The Kepler's 3^rd Law calculator computes the orbital period (T), mass of the system (M), and the distance separating the objects (R).  It also provides the Universal Gravity Constant(G). Click on any of the buttons (RIGHT) to see a calculator with Kepler's 3^rd law solved for that chosen parameter.

Kepler's Laws of planetary motion are as follows:

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 3^rd 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)

where:

• T is the period of the orbit.
• M is the total mass of the system.
• R is the separation distance between the two objects.
• G is the universal gravity constant.

Astronomical Units

Distance Units: The calculator has length unit with defaults of au (astronomical units) which is the mean distance from the Sun to the Earth.  However, users can automatically change the distance units on both the inputs to the calculator and the solved answers via the pull-down menu.  The  distance units are automatically handled and range from extremely small (nano-meters) to truly astronomical including au, light seconds, light minutes, light years, parsecs, kilo-light years and mega-parses.

Mass Units: The calculator has mass units that default to multiples of the mass of the sun (solar_mass).   However, users can automatically change the mass units on both the inputs to the calculator and the solved answers via the pull-down menu.  The  mass units are automatically handled and range from extremely small (grains) to truly astronomical including Earth masses, Jupiter masses and Solar masses.

Time Units: The calculator has time duration units that default to days.   However, users can automatically change the time units on both the inputs to the calculator and the solved answers via the pull-down menu.  The time units are automatically handled and range from extremely small (nanoseconds) to large including weeks, months, years, decades and centuries.  They also include sidereal day and sidereal years.

Astronomy Calculators

• Hubble's Law
• Kepler's 3^rd Law formula T² = (4π • R³)/(G • M)
  • (M) - mass of the system. 
  • (T) - period of the orbit.
  • (R) - separation distance between the two objects.
  • (G) - universal gravity constant
• Small Angle Formula
  • (α) - angle
  • (D) - distance to astronomical object
  • (S) - size or diameter of astronomical object
• Flux and Magnitude formulas
  • Change in Magnitude from Flux Ratio
  • Flux Ratio from Magnitudes
• Telescope formulas
  • Resolving Power of a Telescope
  • Magnification of a Telescope
• Mass formulas
  • Mass from Luminosity
  • Mass from Acceleration and Radius
  • Mass from Speed and Separation
  • Mass of extra-solar planet from mass of star, radius of star orbit and radius of exoplanet orbit
  • Mass of extra-solar planet from mass and velocity of star and velocity of planet
• Relative Size Formulas
  • Relative Size from Relative Temperature and Luminosity
  • Relative Temperature from Relative Size and Luminosity
  • Relative Luminosity from Relative Temperature and Size
• Wavelength Formulas
  • Velocity from shift in Wavelength and Unshifted Wavelength
  • Wavelength Shift from Wavelength and Speed
  • Blackbody Wavelength from Temperature
  • Blackbody Temperature from Peak Wavelength
  • Photon Energy from Wavelength
  • Photon Wavelength from Energy
• Luminosity and other Formulas
  • Distance from absolute and apparent magnitude
  • Radius from Speed and Period
  • Speed of Circular Motion
  • Hubble Time
  • Luminosity from Mass

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• 3D Vector Calculator:
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• Exoplanet Calculator contains formulas for studying planets outside of our Solar System.
• Astronomical Distance Calculator provides the distance from the Earth to numerous astronomical bodies (e.g. Sun, Moon, planets, stars, Milky Way's Center and Edge, Andromeda Galaxy)
• Astronomical Distance Travel Time Calculator computes the time to travel to distant parts of space at different velocities.
• Radius of Perigee
• Radius of Apogee