Astronomy Calc

vCalc Reviewed
Calculator / Last modified by AndrewBudd on 2018/10/22 16:23
Kepler's 3rd Law
(M) - Mass from Period and Separation
(T) - Period from Mass and Separation
(R) - Separation from Mass and Period
(G) - Gravitational Constant
(`alpha`) Angle from size and distance
(s) Size from Distance and angle
(D) Distance from Size and Angle
Difference in magnitudes from Flux Ratio
Flux Ratio from Magnitudes
Resolving Power of a Telescope
Magnification of a Telescope
Mass from Luminosity
Mass from Acceleration and Radius
Mass from Speed and Separation
mass of extra-solar planet from M, r and R
mass of extra-solar-planet from M, v and V
Relative Size from Relative Temperature and Luminosity
Relative Temperature from Relative size and luminosity
Relative Luminosity from relative size and temperature
speed from delta lambda and lambda
Wavelength shift from speed and wavelength
Blackbody wavelength from Temperature
Blackbody Temperature from peak wavelength
Distance from absolute and apparent magnitude
radius from speed and period
Speed of Circular Motion
Hubble Time
Luminosity from Mass
Mass from Luminosity

The Astronomy Calculator includes functions that are useful for studying astronomy. Formulae are organized in different tabs to the right as follows: T2 = (4π • R3)/(G•M)
          Kepler's Third Law

  • Kepler's 3rd Law formulas
  • Small Angle Formula
  • Flux and Magnitude formulas
  • Telescope formulas
  • Mass formulasSmall Angle Formula.png
            Small Angle Formula    α = S / D
  • Relative Size Formulas
  • Wavelength Formulas
  • Luminosity and other Formulas

The Math / Science

Kepler's Laws of planetary motion

Kepler's Laws

  1. The orbit of a planet is an ellipse with the Sun at one of the two foci.
  2. A line segment joining a planet and the Sun sweeps out equal areas in the orbital plane during equal periods of time.
  3. The square of the orbital period (T) is proportional to the cube of the semi-major axis of the the orbit ellipse. 

Kepler's 3rd Law of planetary motion states that the orbital period (T), mass of the system (M), the distance separating the objects (R), and the Universal Gravity Constant (G) are related in the following formula:

                         T2 = (4π • R3)/(G•M)


The Small Angle Formula

The Small Angle Formula relates the angle separation with the size and distance (see diagram) as follows: Small Angle Formula.png

α = S / D


  • (α) is the angle
  • (s) is the size
  • (d) is the distance

Related Astro Calculators:

Astronomy Calculator's Creator

SSpicklemire.jpg  Special thanks to Dr. Stephen Spicklemire, Department Chair, Physics &Earth-Space Science, Associate Professor of Physics at the University of Indianapolis.  Dr. Spicklemire created this calculator and all of the underlying equations (functions) to help his astronomy students.  

 "vCalc is awesome for my astronomy students. With vCalc I can give them real problems that would normally require fairly sophisticated reasoning and mathematics, and now they can do the reasoning, because they’re not daunted by the math. It’s great."   Dr. Steve Spicklemire