Introduction To Astronomy 100 Formula Sheet PDF

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Summary

An Astronomy Formula Sheet, filled with a ton of formulas necessary to succeed in Introduction To Astronomy 100 and pass the class....

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ASTR 100 Constants and Formulas Speed of Light Size of Nanometer Size of Astronomical Unit Size of Light Year Size of Parsec Size of Megaparsec Stefan-Boltzmann Constant Gravitational Constant Hubble’s Constant Temperature of the Sun Luminosity of the Sun Mass of the Sun Radius of the Sun Mass of the Earth Radius of the Earth Radius of Jupiter

c = 3.00 x 108 m/s = 3.00 x 105 km/sec 1 nm = 10-9 m 1 AU = 1.50 x 1011 m = 1.50 x 108 km 1 Ly = 9.46 x 1015 m 1 pc =3.26 Ly 1 Mpc = 106 pc σ = 5.67 x 10-8 W/m2/K4 G = 6.673 x 10-11 m3/kg/s2 H = 72 km/s/Mpc Tʘ = 5780 K Lʘ = 3.83 x 1026 W Mʘ = 2.00 x 1030 kg Rʘ = 6.96 x 108 m MꚚ = 5.97 x 1024 kg RꚚ = 6.378 x 106 m RJupiter = 7.00 x 107 m

Distance traveled by light d=ct d=distance, c=speed of light, and t=time, in seconds Kepler’s Third Law 2

P =a

3

P=Period of a planet or comet’s orbit, in years and a=mean radius of the orbit, in AU Variant of Kepler’s Third Law for Binary Stars 3

M 1+ M 2 =

a 2 P

M1 = mass of one star in solar masses, M2 = mass of the other star in solar masses, a = average distance of the two stars in AU, and P = Period of the star’s orbit in years Relation between Angular and Linear Distance 2 πθ =d /r 360

θ = angular diameter in degrees, d=linear diameter, and r = distance, units on linear diameter and distance are not important, but must match. Escape velocity, the speed necessary to leave the gravitational influence of a body permanently

√

v escape =

2 GM R

G=gravitational constant, M=mass of the planet, moon, etc in kg, and R=radius of the planet, moon, etc in meters Force of gravity F gravity =

G M1 M2 R

2

Fgravity = Force of gravity in Newtons, G = gravitational constant, M1 = mass of one object, M2 = mass of the other object, and R = distance between the centers of the two objects Frequency – wavelength relation for light c=λf

c=speed of light, λ (Greek lower case lambda) = wavelength, and f=frequency Wien’s Law 6

T=

2.898 x 10 λm

T=temperature of a body emitting a black body spectrum in K, λm=wavelength of maximum energy output, in nm (nanometers) Doppler Formula

( ) ⌊ ( λλ ) +1 ⌋ 2

⌊

v=

λ −1 ⌋ λo 2

c

o

v=velocity of an object, c = speed of light, λ = wavelength at which a spectral line appears, and λo = wavelength of that same spectral line in a laboratory

Stefan-Boltzmann Law 2

L=4 π R σ T

4

L = luminosity of a star in W, R= radius of a star in m, σ (Greek lower case sigma) =StefanBoltzmann constant, and T = temperature of a star’s surface in K A variant of the Stefan-Boltzmann law in solar units

( ) √ LL

Tʘ R = Rʘ T

2

ʘ

R=radius, T=temperature, L=luminosity, all quantities marked with ʘ refer to the sun Parallax relationship d pc =

1 p dpc = distance in parsecs and p=parallax in arc seconds

Schwartzschild radius of a black hole Rs =

2 GM 2 c Rs = Size of a black hole in m, G = gravitational constant, M = mass of the black hole in kg, and c = speed of light in m/s

Hubble’s Law v r =Hd Vr=recession velocity, the speed at which the a galaxy appears to be going away from us, H=the Hubble constant, d=distance to the galaxy in Mpc (megaparsecs)...