The Alpha Centauri system includes at least three gravitationally bound stars that are remarkably difficult to observe and measure, despite being the closest star system to the Solar System. We observed the A, B, and C stars through the 0.4m telescopes in the Las Cumbres Observatory (LCO) global network, also employing Our Solar Siblings (OSS) pipeline to calibrate and plate solve the images. We measured the AB pair despite its high magnitudes (Mv of ~1) and small separation (<6”) using novel methods for CCD observations. We measured the AC pair despite the C star’s (Proxima Centauri) low magnitude (MV of ~12), wide separation (< 2’) from the A star, extremely high proper motion, and lack of historical data. Since we could not observe the AC pair in a single image, we used a trigonometric method of measurement from separate plate-solved images. These observation and measurement methods are described, as well as the results and their comparison to their orbital ephemerae. The needs for further observations are provided.