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# Keplers 3rd Law

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**).

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

#### The Science

Kepler's Laws of planetary motion are as follows:

- The orbit of a planet is an ellipse with the Sun at one of the two foci.
- A line segment joining a planet and the Sun sweeps out equal areas in the orbital plane during equal periods of time.
- 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:

**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

**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.

**Related Astro Calculators:**

- Kepler's 3
^{rd}Law Calc has Kepler's 3^{rd}law solved for each parameter. - Astronomy Calculator contains basic formulas for a college level Introduction to Astronomy
- 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

**Keplers 3rd Law**, references 4 equations/constants.