Meaning of "equatorial radius in an orbital plane"

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Discussion Overview

The discussion revolves around the interpretation of "equatorial radius" in the context of solving the inverse geodesic problem using a specific computational tool. Participants explore the implications of defining "North" or "South" in an orbital plane and the relevance of the equatorial radius in relation to ellipsoidal central masses.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • MT questions whether the "equatorial radius" refers to the semi-major axis, apocenter, or pericenter in the context of the orbital plane.
  • Buzz suggests that the equatorial radius may refer to the maximum radius of an ellipsoidal central mass, noting that it could differ from a radially symmetric model.
  • MT agrees with Buzz's point about the central mass being ellipsoidal and proposes that the equatorial radius could be defined as either the semi-major axis or a combination of the semi-major axis and the distance from the foci.
  • Buzz clarifies that for an ellipsoid, all points on the equator are equally distant from the center, implying that the equatorial radius is simply the distance from the center.

Areas of Agreement / Disagreement

Participants express some agreement on the definition of the equatorial radius as the distance from the center of the ellipsoid, but there remains uncertainty regarding the specific context and implications of this definition in relation to the orbital plane.

Contextual Notes

The discussion includes assumptions about the nature of the central mass and its symmetry, as well as the definitions of terms like "equatorial radius" and "North/South" in the orbital context, which may not be universally agreed upon.

M.T
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I wish to solve the inverse geodesic problem numerically using http://geographiclib.sourceforge.net/html/classGeographicLib_1_1Geodesic.html#a455300c36e6caa70968115416e1573a4, and to finish off I need to specify the "equatorial radius". I am not too familiar with this, and do not see immediately what I would define as "North" or "South" in the orbital plane.

Does the "equatorial radius" here refer to the semi-major axis, or perhaps the apocenter or pericenter?
 
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Hi MT:

I noticed that no one has responded to your question for about a day, so I thought I would try to give a useful reply based on my my limited knowledge.

I do not understand the tool you linked to, so this is just a guess. Perhaps the tool takes into account the possibility that the central mass effecting geodesic calculations is not radially symmetric. In that case the equatorial radius may refer to the maximum radius of an ellipsoidal central mass, like the Earth's equatorial radius is larger than its polar radius.

Hope this helps.

Regards,
Buzz
 
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Buzz Bloom said:
Hi MT:

I noticed that no one has responded to your question for about a day, so I thought I would try to give a useful reply based on my my limited knowledge.

I do not understand the tool you linked to, so this is just a guess. Perhaps the tool takes into account the possibility that the central mass effecting geodesic calculations is not radially symmetric. In that case the equatorial radius may refer to the maximum radius of an ellipsoidal central mass, like the Earth's equatorial radius is larger than its polar radius.

Hope this helps.

Regards,
Buzz

Hi Buzz Bloom

Thanks for the reply.

The central mass is assumed ellipsoidal, so I agree with you in that it does not have to be radially symmetric. I guess it also makes sense to define the equator along the largest "diameter", that is ##2a ## with ## a ## being the semi-major axis, but is the radius then (1) ## a ## (distance from centre of ellipsoid) or is it (2) ## c+a ## with ## c ## being the distance from the foci where eg. the Earth is; ## c-a ## being the shortest distance between the Earth and the ellipsoid orbit, and ## c+a ## the longest distance.

would I be right then in assuming you mean the distance from the centre (1)?

Thanks,
MT
 
M.T said:
would I be right then in assuming you mean the distance from the centre (1)?
Hi MT:

Yes, except that no mean is necessary, since for an ellipsoid all points on the equator are equally distant from the center.

Regards,
Buzz
 

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