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How does a radial velocity measurement depend on inclination?

Answer 1

The relative rate changes due to the geometry of the measurement.

If the orbital plane of the orbiting object happens to lie along our line of sight then the measured speed is the true speed of the wobble. However, if the orbital plane is tilted with respect to the Sun then the true speed is higher and the companion is more massive by a factor of #1/sin(i)#, where i is the angle of inclination. Good explanation and graphics here: https://tutor.hix.ai

The Variable Radial Velocity Of Sirius, and the Inclination of its Orbit-Plane is one example that can be found here: https://tutor.hix.ai

This is a student exercise: naap_esp_sg.pdf at astro.unl.edu.

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Answer 2

Everett Abrams

In a circular orbit, radial velocity measurement is independent of orbital inclination; in an elliptical orbit, radial velocity measurement increases with inclination.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.