Enter the semi-major axis and the orbital period into the calculator to determine Kepler’s Constant for a celestial body’s orbit around a larger body, typically a planet around a star or a moon around a planet.
Kepler’s Constant Formula
The following formula is used to calculate Kepler’s Constant.
K = a^3 / P^2
Variables:
- K is Kepler’s Constant (AU^3/year^2)
- a is the semi-major axis of the orbit (Astronomical Units – AU)
- P is the orbital period (years)
To calculate Kepler’s Constant, cube the semi-major axis of the orbit and divide by the square of the orbital period.
What is Kepler’s Constant?
Kepler’s Constant is a value that relates the semi-major axis of an orbit to its orbital period. According to Kepler’s Third Law of Planetary Motion, this constant should be the same for all objects orbiting the same primary body, assuming the orbits are ellipses with the primary body at one focus. It is a fundamental constant in celestial mechanics and is used to describe the motion of planets and other celestial bodies.
How to Calculate Kepler’s Constant?
The following steps outline how to calculate Kepler’s Constant.
- First, determine the semi-major axis of the orbit (a) in Astronomical Units (AU).
- Next, determine the orbital period (P) in years.
- Next, gather the formula from above = K = a^3 / P^2.
- Finally, calculate Kepler’s Constant (K) in AU^3/year^2.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
semi-major axis of the orbit (a) = 1 AU
orbital period (P) = 1 year
