Imagine a planetary system located roughly 35,000 light years from the core of the Andromeda galaxy. A light year represents the distance light covers in a year traveling at 3.0 × 10⁸ m/s. This system orbits the galaxy's center at a velocity of around 250 km/s. What would be the estimated mass of the galaxy's center, if most of the mass is concentrated near the core and the mass within the orbit is spherically distributed, similar to a giant star?