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Astronomy & Space

Orbits, gravity, stars and cosmology

Escape Velocity

Intermediate
ve=2GMrv_e = \sqrt{\frac{2GM}{r}}

Minimum speed to escape a body's gravity.

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Orbital Velocity

Intermediate
v=GMrv = \sqrt{\frac{GM}{r}}

Speed of a circular orbit.

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Kepler's Third Law

Advanced
T2=4π2GMa3T^2 = \frac{4\pi^2}{GM}a^3

Relates orbital period to semi-major axis.

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Schwarzschild Radius

Advanced
rs=2GMc2r_s = \frac{2GM}{c^2}

Event horizon radius of a black hole.

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Hubble's Law

Advanced
v=H0dv = H_0 d

Recession velocity of galaxies with distance.

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Stefan–Boltzmann Law

Advanced
L=4πR2σT4L = 4\pi R^2 \sigma T^4

Luminosity of a star from radius and temperature.

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Redshift

Advanced
z=λobsλemitλemitz = \frac{\lambda_{obs} - \lambda_{emit}}{\lambda_{emit}}

Fractional wavelength shift of light.

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Parallax Distance

Advanced
d=1pd = \frac{1}{p}

Distance in parsecs from parallax angle in arcseconds.

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Surface Gravity

Intermediate
g=GMr2g = \frac{GM}{r^2}

Gravitational acceleration at a body's surface.

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Apparent Brightness

Advanced
b=L4πd2b = \frac{L}{4\pi d^2}

Observed brightness from luminosity and distance.

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Distance Modulus

Advanced
mM=5log10(d)5m - M = 5\log_{10}(d) - 5

Relates apparent and absolute magnitude to distance.

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Light-Year

Basic
d=c×td = c \times t

Distance light travels in a given time.

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Wien's Displacement Law

Intermediate
λmax=bT\lambda_{max} = \frac{b}{T}

Peak emission wavelength of a blackbody.

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Newton's Law of Gravitation

Intermediate
F=Gm1m2r2F = G\frac{m_1 m_2}{r^2}

The attractive force between any two masses.

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Gravitational Potential Energy

Advanced
U=GMmrU = -\frac{GMm}{r}

Energy of a mass in another body's gravitational field.

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Mass–Luminosity Relation

Advanced
LL(MM)3.5\frac{L}{L_\odot} \approx \left(\frac{M}{M_\odot}\right)^{3.5}

How a main-sequence star's brightness scales with its mass.

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Eddington Luminosity

Advanced
LEdd=4πGMmpcσTL_{Edd} = \frac{4\pi G M m_p c}{\sigma_T}

The maximum steady luminosity before radiation blows a star apart.

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Chandrasekhar Limit

Advanced
MCh1.44MM_{Ch} \approx 1.44\,M_\odot

The maximum mass of a stable white dwarf.

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Hawking Temperature

Advanced
T=c38πGMkBT = \frac{\hbar c^3}{8\pi G M k_B}

Temperature of the radiation a black hole emits.

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Photon Sphere Radius

Advanced
rph=3GMc2r_{ph} = \frac{3GM}{c^2}

Radius where gravity bends light into a circular orbit.

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Synodic Period

Intermediate
1S=1P11P2\frac{1}{S} = \left|\frac{1}{P_1} - \frac{1}{P_2}\right|

Time between repeated alignments of two orbiting bodies.

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Gravitational Redshift

Advanced
zGMrc2z \approx \frac{GM}{rc^2}

Fractional stretching of light climbing out of gravity.

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Hill Sphere Radius

Advanced
rHa(m3M)1/3r_H \approx a\left(\frac{m}{3M}\right)^{1/3}

The zone where a body's gravity dominates over its host's.

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