Black_Hole_Equations.html
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• ### EQUATIONS For BH Computations: (19-Nov-2010 Updated: 04-Dec-1:00 AM)

• Gravitational Force (Lbf): F=GM0m0/r2 Where: G is universal gravitational constant, M0 is gravitating body mass, m0 is other body rest mass
• Schwarzschild Radius (Ft) Single Black Hole: Rs=2GM0/c2
• Spin Rate (RPS OR Hz) Binary BH Masses:   M0=M1, Ellipticity=0 : RPS=(GM0/R3)½/2/(2π) Where: R=Dist. Barycenter To Singularity
• Spin Rate (RPS OR Hz) Binary BH Masses: M0<>M1, Ellipticity=0 : RPS=(GM0/R1/(R0+R1)2)½/2/(2π) From Barycenter; R0 is to M0, R1 is to M1
• Spin Rate (RPS OR Hz) Binary BH Masses: M0<>M1, Ellipticity>0 : RPS=(G(M0+M1)/a3)½/(2π) Where: a=SUM semi-major ellipse's a0+a1
• Elliptic Orbit (e) Determination For Ellipticity>0 : (b/a)=(1-e2)½ Where: (a) & (b) are semi-major & semi-minor axes
• Kinetic Energy (Ft-Lb): Ekinetic=½m(v)2
• Gravity Work (Ft-Lb): W=GM0m/R Where: M0>>m; Drop of (m) Is From Infinity To 'R' dist. from M0 CG
• Velocity (Ft/S) From Newtonian Gravity Work: vNewtonian=(2GM0/R)½ Where: Drop Is From Infinity To 'R' dist. from CG
• Relativistic Mass (Slug): mrel=m0/(1-(v/c)2)½
• Gravity Propagation Delay Time: M0=M1 Binary 2*R2*(1+COS(w*time))=(c*time)2 Where: 'w' is (radians/sec) Derived 11-Nov-2010
• Relativistic Speed (Ft/S): v2=2W(1-(v/c)2)½/m0 Where: v=vrel (Ft/S), m0 is rest mass, and W is Newtonian Gravity Energy [Work] (Ft-Lbf)
• Relativistic Speed (Ft/S): vrel=(2(W/m0)2(1/c4+(m0/W)2).5-2(W/m0)2/c2).5 Where: vrel=relativistic [velocity] (Ft/S), W is Newtonian [Work] (Ft-Lbf)
• Acceleration At Schwarzschild Radius (g's): Gaccel=c4/(4*G*MSOL*N)/32.174 Where: MSOL=Solar Mass, N=number of suns, G=Gravitation Constant
• Gravity Radiation Energy[1] ((Ft-Lb)/s): Eg = 32G4(M1M2)2(M1+M2)/5/c5/r5 (Newtonian circular orbits) Where: r=distance Cg to Cg, and v<<c
• α = c•e2•10-7/h

### CONSTANTS: (Refined 07-Nov-2010)

• Speed of Light (Ft/S): c=9.83571056E+8 HP-48G & CRC 76th Edition
• Mass Of The Sun (Slugs): MSUN=1.36356E+29
• Gravitational Constant (Ft4/(Lbf-S4) or Lbf*(Ft/Slug)2: G=3.438E-8 Was using 3.232E-8, 6.67259E-11 mks: Convert G-to-Mks .00194032
REFERENCE: Update 04-Dec-2011