The black hole at the center of our galaxy is known as Sagittarius A* (Sgr A*). Its radius is not precisely defined because black holes are objects with immense gravitational forces that create what is known as an event horizon. The event horizon is the boundary beyond which nothing, including light, can escape the black hole's gravitational pull.
However, we can estimate the size of the event horizon, which is often referred to as the Schwarzschild radius. The Schwarzschild radius represents the radius of a non-rotating black hole with the same mass as Sagittarius A*.
The estimated mass of Sgr A* is about 4.31 million times the mass of the Sun. Using this mass value, we can calculate the Schwarzschild radius using the formula:
R_s = (2GM) / (c^2)
Where: R_s is the Schwarzschild radius, G is the gravitational constant (approximately 6.67430 × 10^(-11) m^3 kg^(-1) s^(-2)), M is the mass of Sgr A*, and c is the speed of light (approximately 3 × 10^8 m/s).
Plugging in the values:
R_s = (2 * 6.67430 × 10^(-11) m^3 kg^(-1) s^(-2) * (4.31 million solar masses * 1.989 × 10^30 kg)) / (3 × 10^8 m/s)^2
After performing the calculation, we find that the estimated Schwarzschild radius for the black hole at the center of our galaxy, Sgr A*, is approximately 12.6 million kilometers (7.8 million miles). This value represents the size of the event horizon or the boundary beyond which nothing can escape the black hole's gravitational pull.