Astronomy Formulas

Aphelion / Perihelion

$R_{a} = a (1 + e)$

$R_{p} = a (1 - e)$

R_{p} = a (1 - e)

$R_{a} = O r b i t A p h e l i o n$

$R_{p} = O r b i t P e r i h e l i o n$

$a = S e m i m a j o r A x i s$

$e = E c c e n t r i c i t y$

Circular Velocity

$v = \sqrt{\frac{G M}{r}}$

$v = c i r c u l a r v e l o c i t y (m / s)$

$G = G r a v i t a t i o n a l C o n s t a n t$

$M = M a s s (k g)$

$r = r a d i u s (m e t e r s)$

Compare LGP

$\frac{L G P_{a}}{L G P_{b}} = {(\frac{D_{A}}{D_{B}})}^{2}$

$L G P = L i g h t G a t h e r i n g < P o w e r$

$D = O p t i c D i a m e t e r$

Distance Modulus

$m - M = - 5 + 5 \log ((d))$

$d = 10^{\frac{m - M + 5}{5}}$

$m = A p p a r e n t m a g n i t u d e$

$M = A b s o l u t e M a g n i t u d e$

$d = D i s t a n c e (p c)$

Doppler Formula

$v = c z$

$v = V e l o c i t y (m / s)$

$c = S p e e d o f l i g h t (m / s)$

$z = R e d s h i f t$

F Ratio

$\frac{L_{f}}{D_{o}}$

$L_{f} = F o c a l L e n g t h$

$D_{O} = O b j e c t i v e D i a m e t e r$

Fusion Explained

$E = m c^{2}$

$E = E n e r g y (J)$

$m = M a s s (k g)$

$c = S p e e d o f l i g h t (m / s)$

Hubble’s Law

$v = H_{0} d$

$v = R e c e s s i o n a l v e l o c i t y (k m / s)$

$H_{0} = H u b b l e ‘ s C o n s t a n t$

$d = D i s t a n c e$

Hubble Time

$T_{u} = \frac{9.778 \times 10^{11}}{H_{0}}$

$T_{u} = A g e o f t h e U n i v e r s e (y e a r s)$

$H_{0} = H u b b l e C o n s t a n t (k m / s / M p c)$

Intensity Ratio

$m_{B} - m_{A} = 2.5 \log$

$(\frac{I_{A}}{I_{B}}) \frac{I_{A}}{I_{B}} = 10^{0.4 (m_{b} - m_{a})}$

$m = M a g n i t u d e$

$I = I n t e n s i t y$

Inverse Squares Law

$I = \frac{L}{4 π d^{2}}$

$I = L i g h t I n t e n s i t y (W / m^{2})$

$L = L u m i n o s i t y (W)$

$d = D i s t a n c e (m)$

Kepler’s Third Law

$M_{A} + M_{B} = \frac{a^{3}}{p^{2}}$

$p^{2} = \frac{a^{3}}{M_{A} + M_{B}}$

$M = M a s s (s o l a r m a s s e s)$

$a = S e m i m a j o r a x i s (A U)$

$p = O r b i t a l P e r i o d (y e a r s)$

Magnification

$M = \frac{F_{o}}{F_{e}}$

$M = M a g n i f i c a t i o n P o w e r$

$F_{o} = O b j e c t i v e f o c a l l e n g t h$

$F_{e} = E y e p i e c e f o c a l l e n g t h$

Mass-Luminosity Relation

$L = M^{3.5}$

$M = M a s s (s o l a r m a s s e s)$

$L = L u m i n o s i t y (S o l a r l u m i n o s i t y)$

Orbit Eccentricity

$e = \frac{c}{a}$

$M = M a g n i f i c a t i o n P o w e r$

$F_{o} = O b j e c t i v e f o c a l l e n g t h$

$F_{e} = E y e p i e c e f o c a l l e n g t h$

Parallax

$d = \frac{1}{p}$

$d = D i s t a n c e (p c)$
$p = P a r a l l a x A n g l e (a r c s e c o n d s)$

Redshift

$z + 1 = \frac{λ_{O}}{λ_{E}}$

$z = R e d s h i f t$

$λ_{O} = O b s e r v e d W a v e l e n g t h$

$λ_{E} = E m i t t e d W a v e l e n g t h$

Relativistic Doppler Shift

$z + 1 = \sqrt{\frac{1 + (v / c)}{1 - (v / c)}}$

$v V e l o c i t y (m / s)$

$c S p e e d o f l i g h t (m / s)$

$z R e d s h i f t$

Resolving Power

$Δ θ = 251643 \frac{λ}{d}$

$Δ θ = A n g u l a r s e p a r a t i o n (a r c s e c s)$

$λ = W a v e l e n g t h$

$d = O p t i c D i a m e t e r$

Schwarzschild Radius

$r_{s} = \frac{2 G m}{c^{2}}$

$r_{s} = S c h w a r t z c h i l d R a d i u s (m e t e r s)$

$G = G r a v i t a t i o n a l C o n s t a n t$

$c = S p e e d o f l i g h t$

$r = r a d i u s (m e t e r s)$

Small Angle Formula

$θ = 206265 \frac{D}{d}$

$Δ θ = A n g u l a r s e p a r a t i o n (a r c s e c s)$

$λ = W a v e l e n g t h$

$d = O p t i c D i a m e t e r$

Stefan-Boltzmann Law

$F = σ T^{4}$

$L = 4 π σ R^{2} T^{4}$

$\frac{L}{L_{⊙}} = {(\frac{R}{R_{⊙}})}^{2} {(\frac{T}{T_{⊙}})}^{4}$

$F = F l u x (l u m i n o s i t y / a r e a) (W / m^{2})$

$σ = S t e f a n - B o l t z m a n n C o n s t a n t$

$T = T e m p e r a t u r e (K)$

$L = L u m i n o s i t y (W)$

$R = R a d i u s (m)$

Stellar Lifetime

$τ = 10^{10} M^{- 2.5}$

$M = M a s s (s o l a r m a s s e s)$

$τ = S t e l l a r L i f e t i m e (y e a r s)$

Universal Gravitation

$F = G \frac{m_{A} m_{B}}{r^{2}}$

$F = G r a v i t a t i o n a l F o r c e (N)$

$G = G r a v i t a t i o n a l C o n s t a n t$

$m = m a s s (k g)$

$r = r a d i u s (m e t e r s)$

Vacuum Frequency

$f = \frac{c}{λ}$

$f = W a v e f r e q u e n c y (H z)$

$c = S p e e d o f L i g h t (m / s)$

$λ = w a v e l e n g t h (m)$

Wien’s Law

Astronomy Formulas

Ra=a(1+e)

Rp=a(1–e)

Ra=Orbit Aphelion

Rp=Orbit Perihelion

a=Semimajor Axis

e=Eccentricity

v=GMr

v = circular velocity (m/s)

G = Gravitational Constant

M = Mass (kg)

r = radius (meters)

LGPaLG Pb=D ADB2

LGP = Light G athering< Po wer

D = Opti cDiameter

m–M=–5+5log (d)

d=10 m–M+55

m = Apparent magnitude

M = Ab solute Mag nitude

d = Di stance (pc)

v=cz

v =Velocity (m/s)

c = Speed of light (m/s)

z = Redshift

Lf Do

Lf = Focal Length

DO = Obj ective Dia meter

E=mc2

E = Energy (J)

m = Mass (kg)

c = Speed of light (m/s)

v=H0d

v =Recessional velocity (km/s)

H0 = Hubble‘s Constant

d = Distance

Tu=9.778× 1011H0

Tu = Age of the Universe (years)

H0 = Hubble Constant (km/s/Mpc)

mB–mA=2.5 log

IAIB IA IB=100.4 mb–m a

m = Magnitude

I = Inte nsity

I=L4π d2

I = Light Intensity (W/ m2)

L = Lumi nosity (W)

d = Dist ance (m)

MA+MB= a3p2

p2=a 3MA+M B

M = Mass (solar mas ses)

a = Semimajor axis (AU)

p = Orbit al Period (years)

M=FoF e

M = Magnif ication Po wer

Fo = Objective focal leng th

F e = Eyepiece focal len gth

L=M3.5

M = Mass (solar mas ses)

L = Luminosity (Solar l uminosity)

e=ca

M = Magnif ication Po wer

Fo = Objective focal leng th

F e = Eyepiece focal len gth

d=1p d = D istance (p c) p = Pa rallax Ang le (arcsec onds)

d = D istance (p c)

p = Pa rallax Ang le (arcsec onds)

z+1= λOλE

z = Redshi ft

λO = Observed Wavelength

λE= Emi tted Wavel ength

z+1=1 +(v/c)1–(v /c)

v Velocity (m/s)

c Speed of light (m/s)

z Redshift

Δθ=251643 λd

Δθ= Angular separation (arcsecs)

λ= Wavelength

d=Optic Diameter

rs=2 Gmc2

rs=Schwartzchild Radius (meters)

G=Gravitational Constant

$R_{a} = a (1 + e)$

$R_{p} = a (1 - e)$

$R_{a} = O r b i t A p h e l i o n$

$R_{p} = O r b i t P e r i h e l i o n$

$a = S e m i m a j o r A x i s$

$e = E c c e n t r i c i t y$

$v = \sqrt{\frac{G M}{r}}$

$v = c i r c u l a r v e l o c i t y (m / s)$

$G = G r a v i t a t i o n a l C o n s t a n t$

$M = M a s s (k g)$

$r = r a d i u s (m e t e r s)$

$\frac{L G P_{a}}{L G P_{b}} = {(\frac{D_{A}}{D_{B}})}^{2}$

$L G P = L i g h t G a t h e r i n g < P o w e r$

$D = O p t i c D i a m e t e r$

$m - M = - 5 + 5 \log ((d))$

$d = 10^{\frac{m - M + 5}{5}}$

$m = A p p a r e n t m a g n i t u d e$

$M = A b s o l u t e M a g n i t u d e$

$d = D i s t a n c e (p c)$

$v = c z$

$v = V e l o c i t y (m / s)$

$c = S p e e d o f l i g h t (m / s)$

$z = R e d s h i f t$

$\frac{L_{f}}{D_{o}}$

$L_{f} = F o c a l L e n g t h$

$D_{O} = O b j e c t i v e D i a m e t e r$

$E = m c^{2}$

$E = E n e r g y (J)$

$m = M a s s (k g)$

$c = S p e e d o f l i g h t (m / s)$

$v = H_{0} d$

$v = R e c e s s i o n a l v e l o c i t y (k m / s)$

$H_{0} = H u b b l e ‘ s C o n s t a n t$

$d = D i s t a n c e$

$T_{u} = \frac{9.778 \times 10^{11}}{H_{0}}$

$T_{u} = A g e o f t h e U n i v e r s e (y e a r s)$

$H_{0} = H u b b l e C o n s t a n t (k m / s / M p c)$

$m_{B} - m_{A} = 2.5 \log$

$(\frac{I_{A}}{I_{B}}) \frac{I_{A}}{I_{B}} = 10^{0.4 (m_{b} - m_{a})}$

$m = M a g n i t u d e$

$I = I n t e n s i t y$

$I = \frac{L}{4 π d^{2}}$

$I = L i g h t I n t e n s i t y (W / m^{2})$

$L = L u m i n o s i t y (W)$

$d = D i s t a n c e (m)$

$M_{A} + M_{B} = \frac{a^{3}}{p^{2}}$

$p^{2} = \frac{a^{3}}{M_{A} + M_{B}}$

$M = M a s s (s o l a r m a s s e s)$

$a = S e m i m a j o r a x i s (A U)$

$p = O r b i t a l P e r i o d (y e a r s)$

$M = \frac{F_{o}}{F_{e}}$

$M = M a g n i f i c a t i o n P o w e r$

$F_{o} = O b j e c t i v e f o c a l l e n g t h$

$F_{e} = E y e p i e c e f o c a l l e n g t h$

$L = M^{3.5}$

$M = M a s s (s o l a r m a s s e s)$

$L = L u m i n o s i t y (S o l a r l u m i n o s i t y)$

$e = \frac{c}{a}$

$M = M a g n i f i c a t i o n P o w e r$

$F_{o} = O b j e c t i v e f o c a l l e n g t h$

$F_{e} = E y e p i e c e f o c a l l e n g t h$

$d = \frac{1}{p}$

$d = D i s t a n c e (p c)$
$p = P a r a l l a x A n g l e (a r c s e c o n d s)$

$d = D i s t a n c e (p c)$

$p = P a r a l l a x A n g l e (a r c s e c o n d s)$

$z + 1 = \frac{λ_{O}}{λ_{E}}$

$z = R e d s h i f t$

$λ_{O} = O b s e r v e d W a v e l e n g t h$

$λ_{E} = E m i t t e d W a v e l e n g t h$

$z + 1 = \sqrt{\frac{1 + (v / c)}{1 - (v / c)}}$

$v V e l o c i t y (m / s)$

$c S p e e d o f l i g h t (m / s)$

$z R e d s h i f t$

$Δ θ = 251643 \frac{λ}{d}$

$Δ θ = A n g u l a r s e p a r a t i o n (a r c s e c s)$

$λ = W a v e l e n g t h$

$d = O p t i c D i a m e t e r$

$r_{s} = \frac{2 G m}{c^{2}}$

$r_{s} = S c h w a r t z c h i l d R a d i u s (m e t e r s)$

$G = G r a v i t a t i o n a l C o n s t a n t$

$c = S p e e d o f l i g h t$