PHY4006 equations
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| 🇬🇧 | 🇬🇧 |
| Absorb fraction of radiation | Mk/4pir^2 |
| Radiation force | Mk/4pi^2 *L/c |
| Eddington luminosity with efficenty | Nu*Macc*c^2 |
| Eddington mass with luminosity | Ledd/c^2*nu |
| Eddington mass without luminosity | 4piGM/kcnu |
| Effective temperature | (L/4piSigmasbR^2)^0.25 |
| Accretion rate for wind fed accretion | Momega(GM/a)^2*Vomage^-4 |
| Wind fed capture radius | 2GM/Vomage^2 |
| Luminosity of disk | GM/2R*Macc |
| Luminosity of disk with Luminosity Acrretion | Ldisk=0.5Lacc |
| Temperture of accretion disk | (3GMMacc/8pir^3sigmasb)^0.25*(1-(R/r)^0.5)^0.25 |
| Schwarzchild ISCO | 6GM/c^2 |
| Kerr ISCO | GM/c^2 |
| Lamour formula | Q^2a^2/16*pi^2*episolon*c^3 sin^2(0) |
| Spectrum of radiation | 2q^2(a)^2/3eplision*c^2 |
| Thermal Bremsstrahlung | 6.8e^-51*Z^2*T^-0.5*ni*ne*gff*exp(-hc/kT) |
| Thermal Bremsstrahlung without frequencies | 1.4e^-40*Z^2*T*0.5*ni*ne*gff |
| Lamour radius | Gamma*m*v/qB |
| Synchrontron power radiation | 1.25*sigmaT*c*Umag*gamma^2*beta^2 |
| Umag | B^2/2Mu |
| Beta | V/c |
| Sychrontron power radiation for all | 1.25*sigmaT*c*Umag*gamma^2*beta^2*ne |
| Doppler shift | Gamma*v(1-beta*cos(0)) |
| Aberration | Cos(0)-beta/1-beta*cos(0) |
| Sychrontron pulse diraction | (gamma^3*omegaB)^-1 or m/gamma^2*q*B |
| Sychrontron pulse diraction genereal | (gamma^3*omegaB*sin(alpha))^-1 |
| Total synchrotron power | Gamma^3*omegaB/2pi |
| Compton scattering frequancy and energy | Gamma^2v or gamma^2E |
| Reconnection rate of solar flare (Mo) | 1/sqrt(Rm) |
| Sweet-Parker reconnection dissipation energy | 1/4pi *B^2*L^2*va*Mo*tauf |
| Reconnection rate of solar flares (shock) | Pi/8ln(Le/Delta) approx pi/8ln(Rm) |
| Fermi energy | H^2/8me * (3Ne/piN)^2/3 |
| Total Fermi energy (non rel) | 3/5*Ne*eplisionF |
| Total Fermi energy (rel) | 3/4*Ne*eplisionF |
| Total energy of a cool star (non rel) | 3/5*Ne*Efe*eplsion - 3/5 *GM^2/R |
| Radius if a WD | Xh^2/4me * (9xN/4pi^2)^2/3 * 1/GNmp^2 |
| Total energy of star (rel) | 3/4*Ne*Efe*eplsion - 3/5 *GM^2/R |
| Fermi energy (rel) | Hc/2 * (3Ne/piV)^1/3 |
| Chandrasekhar limit | 3/16 * (125pi)^0.5*x^2*(hc/2pi*G*mp^2)^1.5 |
| Total energy of neutron (non rel) | 3/5 * Nn*epsilonF,n |
| Fermi energy of neutron | H^2/8mn * (3Nn/piV)^2/3 |
| Radius of a NS | H^2/4G*N^1/3*mp^3 * (9/4pi^2)^2/3 |
| Energy loss rate from pulasr rotation | -4pi^2*I*T/T^3 |
| Schwarzschild radius | 2GM/c^2 |
| Surface gravity of a BH (k) | C^4/4GM |
| First law of BH mechanices | DM = 1/8piG * kdA + OmegadJ + PhidQ |
| Hawking temperature | Hbar*c^3/8pi*Kb*GM |
| Energy radiated from a BH | -de/dt = 4pi*Rshw*sigma*Th^4 |
| Free-fall time of collapse for SNe | Sqrt(3/2piG*rho) |
| Gravitational wave frequency | 2*sqrt(G(M1+M2)/a^3) |
| Total time for a GW binary to merge | 5/256 * c^5/G^3 * a^4/M1M2(M1+M2) |
| Confinement radius | Gamma*mc/q*B |
| Strong shock jump conditions | Rhod/rhou = 4 or vu/vd = 4 |
| Cherenkov Radiation: opening angle | Cos(0) = 1/n*beta |
| Homestake: Rate of neutrinos measured in detector | Phi*sigma*n*V |
| Probability of an oscillation | Sin^2(20)sin^2(1.27Delta*m^2*l/Ev) |