Keplers 3rd Law

vCalc Reviewed
Calculator / Last modified by KurtHeckman on 2018/04/24 14:05
(M)-Mass from Period and Separation
(T)-Period from Mass and Separation
(R) -Separation from Mass and Period
(G) Gravitational Constant
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The Kepler's 3rd 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).

INSTRUCTIONS: Click on any of the buttons to see a calculator with Kepler's 3rd law solved for that chosen parameter.

The Science

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 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)

where:

Distance Units: The calculator has length unit with defaults of ua (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 ua, light seconds, light minutes, light years, parsecs, kilo-parsecs and kilo-light years.

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.

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