Final answer:
Electron orbits are quantized, meaning they exist at specific, discrete energy levels, while planetary orbits are continuous. The correspondence principle suggests that quantization effects become less noticeable and converge towards classical physics in large systems, like planetary orbits.
Step-by-step explanation:
The allowed orbits for electrons in atoms and planetary orbits around the sun are fundamentally different due to the nature of the physical laws that govern them. The electron orbits in atoms are quantized, which means electrons can only exist in specific, discrete energy levels and cannot reside in between these levels. This is part of what Bohr's model of the atom describes, explaining why we see discrete atomic spectra. In contrast, planetary orbits are considered to be continuous, allowing planets to revolve around the sun at virtually any distance and speed, given the right initial conditions.
The correspondence principle comes into play as quantum mechanics transitions into classical physics for systems with large quantum numbers. For example, the quantized orbits of an electron in an atom become less noticeable and more akin to classical orbits when dealing with larger macroscopic systems like planets, where we do not see quantization effects because of the massive scale involved compared to atomic particles.
Justifying this explanation, the quantization of electron orbits is observable in the discrete lines of atomic spectra, as energy emitted follows specific values corresponding to electron transitions between allowed orbits. Conversely, no such discrete spectra exist for planetary motion, which operates under Newton's laws of gravitation that predict continuous orbital paths.