512 0.04 -47.0262 -9.8777 0.05 -68.4712 12.887 0.06 -85.3082 30.898 0.07 -98.2042 44.8125 0.08 -107.8964 55.376 0.09 -115.0527 63.2729 0.1 -120.2269 69.0753 0.11 -123.8586 73.2401 0.12 -126.2891 76.1237 0.13 -127.781 78.0016 0.14 -128.536 79.0863 0.15 -128.709 79.5415 0.16 -127.7605 79.494 0.17 -126.8041 79.0427 0.18 -126.8041 78.2647 0.19 -125.6072 77.2209 0.20 -124.2145 75.9595 0.21 -122.6616 74.5189 0.22 -120.9769 72.9797 0.23 -119.1829 71.2167 0.24 -117.2981 69.3997 0.25 -115.337 67.4949 0.26 -113.3116 65.5155 0.27 -111.2316 63.472 0.28 -109.1046 61.3731 0.29 -106.9369 59.226 0.30 -104.7337 57.0363 0.31 -102.499 54.8086 0.32 -100.2361 52.5468 0.33 -97.9475 50.2538 0.34 -95.6351 47.9319 0.35 -93.3004 45.5828 0.36 -90.9445 43.2081 0.37 -88.5681 40.8085 0.38 -86.1715 38.3847 0.39 -83.755 35.9371 0.40 -81.3183 33.4655 0.41 -78.8613 30.9699 0.42 -76.3833 28.4499 0.43 -73.8837 25.9049 0.44 -71.3616 23.334 0.45 -68.8162 20.7364 0.46 -66.2462 18.111 0.47 -63.6505 15.4566 0.48 -61.0276 12.7718 0.49 -58.3761 10.055 0.50 -55.6943 7.3047 0.51 -52.9804 4.5189 0.52 -50.2325 1.6958 0.53 -47.4487 -1.1668 0.54 -44.6266 -4.0711 0.55 -41.7641 -7.0196 0.56 -38.8585 -10.0149 0.57 35.9072 -13.0598 0.58 -32.9074 -16.1573 0.59 -29.8559 -19.3105 0.60 -26.7496 -22.523 0.61 -23.5849 -25.7985 0.62 -20.3581 -29.1409 0.63 -17.0652 -32.5545 0.64 -13.7019 -36.0538 0.65 -10.2636 -39.6139 0.66 -6.7452 -43.27 0.67 -3.1415 -47.0178 0.68 0.5533 -50.8636 0.69 4.3454 -54.814 0.70 8.2415 -58.8761 0.71 12.2487 -63.058 0.72 16.3749 -67.3678 0.73 20.6284 -71.8148 0.74 25.0183 -76.4088 0.75 29.5541 -81.1604 0.76 34.2464 -86.081 0.77 39.1062 -91.1829 0.78 44.1451 -96.4791 0.79 49.3656 -101.9834 0.80 54.8104 -107.7102 0.81 60.4622 -113.6744 0.82 66.3436 -119.8905 0.83 72.4661 -126.37325 0.84 78.8389 13,31,323 0.85 85.4668 -140.178 0.86 92.3481 -147.511 0.87 99.4691 -155.1216 0.88 106.7983 -162.9819 0.89 114.275 -171.035 0.90 121.7936 -179.1785 0.91 129.1785 -187.2385 0.92 136.1479 -194.9317 0.93 142.2612 -201.8105 0.94 146.85 -207.1892 0.95 148.943 -210.0625 0.96 147.222 -209.0545 0.97 140.1021 -202.4915 0.98 126.0767 -188.7524 0.99 104.4128 -166.9883 1.00 75.9467 -137.9679 Sum -2501.6593 1328881.091 Average -25.016593 13288.81091

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