DETERMINATION OF VISUAL DOUBLE STAR ORBIT TRAJECTORY USING SEMIDEFINITE PROGRAMMING

• Main Author: YASINTA (NIM: 10114077), NADA
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/29465
• Institution: Institut Teknologi Bandung

Semidefinite programming is an optimization field to minimize or maximize linear objective function problem with positive semidefinite matrix constraints. Semide-finite programming is an extension of linear programming so that the interior point method that applies to linear programming can be used to complete semide-finite programming with some adjustments. One of the applications of semide-finite programming that is studied in this final project is to determinate the orbital trajectory of the visual double star. A visual double star is a star system consisting of two stars (primary star and secondary star) which are located close to each other. The gravitational force causes both stars to orbit each other. The movement of the secondary star orbit against the primary star satisfies Kepler’s Law of ellip-tical orbital trajectory and constant areal velocity. A mathematical model will be constructed to determine the orbital trajectory of the visual double stars that will be solved using semidefinite programming accompanied by calculating the mean error of the model. The model obtained will be used to calculate the orbit of the visual double star ADS 11520, ADS 10768, and ADS 9982 using observation data in the form of the position data (ρ,θ) and observation time (t). Orbit calculation results are displayed in the form of orbital elements. Two criteria are used to minimize the difference in observation data with the model, the sum of absolute criterion and sum of quadratic criterion. Based on the simulation results, minimize the sum of absolute criterion will result in a more stable model even though there is outlier data. The orbit calculation model will generate a unique elliptical curve trajectory for each star data and it will give a better result when the data evenly distributed in each quadrant.