The planet's orbit (below) is S-type, coplanar and retrograde.
A planet of negligible mass orbits a binary star
system in which the 2 stars have circular orbits and equal mass.
The planet's orbit is quasi-circular around the parent star.
The planet's free eccentricity is approx 0.
The planet's period is approx 1 binary period.
The distance of the planet from its parent star is
maximum approx 0.76 binary semimajoraxis,
minimum approx 0.57 binary semimajoraxis.
The orbit is described and animated
here
(it's the 4th orbit on that page, shaped like an ice-cream scoop).
The planet's semi-major axis is approx 0.65 binary semimajoraxis, whereas figures stated in the scientific journals for the largest possible stable S-type semimajor axis are generally approx 0.25 binary semimajoraxis.
The screenshot below shows the orbit run for approx 295 binary periods
(blue=planet, red=star, yellow=star).
The screenshot below shows the orbit run for approx 3767 binary periods
(blue=planet, red=star, yellow=star).
The planet's orbit (below) is P-type, coplanar and retrograde.
A planet of negligible mass orbits a binary star
system in which the 2 stars have circular orbits and equal mass.
The planet's orbit is quasi-circular around the system barycentre.
The planet's free eccentricity is approx 0.
The planet's period is approx 0.33 binary period.
The distance of the planet from the system barycentre is
maximum approx 0.65 binary semimajoraxis,
minimum approx 0.46 binary semimajoraxis.
The orbit is described
here
(it's the 5th orbit on that page, shaped like a rounded 8-pointed star).
The planet's semi-major axis is approx 0.55 binary semimajoraxis, whereas figures stated in the scientific journals for the smallest possible stable P-type semimajor axis are generally approx 2 binary semimajoraxis.
The screenshot below shows the orbit run for approx 195 binary periods
(blue=planet, red=star, yellow=star).
These are not special cases. There are a vast number of stable orbits well outside the stable regions stated in the scientific journals.
For binary stars of equal mass and with circular orbits,
the critical semi-major axis for stable planetary orbits is...
For S-type orbits: greater than 0.65 (whereas other researchers state approx 0.25).
For P-type orbits: less than 0.55 (whereas other researchers state approx 2.0).
(unit = binary semi-major axis).
The stable regions for both S-type and P-type planetary orbits are larger than stated by other researchers.
For binary stars of unequal mass and/or eccentric orbits the stable regions for planetary orbits are also larger than stated by other researchers.
The biggest reason for under-estimation of the stable zones in the scientific journals
is that researchers have in general concentrated on prograde orbits,
and have in fact found the correct critical semi-major axis results for prograde orbits.
Some researchers have also considered retrograde orbits and in at least one study stated that retrograde orbits
are slightly more stable than prograde.
The stable zones for S-type and P-type orbits are much larger than found by other studies.
All of the many stable orbits in the proposed large extensions of the stable zones are retrograde
(i.e. with relative orbital inclination in the range 180 degrees to 90 degrees).
