Learning never exhausts the mind
Home >  Astronomy > Learn Astronomy > List of Astronomy Math Equations with Workings

# List of Astronomy Math Equations with Workings

Last Updated on by

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

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

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

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

## Gravity & Orbits

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? 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

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 particleWhat 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

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

Ratio of Fluxes Equation 18 - Ratio of Fluxes
Ratio of flux between two stars with apparent magnitudes m and n and measured fluxes of Fm and Fn.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 (FM) using the inverse square law for a star at distance d (parsecs), with observed flux Fm.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, me is the mass of the electron, mp is the mass of the proton, ρ is the density, and μe = Ne / Np is the ratio of electron number to proton number.Electron Degeneracy Pressure
Wien's Displacement Law Equation 61 - Wien's Displacement Law

## Cosmology

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 galaxySystem Development Life Cycle 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 (fmax) 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  