Question

What would be the Schwarzschild radius, in light years, if our Milky Way galaxy of 100 billion stars collapsed into a black hole? (Assume each star has the same mass as the sun.)

Compare this to our distance from the center, about 27,000 light years

Answer 1

The Schwarzschild radius of the Milky Way if it collapsed into a black hole would be approximately 0.125 light years, which is significantly smaller than the distance from our solar system to the galaxy's center, which is about 27,000 light years.

Step-by-step explanation:

To calculate the Schwarzschild radius (Rs) of a black hole with a given mass, we use the formula:

Rs = 2GM/c2

Where:

G is the gravitational constant (6.674×10-11 m3kg-1s-2).

M is the mass of the black hole.

c is the speed of light in vacuum (299,792,458 m/s).

If the entire Milky Way, with an estimated mass of 8.0 × 1011 solar masses, collapsed into a black hole, its Schwarzschild radius can be calculated as follows:

Rs = 2G(8.0 × 1011 × Msolar)/c2 = 2(6.674×10-11)(8.0 × 1011 × 1.9885 × 1030)/(299,792,4582)

Rs ≈ 1.18×1012 kilometers

Converting kilometers to light years (1 light year ≈ 9.461 × 1012 kilometers), we get:

Rs ≈ 0.125 light years

This Schwarzschild radius is much smaller than our distance from the center of the Milky Way, which is about 27,000 light years. Therefore, if our galaxy were to collapse into a black hole, it would be a point in space quite tiny compared to the vast distances within the galaxy.