Final answer:
The Schwarzschild radius for the black hole at the center of our galaxy with a mass of 4 million solar masses is approximately 1.48 km.
Step-by-step explanation:
The Schwarzschild radius of a black hole is given by the formula:
Rs = 2GM / c^2
where G is the gravitational constant, M is the mass of the black hole, and c is the speed of light. For the black hole at the center of our galaxy with a mass of 4 million solar masses (4 × 10^6 M☉), we can substitute the values into the formula:
Rs = 2 × (6.67 × 10^-11 N·m²/kg²) × (4 × 10^6) × (1.99 × 10^30 kg) / (3.00 × 10^8 m/s)^2
Calculating this gives us:
Rs ≈ 1.48 km
Therefore, the Schwarzschild radius for the black hole at the center of our galaxy is approximately 1.48 km.