# Equations

In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true.

## Geometry & Trigonometry

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

Circle, circumference of | Equation 1 - Circle, circumference of | Calculating the circumference of a circle. | |

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

## 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. | |

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. |

## 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 | |

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

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. | |

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

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

Luminosity ratio of magnitudes | Equation 40 - Luminosity ratio of magnitudes |

## 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. | |

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. | |

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

Gravitational force | Equation 45 - Gravitational force | ||

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. |

## 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. | |

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

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 | |

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. | |

Normal gas pressure | Equation 49 - Normal gas 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) | |

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. |

## 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} | |

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

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}. | |

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. | |

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.} |

## Cosmology

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

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

Temperature scale factor | Equation 32 - Temperature scale factor | Temperature of the universe through time as a function of scale factor. | |

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). | |

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

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

## 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. | |

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

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