1. We will now solve a problem for a smaller black hole. The first gravitational wave event was observed on Mon, Sep 14, 2015. The two stellar mass black holes that fell into each other and created a bigger black hole sent ripples in spacetime, that LIGO observed . Assuming one black hole had a mass of 30 suns and the other had a mass of 50 suns, let's investigate how large an 80 solar mass black hole is. Size of a black hole means its radius, ie. where the event horizon is. Event horizons are one-way surfaces, meaning once you cross the event horizon of the black hole, you cannot go back the other way. This is true, even for light1. You can imagine a projection of a black hole from 3-d to 2-d in this image. The edge of the vortex represents the event horizon. But, Black holes and their event horizon are spherical, at least in the simplest spacetimes ( Schwarzschild). That makes a black hole look like a ball in 3-space dimensions and 1-time dimension. The distance from the center of that black hole ball to its event horizon surface is calculated with this formula ????????h = 2????????/????2 The variables in this equation are the mass of the black hole ????, and ????????his the event horizon in units of meters, when you use the constants of: ???? = 6. 67 1011 ????????2/????????2 ???? = 3.00108????/????. a. Solve for the event horizon of an 80 solar mass black hole _______________________. (Note to self: figure out a mass in kilograms.) b. Convert this number into miles