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I'm now officially confused about the usage of "tangential" when breaking down orbital velocity components. It started with edits and comments on this answer to Orbital speed is (vector) sum of tangential and normal speed?

I've (possibly/probably incorrectly) used "tangential" to refer to the velocity component perpendicular to radial in Low-thrust spiraling to escape, is the flight path angle (gamma) at C3=0 always 39 degrees? and also in How to calculate the flight path angle, γ, from a state vector?. I say possibly/probably inccorectly because the the velocity should always be tangent to the orbit. But rather than correct me, @MarkAdler's answer to the first question continues the distinction between tangential velocity and the direction of motion:

Below is the same plot for when accelerating tangentially, as opposed to in the velocity direction.

and @TomSpilker's answer to the second question does likewise:

In addition to $\gamma$, the angle between the tangential direction and the velocity vector, there is $\beta$, the angle between the radial direction and the velocity vector.

However, the diagram below from Julio@'s answer to ** suggests the component perpendicular to the radial direction might be called normal velocity.

Question: How can the tangential velocity of an elliptical Kepler orbit not be tangent to the orbit, but instead be perpendicular to the radial component? Help me Mr. Wizzard!

enter image description here

Source

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    $\begingroup$ There seems to be indeed some confusion of vocabulary, with "tangential" used instead of "transverse". See, for example, daviddarling.info/encyclopedia/T/transversevel.html . $\endgroup$
    – Litho
    Oct 8, 2019 at 15:39
  • $\begingroup$ @Litho Oh, that's cool! Would you be willing to post that exact comment as another answer? It helps me understand why the authors of the linked answers didn't correct me. $\endgroup$
    – uhoh
    Oct 8, 2019 at 15:44
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    $\begingroup$ @Litho wait, I think I see what's happening. Searching that image, I found this Astronomy presentation (starting on slide 2) In this context the velocity is tangent to the sphere that contains the object being observed from the center of the sphere. For stellar motion, there is radial velocity (usually from Doppler shift) and tangential velocity (usually from proper motion). That's a different context than the velocity components of an object in a Kepler orbit being analyzed mathematically, but it seems to have "leaked" $\endgroup$
    – uhoh
    Oct 8, 2019 at 15:49
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    $\begingroup$ I don't know what the correct term for $v_n$ in your diagram is, but surely the correct term for $v$ is simply "velocity". And yes, the velocity of any object moving along a continuous and differentiable trajectory is always tangential to said trajectory, by definition. $\endgroup$
    – Ilmari Karonen
    Oct 8, 2019 at 22:05

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The terms radial and tangential are relative to the central body NOT the instantaneous vector, so if the radial velocity is nonzero, then the tangential component is orthogonal to that and parallel to the planet's horizon. It is Vtangent * R that is the angular momentum that is conserved in a Kepleran orbit.

Momentarily at apogee and perigee Vtan = V.

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    $\begingroup$ Welcome to Stack Exchange and thank you for your post! Since this disagrees with the other answer, I've unaccepted it for now. However unlike the other answer, your answer is completely unsupported. Answers generally need to support claims by citing sources and/or adding supporting links. They need to go beyond asserting things or "take my word for it" answers. Is it possible to do so here? Thanks! $\endgroup$
    – uhoh
    Feb 26, 2021 at 23:09

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