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Home/Astronomy & The Sky/Venus Phases (Galileo)

Venus Phases (Galileo)

Heliocentric geometry: full disk vs crescent at inferior conjunction; Earth-view inset.

Orbit sketch (scaled)

2.1 rad
0 rad
0.42

Measured values

Illuminated fraction86.6 %
Elongation (180°−φ)137.0 °

About this model

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.