# Kepler’s Third Law

Kepler’s third law relates the motion of different planets to one another. It is also called the law of harmonies. It states that:

**The square of the orbital period of a planet ( T) is directly proportional to the cube of the semimajor axis(a) of its orbit.**

In equation form, it can be expressed as:

T^{2}/a^{3}=constant,

Or, alternatively, if we have two planets of orbital periods T and T’ and semimajor axes a and a’:

T^{2}/a^{3}= T’^{2}/a’^{3}.

Since this ratio is always the same, planets with bigger orbits (bigger *a*) will have longer years (bigger *T*): That is, it will take them longer to complete an orbit.

We call the constant of proportionality between *T ^{2}* and

*a*Kepler’s constant, or

^{3}*K*. Its value is the same for the orbit of every planet in the Solar System. However, every orbital system will have its own value of

*K*shared by every orbiting body in that system, but possibly different from that of other systems.

**Figure:** By Kepler's third law, orbits with a bigger semimajor axis have longer periods. This means that, in the interval of time from T=0 to T=1, a planet with a smaller orbit would cover a bigger portion of its orbit.