Black Hole Equations

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Formula used to illustrate how a mass curves space

Inside the body of the mass (such as a star)
z(r)=sqrt(R³_/ 2M) [sqrt(1 - (1 - (2Mr²_/ R³)))] for r <= R
Outside the body of the mass (such as a star)
z(r)=sqrt(R³_/ 2M) [sqrt(1 - (1 - (2M _/ R)))] + sqrt(8M (r - 2M)) - sqrt(8m (R - 2M)) for r >= R

Where R is the radius of the star, M is the mass, and r is the radial vector.

Formula used to approximate the mass of a black hole (derived from Newton's law of gravitation and the fact that the speed of a circularly orbiting object is the circumference divided by the period)

M_b=C_o³_/ 2(pi)GP_o²

Where M_b is the mass of a black hole, C_o is the circumference of a circular orbit around the hole, P_o is the period of orbit (time required to circle hole once,) and G is Newtons gravitational constant 1.327x10¹¹kilometers³ per second² per solar mass.

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