- The elliptical orbits
of this
gavitational two-body system
are determined by
Newtonian physics
(what is universal about the
physical system)
and initial conditions
(what is peculiar or individual about the
physical system).
- Gravity is, of course, the
force that pulls the
astro-bodies in
orbits.
- Now in astro jargon,
an apsis (plural apsides)
is an extreme point in the orbit
of an astronomical objects.
The two kinds of apsides: periapsis and apoapsis.

- The periapsis
(AKA pericenter)
is the arrangement of closest separation and the term is
also sometimes used for the closest separation distance.
- The
apoapsis
(AKA apocenter)
is the arrangement of farthest separation and the term is
also sometimes used for the farthest separation distance.
A physical fact for orbits is that astro-bodies move slowest at apoapsis and fastest at periapsis.

- The apse line (AKA line of apsides
is drawn through the periapsis
and apoapsis.
- By normal convention, the relative
mean orbital radius
(AKA relative semi-major axis) is
defined to be
r_mean = (1/2)( r_periapsis + r_apoapsis ),

where r_periapsis is the periapsis separation and r_apoapsis is the apoapsis separation.

- The relative orbit is also
an elliptical orbit
with semi-major axis r, in fact.
The periapsis
and apoapsis distances are given by,
respectively,
r_periapsis = r_mean*(1 - e) and r_apoapsis = r_mean*(1 + e) ,

where e is the eccentricity of the relative elliptical orbit.

The actual elliptical orbits relative to the barycenter are scaled down versions of the relative elliptical orbit. The scale radii for any epoch are

r_1 = r*(m_2/m) and r_2 = r*(m_1/m) ,

where 1 is the index for astro-body 1, 2 is the index for astro-body 2, r is the relative separation distance, and m = m_1+m_2 is the total mass. As you can see, if m_1 >> m_2, we have r_1 ≅ 0$ and r_2 ≅ r. This just shows that if m_1 >> m_2, we effectively have astro-body 2 orbiting astro-body 1 which is effectively at rest at the barycenter.

- In most real
orbits,
perturbations
cause noticeable deviations from exact
gavitational two-body system
behavior.
- There is special-case names for the apsides
of familiar
astronomical objects
(see Wikipedia: Apsis: Terminology).
But yours truly thinks mostly these are overly fancy, except for
the most familiar
astronomical objects: e.g.,
- Earth: perigee and apogee, where suffix gee is derived from Greek Earth goddess Gaia.
- Sun: perihelion and aphelion, where suffix helion is derive from Greek Sun god Helios.
- star: periastron and apastron, where suffix astron is ancient Greek language word for star.

Other than the example cases, if one wants a fancy name, yours truly suggests just prefix the name by peri- or ap-: e.g., peri-Jupiter and and ap-Jupiter.

Caption: A cartoon of a gravitationally-bound 2-body system with the spherically-symmetric bodies orbiting in elliptical orbits the system center of mass (i.e., barycenter in the context of celestial mechanics) marked by a red cross. The barycenter is a focus for both elliptical orbits and is at rest or in relative to an inertial frame. The other focuses for the elliptical orbits are just empty points in space.

Features:

Image link: Wikimedia Commons: File:Periapsis apoapsis.png.

Local file: local link: orbit_.html.

File: Orbit file: orbit_apsis.html.