The Ptolemaic system, which places the Earth at the center of the universe, cannot predict the phases of Venus. This is because it assumes Venus orbits the Earth directly, and therefore its illuminated side would always face us, resulting in only a single "phase" - a full, bright Venus.

Here's why:

* Earth-Centered View: The Ptolemaic model places Earth at the center, with the Sun, Moon, and planets revolving around it.

* Direct Orbit: Venus is assumed to be orbiting the Earth directly in a smaller circle than the Sun's orbit. This leads to Venus being illuminated from the Sun's side, always appearing as a bright, full object.

However, we know Venus exhibits phases, similar to the Moon:

* Galileo's Observations: Galileo's telescope observations in the 17th century revealed Venus's phases, demonstrating it orbits the Sun, not the Earth.

* Heliocentric Model: The heliocentric model, with the Sun at the center, explains Venus's phases. As Venus orbits the Sun, the illuminated side facing us changes, leading to the observed phases.

Therefore, the Ptolemaic system is unable to predict the phases of Venus, as it is a fundamental flaw of the model.