No, the relationship that Kepler discovered was between the length of the long axis of the ellipse, and the period of the planet.

It is possible for a comet with a very long skinny orbit, and an asteroid with a nearly circular orbit to have the same minor axis length, but obviously, the comet will have a much longer orbital period. For example, Halley's comet has a semiminor axis of about 3.5AU. An asteroid in a circular orbit with the same semi-minor axis would have a period of about 6 years, compared to Halley's period of 76 years.

I don't fully understand why you ask about various types of mean, but I can't think of anything related.

No, the relationship that Kepler discovered was between the length of the long axis of the ellipse, and the period of the planet.

It is possible for a comet with a very long skinny orbit, and an asteroid with a nearly circular orbit to have the same minor axis length, but obviously, the comet will have a much longer orbital period. For example, Halley's comet has a semiminor axis of about 3.5AU. An asteroid in a circular orbit with the same semi-minor axis would have a period of about 6 years, compared to Halley's period of 76 years.

If you know the semi-minor axis, and the perihelion distance (for example), then it would be possible to work out the semi-major axis, and the relative orbital period, but you would need more information than just the semi-minor axis.

No, the relationship that Kepler discovered was between the length of the long axis of the ellipse, and the period of the planet.

It is possible for a comet with a very long skinny orbit, and an asteroid with a nearly circular orbit to have the same minor axis length, but obviously, the comet will have a much longer orbital period. For example, Halley's comet has a semiminor axis of about 3.5AU. An asteroid in a circular orbit with the same semi-minor axis would have a period of about 6 years, compared to Halley's period of 76 years.

I don't fully understand why you ask about various types mean, but I can't think of anything related.

No, the relationship that Kepler discovered was between the length of the long axis of the ellipse, and the period of the planet.

It is possible for a comet with a very long skinny orbit, and an asteroid with a nearly circular orbit to have the same minor axis length, but obviously, the comet will have a much longer orbital period. For example, Halley's comet has a semiminor axis of about 3.5AU. An asteroid in a circular orbit with the same semi-minor axis would have a period of about 6 years, compared to Halley's period of 76 years.

I don't fully understand why you ask about various types of mean, but I can't think of anything related.