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For a satellite I know the period T and frequency f = 1/T. For instance, for an earth skimming satellite with period T = 5100 seconds, the frequency is f = 0.00019 1/sec. What does the number 0.00019 represent? Is it the angle in radian per second?

And how do I visualize the wavelength of the satellite's orbit?

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If the satellite has a period of $T$ seconds (so it makes one complete revolution in this time), then its frequency of revolution $\frac{1}{T}\ s^{-1}$ represents the number of revolutions it makes per second (assuming circular orbit). So if $T=5100\ s$ then the satellite makes $0.00019$ revolutions per second, or $f=0.00019\ s^{-1}$.

If you wanted to determine the angular frequency, or the frequency in radians per second, then you would calculate $$\omega=\frac{2\pi}{T}=2\pi f\approx 0.0012\ \text{radians}\ s^{-1}$$

You might think that since an object has a frequency, then it should have a wavelength. But here, frequency or angular frequency are terms associated with the speed or velocity of the object. E.g., angular frequency being the magnitude of its angular velocity, which is a (pseudo) vector. In this particular case, physically the object does not possess a wavelength. Wavelengths are associated with waves, so in the context of your question, we don't really attribute a wavelength to such a situation.

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    $\begingroup$ Just for completeness, note that your explanation of frequency only applies to circular orbits. For elliptical orbits, the fraction of a complete revolution per second is not a constant. The constant would be the area swept by a radial from the planet to the satellite. $\endgroup$
    – Bill N
    Commented Feb 5, 2022 at 1:39
  • $\begingroup$ That’s correct. Edited. Thanks $\endgroup$
    – joseph h
    Commented Feb 5, 2022 at 6:56
  • $\begingroup$ Things were clearer in the olden days when I was a kid, before the unit s${}^{-1}$ became Hz. The unit of frequency was 'cps', cycles per second. $\endgroup$
    – garyp
    Commented Feb 5, 2022 at 14:10

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