I am assuming that it means the frequency of a planet on its orbit.

But why do we specifically say Keplerian? Is there some other kind of definition of frequency we use for astronomical bodies in space that requires us to emphasise that it is Keplerian?


1 Answer 1


Is there a limit to how fast a pulsar or other large, massive, dense body can spin?

The answer is yes! If it spins faster than a massless satellite in equatorial orbit at zero altitude, then it won't be stable. This is because any particle moving faster would migrate into a higher orbit. And how do we go about calculating the period of such a theoretical satellite? By applying Kepler's third law in this form: $M=A^3/P^2$, where $M$ is the mass of the pulsar, $A$ is the equatorial radius, and $P$ is the orbital period. (We also may have to adjust for oblateness).

This is much better said by Haensel et. al [2008]:

The frequency $f$ of stable rotation of a star of gravitational mass $M$ and baryon mass lower than the maximum allowable for non-rotating stars is limited by the (Keplerian) frequency $f_{\rm K}$ of a test particle co-rotating on an orbit at the stellar equator.

So we call $f_k$ a "Keplerian frequency" because it is the maximum possible rotational frequency for a star, and we calculate it using Kepler's 3rd law. The Keplerian frequency is important because it helps bound the size and mass of pulsars and other rapidly rotating bodies.


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