Not every meaningful point in a chart is a planet — some of the most talked-about placements are mathematical points or minor bodies with no physical mass at the position at all.
The Vertex is a mathematically derived point — not a planet or a visible body — marking a second, less prominent intersection of the ecliptic with the horizon system, sometimes called a "secondary Descendant." In modern astrology it has picked up a strong association with fated encounters, particularly significant relationships that feel less like a choice and more like something that was always going to happen.
The Part of Fortune (or Lot of Fortune) is the oldest and most important of the Hellenistic "Arabic Parts" or "Lots" — a calculated point derived from the positions of the Sun, Moon, and Ascendant, rather than an observed body. It is traditionally read as marking the area of life where a person experiences the most natural ease, embodied wellbeing, and good fortune, and its calculation differs between day charts and night charts, a sect-based distinction that is characteristic of Hellenistic technique generally.
Chiron is a small minor planet (technically a centaur, orbiting between Saturn and Uranus) discovered in 1977, whose mythological namesake — a centaur who was an immortal healer yet suffered from an incurable wound — gave rise to its astrological reputation as the 'Wounded Healer' placement: the sign and house where a person's deepest, most persistent pain is also, paradoxically, the source of their greatest capacity to help others with the same wound.
The North Node and South Node are not physical bodies but the two points where the Moon's orbital path crosses the ecliptic — mathematically opposite each other by definition. In most modern interpretive traditions the South Node represents inherited patterns, past-life comfort zones, or default tendencies, while the North Node represents the direction of growth a person is meant to be moving toward across their lifetime, making the Node axis one of the most consulted points for questions of life purpose.
Black Moon Lilith is another mathematical point rather than a body — the location of the empty focus of the Moon's elliptical orbit around Earth (distinct from any actual asteroid also named Lilith). Named for the folkloric first-wife figure of Jewish mythology who refused subordination, it is astrologically associated with untamed instinct, repressed rage, and whatever a person has been culturally pressured to suppress about their own raw desire or autonomy — one of the more psychologically loaded points in the modern astrological toolkit.