Dhruve = (by performing Samyama) on the polar-star; tad-gati = (of) their movement; jnanam = knowledge.
One can get the knowledge of the movement of the stars by performing samyama on the polar star.
The two terms used in Sanskrit about the fundamental truth of the world are rta & satyam. These terms can be applied at various levels, gross and subtle. While Satyam may be the fundamental truth about the constitution of the governs the universe. Same is true in the sphere of Astronomy also. The great master Patanjali, as we saw in previous issue (Sutra III/28), gives us the trick to know the fundamental nature of the heavenly bodies by asking us to perform Samyama on the moon, their smallest unit. But it is equally important in astronomy to know the laws that govern the movements of stars etc. The movement and speed of a body is always relative, compared to a fixed position. Dhruva (the very meaning of which suggests a fixed position) is the only star in the known sky that is relatively fixed (it also moves a little once in 2000 years or so according to some concept).
Knowledge of a basic principle or law helps us to know the progressive laws based on that fundamental principle. Thus, by performing Samyama on Dhruva, the polar Star, we can get the knowledge of the movement of other stars.