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Astronomy Formula Sheet
Intensity Ratio:
mA ´ mB “ 2. 5 log
ˆ I
A IB
IB
IA^ “^10
- 4 pmA´mB q
m “ Magnitude I “ Intensity
Small Angle Formula: (^) θ “ 206265 D d
θ “ Angular Diameter (arcsecs) D “ Diameter d “Distance
Circular Velocity: (^) v “
c GM r
v “ circular velocity (m/s) G “ Gravitational Constant M “ Mass (kg) r “ radius (meters)
Resolving Power: (^) ∆θ “ 251643 λd
∆θ “ Angular separation (arcsecs) λ “ Wavelength d “ Optic Diameter
Compare LGP: (^) LGPLGPA B
ˆ D
A DB
˙ (^2) LGP “ Light Gathering Power D “ Optic Diameter
Magnification: (^) M “ F FO E
M “ Magnification Power FO “ Objective focal length FE “ Eyepiece focal length
Wien’s Law: λpeak “ (^2900000) T^ λ Tpeak “ Temperature (K)^ “^ Peak wavelength (nm)
Stefan-Boltzmann Law:
F “ σT 4 L “ 4 πσR^2 T 4 L Ld^ “
ˆ R
Rd
˙ 2 ˆ T
Td
F “ Flux (luminosity/area) (W/m^2 ) σ “ Stefan-Boltzmann Constant T “ Temperature (K) L “ Luminosity (W) R “ Radius (m)
Redshift: z^ `^1 “^ λ λOE
z “ Redshift λO “ Observed Wavelength λE “ Emitted Wavelength
Doppler Formula: v “ cz
v “ Velocity (m/s) c “ Speed of light (m/s) z “ Redshift
Relativistic Doppler Shift: (^) z ` 1 “
d 1 ` pv{cq 1 ´ pv{cq
v “ Velocity (m/s) c “ Speed of light (m/s) z “ Redshift
Hubble’s Law: v “ H 0 d
v “ Recessional velocity (km/s) H 0 “ Hubble’s Constant d “ Distance
Fusion Explained: (^) E “ mc^2
E “ Energy (J) m “ Mass (kg) c “ Speed of light (m/s)
Parallax: d^ “^
p
d “ Distance (pc) p “ Parallax Angle (arcseconds)
F Ratio: (^) DLfO^ L DfO^ “ “^ Focal Length Objective Diameter
Distance Modulus: m^ ´^ M^ “ ´^5 ^5 logpdq d “ 10 m´M^5^5
m “ Apparent magnitude M “ Absolute Magnitude d “ Distance (pc)
Orbit Eccentricity: e “ ca
e “ Orbital Eccentricity c “ Distance from focus to center a “ semimajor axis
Aphelion/Perihelion: R Ra^ “^ ap^1 `^ eq p “^ ap^1 ´^ eq
Ra “ Orbit Aphelion Rp “ Orbit Perihelion a “ Semimajor Axis e “ Eccentricity
Kepler’s 3rd Law:
MA ` MB “ a
3 p^2 p^2 “ a
3 MA ` MB
M “ Mass (solar masses) a “ Semimajor axis (AU) p “ Orbital Period (years)
Mass-Luminosity Relation: (^) L “ M 3.^5 M L ““ Luminosity (Solar luminosity)Mass (solar masses)
Stellar Lifetime: (^) τ “ 1010 M ´^2.^5 M τ “^ “ Stellar Lifetime (years)^ Mass (solar masses)
Schwarzschild Radius: rs “ 2 Gmc 2
rs “ Schwartzchild Radius (meters) G “ Gravitational Constant c “ Speed of light r “ radius (meters)
Universal Gravitation: F^ “^ GmA rm 2 B
F “ Gravitational Force (N) G “ Gravitational Constant m “ mass (kg) r “ radius (meters)
Inverse-Squares Law: (^) I “ (^4) πdL 2
I “ Light Intensity (W/m^2 ) L “ Luminosity (W) d “ Distance (m)
Vacuum Frequency: f “ (^) λc
f “ Wave frequency (Hz) c “ Speed of Light (m/s) λ “ wavelength (m)
Hubble Time: TU “^9.^778 ˆ^10
11 H 0
TU “ Age of the Universe (years) H 0 “ Hubble Constant (km/s/Mpc)
