Sidereal vs. solar days: in one tropical year, is the number of sidereal days less than, equal to, or greater than the number of mean solar days?

Introduction / Context:
A sidereal day measures Earth’s rotation relative to distant stars; a mean solar day measures rotation relative to the Sun. Because Earth orbits the Sun while rotating, there is a subtle difference in counts over the course of a year.

Given Data / Assumptions:

• Length of the tropical year ≈ 365.2422 mean solar days.
• Length of one sidereal day ≈ 23 h 56 m 4 s (≈ 0.99727 mean solar days).

Concept / Approach:
Each day, Earth turns a bit more than 360° relative to the stars to bring the Sun back to the local meridian. Over one complete revolution around the Sun, this amounts to roughly one additional full rotation relative to the stars.

Step-by-Step Solution:
Number of sidereal days per year ≈ (length of year in solar days) / (length of one sidereal day in solar-day units).≈ 365.2422 / 0.99727 ≈ 366.24.Thus the count exceeds the number of solar days by ~1.

Verification / Alternative check:
Geometric reasoning: one extra star-relative rotation is needed each year to compensate for Earth’s orbital progression.

Why Other Options Are Wrong:
“Equal” and “one less” contradict the orbital geometry; “two more” is far too large.

Common Pitfalls:
Confusing “length of a sidereal day” with “number of sidereal days per year.”

Final Answer:
One more than mean solar days