# All Astrodynamics Formulas List

## Luminosity of Cepheid Variable

#### Formula:

log10 (L)/Lo ≃ 1.15 * log10 Pd + 2.47

Where,

(L) =Mean Cepheid Luminosity
Lo = Solar Luminosity
Pd = Pulsation Period

## Absolute Visual Magnitude of Cepheid Variables

#### Formula:

Mv ≃ -2.76 log10 Pd - 1.40

Where,

Mv = Absolute Visual Magnitude
p = Pulsation Period

## Black Hole Evaporation Time

#### Formula:

τe ∼ (M3 / Mo3) ×1066

Where,

τe = Evaporation Time
M = Mass of Body
Mo = Solar Mass

## Black Hole Temperature

#### Formula:

T = (h/2π)c3 / (8πGMk)

Where,

T = Temperature
h = Planck Constant
G = Constant of Gravitation
M = Mass of Body
c = Speed of Light
k = Boltzmann Constant

## Cosmological Recession Velocity

#### Formula:

v = Ho * d

Where,

v = Cosmological Recession Velocity
Ho = Hubble Parameter
d = Distance

## Relativistic Pressure

#### Formula:

P = [ ((h/2π)c (3π2)1/3) / 4] * (ρ / mn)4/3

Where,

P = Relativistic Pressure
h = Planck Constant
c = Speed of Light
ρ = Density
mn = Neutron Mass

## Neutron Star Degeneracy Pressure by Non-Relativistic Neutrons

#### Formula:

P = ( (3π2)2/3 / 5) * ((h/(2*3.14))2 / mn) * (ρ / mn)5/3

Where,

P = Degeneracy Pressure
h = Planck Constant
mn = Neutron Mass
ρ = Density

## Chandrasekhar Mass

#### Formula:

Mch ≃ 1.46 * Mo

Where,

Mch = Chandrasekhar Mass
Mo = Solar Mass

## Angular Radius of Einstein Ring

#### Formula:

θ2 = (4GM / c2) * ((ds-d) / (ds*d))

Where,

G = Constant of Gravitation
M = Lens Mass
c = Speed of Light
ds = Distance from Observer to Source
d = Distance from Observer to Lens

## Absolute Magnitude of Sun I Band

#### Formula:

MI ≃ -7.68 log10 (2vrot / sin i) - 2.58

Where,

MI = Iband Absolute Magnitude
vrot = Observed Maximum Rotation Velocity
i = Galactic Inclination

#### Formula:

rs = 2GM / c2

Where,

rs = Black Hole Schwarzschild Radius
G = Constant of Gravitation
M = Mass of Body
c = Speed of Light

## Black Hole Gravitational Redshift

#### Formula:

Black Hole Gravitational Redshift
v / vr = (1 - (2GM / rc2))1/2

Where,

v = Frequency at Infinity
vr = Frequency at r
G = Constant of Gravitation
M = Mass of Body
r = Distance from Mass Center
c = Speed of Light

## Gravitational Wave Luminosity

#### Formula:

Lg = (32/5) * (G4 / c5) * (m12 m22 * (m1 + m2)) / a5

Where,

G = Constant of Gravitation
a = Mass Separation
c = Speed of Light
m1, m2 = Orbiting Mass

## Cosmological Lambda Density Parameter

#### Formula:

ΩΛ = Λ / (3 * H2)

Where,

ΩΛ = Lambda Density Parameter
Λ = Cosmological Constant
H = Hubble Parameter

## Hubble Parameter at Redshift

#### Formula:

H(z) = Ho * (1+z )3/2

Where,

H(z) = Hubble Constant At Redshift
Ho = Hubble Parameter At Present Epoch
z = Redshift

#### Formula:

vr = H * d

Where,

H = Hubble Parameter
d = Proper Distance

## Friedmann Equation Based on Pressure

#### Formula:

h = (-4*π/3) * (G*R) * (ρ+(3*p/c2)) + (Λ*R2 /3)

Where,

h = Friedmann Equation Based on Pressure
R = Cosmic Scale Factor
π = 3.14
G = Constant Of Gravitation
ρ = Density
p = Pressure
c = Speed Of Light
Λ = Cosmological Constant

## Friedmann Equation

#### Formula:

h = ((8*π/3)*G*ρ*R2) - (k*c2) + (Λ*R2)/3

Where,

h = Friedmann Equation
G = Constant Of Gravitation
π = 3.14
ρ = Density
R = Cosmic Scale Factor
k = Curvature Parameter
c = Speed Of Light
Λ = Cosmological Constant

## Eddington Luminosity Limit based on Solar Mass

#### Formula:

LE = (1.26*1031) * (M / M☉)

Where,

LE = Eddington Limiting Luminosity
M = Stellar Mass
M☉ = Solar Mass

## Eddington Luminosity Limit

#### Formula:

LE = (4 * π * G * M * mp * c) / ( σT)

Where,

LE = Eddington Limiting Luminosity
G = Constant Of Gravitation
M = Stellar Mass
π = 3.14
mp = Mass Of Proton
c = Speed Of Light
σT = Thomson Cross Section

## Cosmological Redshift

#### Formula:

z = (λobs - λem) / λem

Where,

z = Cosmology Redshift
λobs = Observed Wavelength
λem = Emitted Wavelength

## Cosmological Matter Density Parameter

#### Formula:

Ωm = (8*π*G*ρ) / (3*H2)

Where,

Ωm = Matter Density Value
G = Constant Of Gravitation
ρ = Density
H = Hubble Value

## Cosmological Curvature Density Parameter

#### Formula:

Ωk = -(k*c2) / (R2*H2)

Where,

Ωk = Curvature Density parameter
k = Curvature
c = Speed Of Light
R = Cosmic Scale Factor
H = Hubble Value

## Cosmology Critical Density

#### Formula:

ρcrit = (3*H2) / (8*π*G)

Where,

ρcrit = Critical Density
π = 3.14
H = Hubble Parameter
G = Constant Of Gravitation

## Rotational Velocity of Star using Distance

#### Formula:

V = (350 × (x/10000))/(1 + (x/10000)2)(3/4)

Where,

V = Rotational Velocity
X = Distance of Star from Center of the Galaxy

## Rotational Velocity of Star

#### Formula:

Rotational Velocity (Rv)= √(a2 - b2)

Where,

a = Space Velocity
b = Tangential Velocity

## Astronomy Wavelength

#### Formula:

Wavelength = C / F

Where,

C = Speed Of Light(299792458 m/s)
F = Frequency

#### Formula:

R = (2 × π × n) / 60

Where,

n = Revolutions per Minute

## Beta Angle

#### Formula:

β(t) = arcsin( cos(δs(t)) x sin(i) x sin(Ω(t) - Ωs(t)) + sin(δs(t)) x cos(i))

Where,

δs(t) = Declination of the Sun
i = Inclination of Orbit
Ω(t) = Position of the Ascending Node
Ωs(t) = Right Ascension of the Sun
β(t) = Beta Angle