## Geometry & Trigonometry

Title | Equation | Description | Further Reading |
---|---|---|---|

Circle, circumference of | Equation 1 - Circle, circumference of | Calculating the circumference of a circle. | How Large is the Earth? |

Sphere, Surface Area of | Equation 21 - Sphere, Surface Area of | The surface area of a sphere of radius r. | Luminosity and Flux of Stars |

## Size & Distance

Title | Equation | Description | Further Reading |
---|---|---|---|

Distance Calculation using Parallax | Equation 10 - Distance Calculation using Parallax | The distance to an object in parsecs is equal to 1 AU over the parallax in arc seconds. | The Astronomical Magnitude Scale |

Angular Size Calculation | Equation 12 - Angular Size Calculation | Calculate the angular size of an object based on its apparent size and distance between measure and observer, where theta is the angular size in radians, Sap is the apparent size in mm and l is the distance between the measure and the observer. | What is Angular Size? |

## Magnitude

Title | Equation | Description | Further Reading |
---|---|---|---|

Pogsons Relation | Equation 20 - Pogsons Relation | Pogson's Relation is used to find the magnitude difference between two objects expressed in terms of the logarithm of the flux ratio | The Astronomical Magnitude Scale |

Absolute Magnitude Relation | Equation 23 - Absolute Magnitude Relation | Very similar to Pogsons Relation for apparent magnitudes, this equation shows the relation for absolute magnitudes. | The Astronomical Magnitude Scale |

Distance Modulus | Equation 25 - Distance Modulus | Distance modulus can be used to find a relationship between a stars absolute magnitude and its apparent magnitude given a distance, d, in parsecs. | Parallax, Distance and Parsecs |

Absolute Magnitude | Equation 31 - Absolute Magnitude | Calculating the Absolute Magnitude of a star within our galaxy. | The Astronomical Magnitude Scale |

Bolometric Magnitude | Equation 39 - Bolometric Magnitude | Bolometric magnitude is related to the luminosity ratio | The Astronomical Magnitude Scale |

Luminosity ratio of magnitudes | Equation 40 - Luminosity ratio of magnitudes | The Astronomical Magnitude Scale |

## Gravity & Orbits

Title | Equation | Description | Further Reading |
---|---|---|---|

Kelpers Law of Planetary Motion | Equation 2 - Kelpers Law of Planetary Motion | Keplers law of Planetary Motion is simple and strait forward: The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of their orbits. | Kepler's Laws of Planetary Motion |

Gravitational interaction | Equation 43 - Gravitational interaction | Gravitational interaction is the most important force, and so the most useful definition of the potential energy. For two-body problems, potential energy, U, is given by this formula. | What is XML? |

Centripetal force | Equation 44 - Centripetal force | An orbiting body, at radius r, experiences the centripetal force Fc, which keeps it moving in a circle. | What is XML? |

Gravitational force | Equation 45 - Gravitational force | What is XML? | |

Schwarzschild radius | Equation 50 - Schwarzschild radius | The Schwarzschild radius is the radius of a sphere such that, if all the mass of an object were to be compressed within that sphere, the escape velocity from the surface of the sphere would equal the speed of light. | What Is a Black Hole? Black Holes Explained - From Birth to Death |

## Energy

Title | Equation | Description | Further Reading |
---|---|---|---|

Energy of a Photon | Equation 29 - Energy of a Photon | The energy of a photon in Joules is equal to h (Planck constant) times by its frequency. | The Nature of Light |

Frequency of Light | Equation 30 - Frequency of Light | The frequency of light is dependant on the speed of light (c) and it's wavelength. | The Nature of Light |

Kinetic energy of a particle | Equation 42 - Kinetic energy of a particle | The fundamental definition of the kinetic energy of a particle is given by the formula, where v is the velocity of the particle | What is XML? |

The energy of a photon | Equation 46 - The energy of a photon | The energy, E, of a photon where h is Planck's constant, v is the frequency of the wave, c is the speed of light and λ is the wavelength. | Software Design Concepts |

Normal gas pressure | Equation 49 - Normal gas pressure | Electron Degeneracy Pressure |

## Time

Title | Equation | Description | Further Reading |
---|---|---|---|

Local Sidereal Time | Equation 14 - Local Sidereal Time | Use this formula to calculate local sidereal time given the Greenwich sidereal time plus your longitude (east of Greenwich) | Sidereal Time, Civil Time and Solar Time |

Relationship between LST, HA and RA | Equation 17 - Relationship between LST, HA and RA | These equations show the relationsip between Local Sidereal Time, Hour Angle and Right Ascension. | Sidereal Time, Civil Time and Solar Time |

## Solar Physics

Title | Equation | Description | Further Reading |
---|---|---|---|

Ratio of Fluxes | Equation 18 - Ratio of Fluxes | Ratio of flux between two stars with apparent magnitudes m and n and measured fluxes of F and _{m}F._{n} | Luminosity and Flux of Stars |

Flux and Luminosity | Equation 22 - Flux and Luminosity | This equation shows the relationship between the observed flux of a star and its luminosity. | Luminosity and Flux of Stars |

Inverse Square Law for Flux | Equation 24 - Inverse Square Law for Flux | This equation gives a stars absolute flux (F_{M}) using the inverse square law for a star at distance d (parsecs), with observed flux F_{m}. | Luminosity and Flux of Stars |

Stefan-Boltzmann Law | Equation 26 - Stefan-Boltzmann Law | Also known as Stefan's law, states that the total energy radiated per unit surface area of a black body in unit time, is directly proportional to the fourth power of the black body's thermodynamic temperature T. | Hertzsprung-Russell Diagram and the Main Sequence |

Electron degeneracy pressure | Equation 38 - Electron degeneracy pressure | Electron degeneracy pressure in a material can be computed, where h is Planck's constant, m_{e} is the mass of the electron, m_{p} is the mass of the proton, ρ is the density, and μ_{e = Ne / Np is the ratio of electron number to proton number.} | Electron Degeneracy Pressure |

Wien's Displacement Law | Equation 61 - Wien's Displacement Law | What is Black Body Radiation? |

## Cosmology

Title | Equation | Description | Further Reading |
---|---|---|---|

Redshift | Equation 27 - Redshift | Redshift calculation based on observed wavelengths. | Redshift and Blueshift |

Temperature scale factor | Equation 32 - Temperature scale factor | Temperature of the universe through time as a function of scale factor. | Cosmic Scale Factor and Expansion of the Universe |

Temperature redshift. | Equation 33 - Temperature redshift. | Temperature of the universe expressed as a function of redshift. T0 represents the temperature of the universe today (~2.7K). | Redshift and Blueshift |

Proper Distance | Equation 35 - Proper Distance | Proper distance x(t) corresponding to different epochs in terms of the comoving radial distance coordinate r. | Redshift and Blueshift |

Redshift and Scale Factor | Equation 36 - Redshift and Scale Factor | Relationship between redshift and scale factor for another epoch. | Redshift and Blueshift |

Hubble's Law | Equation 47 - Hubble's Law | The linear relationship between recession velocity, v, and the distance, x, of a local galaxy | System Development Life Cycle |

Planck’s Law of Blackbody Radiation | Equation 58 - Planck’s Law of Blackbody Radiation | Formula to determine the spectral energy density of the emission at each wavelength (Eλ) at a particular absolute temperature (T). | What is Black Body Radiation? |

Wien’s Displacement Law | Equation 59 - Wien’s Displacement Law | The frequency of the peak of the emission (f_{max}) increases linearly with absolute temperature (T) | What is Black Body Radiation? |

Stefan–Boltzmann Law | Equation 60 - Stefan–Boltzmann Law | Relates the total energy emitted (E) to the absolute temperature (T). | What is Black Body Radiation? |

## Relativity

Title | Equation | Description | Further Reading |
---|---|---|---|

Special theory of relativity | Equation 41 - Special theory of relativity | The special theory of relativity states that mass and energy are equivalent. | What is XML? |

Lorentz factor | Equation 48 - Lorentz factor | The factor by which time, length, and relativistic mass change for an object while that object is moving. | The Speed of Light |

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