Venus Phases (Galileo)

Galileo's telescopic discovery that Venus shows a **full set of phases**—similar to the Moon but with sizes that change with geometry—was strong evidence for **Copernicus**. In a heliocentric layout, Venus is an **inner** planet: near **superior conjunction** it appears almost **full** but **small**; near **inferior conjunction** it is a **large crescent** (or new, depending on alignment). A simple **geocentric** epicycle can mimic some phases but struggles with the **combined** pattern of **phase** and **angular size** that Galileo sketched. This simulator uses a **coplanar** Sun-centered cartoon with adjustable positions; the inset disk is the **Earth-facing** illumination from the **phase angle** at Venus.

Who it's for: History of astronomy and introductory solar-system geometry after Moon phases.

Key terms

  • Venus phases
  • Galileo
  • Heliocentrism
  • Inferior planet
  • Phase angle
  • Elongation
  • Copernican model

How it works

**Galileo** saw **Venus** swing from a **full** disk (superior conjunction, far side) to a **thin crescent** near **inferior conjunction** when Venus passes between Earth and the Sun. In a **geocentric** picture such a full phase at “greatest elongation” is hard to arrange; in **heliocentrism** inner planet phases follow naturally from geometry. This page uses a **coplanar** top view (Sun at center) and draws the **terminator** from the **phase angle** at Venus; the inset is the **Earth-facing** disk. Radii are **not** to true scale.

Key equations

Lit fraction ≈ (1 + cos φ)/2 · φ = angle between V→E and V→S at Venus

Frequently asked questions

Why does a "full" Venus look small through a telescope?
Full phase occurs near superior conjunction on the far side of the Sun from Earth, so Venus is nearly at its greatest distance—small angular diameter.
Is this a planetarium-quality ephemeris?
No. Inclinations, synodic details, and finite Sun size are omitted; the goal is phase-angle geometry.