Fundamental constants in SI units:
from scipy import constants
c = constants.c
G = constants.G
c, G
(299792458.0, 6.6743e-11)
Msol = 1.98848e30
Rsol = 6.96e8
0.012*Rsol/1000
8352.00000000000
bodies = [(5.972e24, 6.371e6), (Msol, Rsol), (0.6*Msol, 8e6), (1.4*Msol, 1.2e4)]
bodies
[(5.97200000000000e24, 6.37100000000000e6), (1.98848000000000e30, 6.96000000000000e8), (1.19308800000000e30, 8.00000000000000e6), (2.78387200000000e30, 12000.0000000000)]
for m0, r0 in bodies:
npi = n(pi)
print("m0/Msol: ", m0/Msol)
print("r0 [km]: ", r0/1e3)
xi = G*m0/(c^2*r0)
print("m0/r0: ", xi)
chis = asin(sqrt(2*xi))
print("chis: ", chis)
rho0 = 3*m0/(4*npi*r0^3)
print("rho0: ", rho0)
tau_end = npi*G*m0/(c*sin(chis))^3
tau_end1 = sqrt(3*npi/(32*G*rho0))
print("tau_end [s]: ", tau_end, " test: ", tau_end1 - tau_end)
print("tau_end [min]: ", tau_end/60.)
xx = (2*chis - sin(2*chis))/npi
tau_star = (1 - xx)*tau_end
print("tau_star [s], [min] : ", tau_star, tau_star/60.)
print("tau_end - tau_star [s] [μs]: ", xx*tau_end, xx*tau_end*1e6)
xx = (3*chis - sin(3*chis))/npi
tau_bh = (1 - xx)*tau_end
print("tau_bh [s], [min] : ", tau_bh, tau_bh/60.)
print("tau_end - tau_bh [s] [μs]: ", xx*tau_end, xx*tau_end*1e6)
rho_hb = 3*c^6/(4*npi*(G^3*m0^2))*sin(chis)^6/(1 - cos(3*chis))^3
rho_hb_chis2 = 2*c^6/(243*npi*(G^3*m0^2))*(1 + 1.25*chis^2)
print("rho_hb, rho_hb_chis2", rho_hb, rho_hb_chis2)
print(" ")
m0/Msol: 3.00329900225298e-6 r0 [km]: 6371.00000000000 m0/r0: 6.96107818665463e-10 chis: 0.0000373124059526723 rho0: 5513.25873858909 tau_end [s]: 894.650739950216 test: 2.27373675443232e-13 tau_end [min]: 14.9108456658369 tau_star [s], [min] : 894.650739950197 14.9108456658366 tau_end - tau_star [s] [μs]: 1.97243235532305e-11 0.0000197243235532305 tau_bh [s], [min] : 894.650739950150 14.9108456658358 tau_end - tau_bh [s] [μs]: 6.65695968164489e-11 0.0000665695968164489 rho_hb, rho_hb_chis2 1.79366489259658e29 1.79366485475957e29 m0/Msol: 1.00000000000000 r0 [km]: 696000.000000000 m0/r0: 2.12166252470360e-6 chis: 0.00205993472016873 rho0: 1408.00727612437 tau_end [s]: 1770.33421572414 test: -2.27373675443232e-13 tau_end [min]: 29.5055702620691 tau_star [s], [min] : 1770.33420915658 29.5055701526097 tau_end - tau_star [s] [μs]: 6.56756124734685e-6 6.56756124734685 tau_bh [s], [min] : 1770.33419355865 29.5055698926441 tau_end - tau_bh [s] [μs]: 0.0000221654956950720 22.1654956950720 rho_hb, rho_hb_chis2 1.61785928258533e18 1.61785928257148e18 m0/Msol: 0.600000000000000 r0 [km]: 8000.00000000000 m0/r0: 0.000110750783789528 chis: 0.0148834782166719 rho0: 5.56306209209834e8 tau_end [s]: 2.81644165605950 test: 0.000000000000000 tau_end [min]: 0.0469406942676583 tau_star [s], [min] : 2.81643771526589 0.0469406285877648 tau_end - tau_star [s] [μs]: 3.94079361323390e-6 3.94079361323390 tau_bh [s], [min] : 2.81642835661760 0.0469404726102933 tau_end - tau_bh [s] [μs]: 0.0000132994419055579 13.2994419055579 rho_hb, rho_hb_chis2 4.49527431296783e18 4.49527411079676e18 m0/Msol: 1.40000000000000 r0 [km]: 12.0000000000000 m0/r0: 0.172278997005933 chis: 0.627336667606611 rho0: 3.84606761922848e17 tau_end [s]: 0.000107114744196599 test: -1.35525271560688e-20 tau_end [min]: 1.78524573660999e-6 tau_star [s], [min] : 0.0000967419690647016 1.61236615107836e-6 tau_end - tau_star [s] [μs]: 0.0000103727751318976 10.3727751318976 tau_bh [s], [min] : 0.0000754041445678369 1.25673574279728e-6 tau_end - tau_bh [s] [μs]: 0.0000317105996287623 31.7105996287623 rho_hb, rho_hb_chis2 1.38058663403609e18 1.23149732066000e18