Astronomy Formula Cheat Sheet, Cheat Sheet of Astronomy

Download Astronomy Formula Cheat Sheet and more Cheat Sheet Astronomy in PDF only on Docsity! Astronomy Formula Sheet Intensity Ratio: mA ´mB “ 2.5log ˆ IA IB ˙ IB IA “ 100.4pmA´mBq 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 λ d ∆θ “ Angular separation (arcsecs) λ “ Wavelength d “ Optic Diameter Compare LGP: LGPA LGPB “ ˆ DA DB ˙2 LGP “ Light Gathering Power D “ Optic Diameter Magnification: M “ FO FE M “ Magnification Power FO “ Objective focal length FE “ Eyepiece focal length Wien’s Law: λpeak “ 2900000 T λpeak “ Peak wavelength (nm) T “ Temperature (K) Stefan-Boltzmann Law: F “ σT 4 L “ 4πσR2T 4 L Ld “ ˆ R Rd ˙2ˆ T Td ˙4 F “ Flux (luminosity/area) (W/m2) σ “ Stefan-Boltzmann Constant T “ Temperature (K) L “ Luminosity (W) R “ Radius (m) Redshift: z ` 1 “ λO λE 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 “ H0d v “ Recessional velocity (km/s) H0 “ Hubble’s Constant d “ Distance Fusion Explained: E “ mc2 E “ Energy (J) m “ Mass (kg) c “ Speed of light (m/s) 1 Parallax: d “ 1 p d “ Distance (pc) p “ Parallax Angle (arcseconds) F Ratio: Lf DO Lf “ Focal Length DO “ Objective Diameter Distance Modulus: m´M “ ´5` 5logpdq d “ 10 m´M`5 5 m “ Apparent magnitude M “ Absolute Magnitude d “ Distance (pc) Orbit Eccentricity: e “ c a e “ Orbital Eccentricity c “ Distance from focus to center a “ semimajor axis Aphelion/Perihelion: Ra “ ap1` eq Rp “ ap1´ eq Ra “ Orbit Aphelion Rp “ Orbit Perihelion a “ Semimajor Axis e “ Eccentricity Kepler’s 3rd Law: MA `MB “ a3 p2 p2 “ a3 MA `MB M “ Mass (solar masses) a “ Semimajor axis (AU) p “ Orbital Period (years) Mass-Luminosity Relation: L “M3.5 M “ Mass (solar masses) L “ Luminosity (Solar luminosity) Stellar Lifetime: τ “ 1010M´2.5 M “ Mass (solar masses) τ “ Stellar Lifetime (years) Schwarzschild Radius: rs “ 2Gm c2 rs “ Schwartzchild Radius (meters) G “ Gravitational Constant c “ Speed of light r “ radius (meters) Universal Gravitation: F “ G mAmB r2 F “ Gravitational Force (N) G “ Gravitational Constant m “ mass (kg) r “ radius (meters) Inverse-Squares Law: I “ L 4πd2 I “ Light Intensity (W/m2) L “ Luminosity (W) d “ Distance (m) Vacuum Frequency: f “ c λ f “ Wave frequency (Hz) c “ Speed of Light (m/s) λ “ wavelength (m) Hubble Time: TU “ 9.778ˆ 1011 H0 TU “ Age of the Universe (years) H0 “ Hubble Constant (km/s/Mpc) 2