Question

What is the Schwarzschild radius for the black hole at the center of our galaxy if it has the mass of 4 million solar masses?

a) 1.48 km
b) 2.95 km
c) 4.42 km
d) 5.89 km

Answer 1

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.