What is the radius of the event horizon (or Schwartzchild radius) of approximately 4 million solar masses at the center of our galaxy?

A. 1200 m; B. 12*10^6 km; C. 12*10^9 km; D. 12*10^12 km.

To find the radius of the event horizon (or Schwarzschild radius) of an object, we can use the formula:

r = (2GM) / c^2

Where:
- r is the radius of the event horizon
- G is the gravitational constant (approximately 6.674 * 10^-11 m^3/kg/s^2)
- M is the mass of the object
- c is the speed of light in a vacuum (approximately 299,792,458 meters per second)

In this case, we have the mass of the object, which is 4 million solar masses. To convert this to kilograms, we need to know the mass of the Sun, which is approximately 1.989 * 10^30 kilograms.

4 million solar masses = 4 * 10^6 * 1.989 * 10^30 kg

Next, we substitute these values into the formula:

r = (2 * (6.674 * 10^-11 m^3/kg/s^2) * (4 * 10^6 * 1.989 * 10^30 kg)) / (299,792,458 m/s)^2

Calculating this expression will give us the radius of the event horizon in meters. To convert this to one of the given options, let's evaluate the expression:

r ≈ 1.1918 * 10^13 meters

Comparing this to the given options:
A. 1200 m - Way too small
B. 12 * 10^6 km - 12 * 10^6 km = 1.2 * 10^7 km ≈ 1.2 * 10^10 meters - Close, but still too small
C. 12 * 10^9 km - 12 * 10^9 km = 1.2 * 10^10 km ≈ 1.2 * 10^13 meters - Closest option
D. 12 * 10^12 km - Way too large

Therefore, the correct answer is option C. The radius of the event horizon is approximately 12 * 10^9 km.