Star-Planet System & Center of Mass 1. The problem statement, all variables and given/known data Even with the best telescopes currently available, planets orbiting even the stars closest to the earth are too dim compared to their parent stars to be imaged directly. However, one might indirectly detect a planet's presence by observing its gravitational effect on the star. Assuming that the star-planet system is very far from other stars, it will be essentially isolated, so its center of mass should move in a straight line. If the planet's mass is large enough, the system's center of mass will be displaced significantly from the star's center of mass. When the planet orbits the star, therefore, the planet and the star really both orbit the system's center of mass (like a pair of waltzing ballroom dancers), as shown in figure C4.6 (this figure is just an illustration, not necessary to solve this problem). We might therefore hope to detect a planet by observing how much a star's position "wobbles" around its general line of motion. How difficult would this be? Assume that the star in question is a red dwarf that has a mass of about 0.30 times that of the sun (whose mass is 2.0 * 10^30 kg) and that the planet has 1.5 times the mass of Jupiter (whose mass is 1.9 * 10^27 kg) orbiting at a distance of about 1.5 * 10^12 m (about 10 times the distance from the earth to the sun). (a) About how far is the star's center of mass from the system's center of mass? (b) If the star is 8.1 ly from us, what will be the star's maximum angular distance from the system's center of mass as seen by an earth-based telescope? Express your result in milliarcseconds, where 1 milliarcsecond = 1 mas = (1/3,600,000) degrees. 2. Relevant equations 3. The attempt at a solution I don't even understand the problem... any hints appreciated!