Equation of time – number of zero crossings in one year The equation of time is the difference between apparent solar time and mean solar time. Over a complete year, how many times does this difference become exactly zero?

Introduction / Context:
The equation of time explains why sundial time differs from clock time. It arises from Earth's orbital eccentricity and the obliquity (tilt) of the ecliptic. Knowing its zero crossings helps interpret sundial readings and time-based astronomical observations.

Given Data / Assumptions:

• Apparent solar time follows the Sun's actual apparent motion.
• Mean solar time is uniform, defined by a fictitious mean Sun.
• One full tropical year is considered.

Concept / Approach:
The equation of time E(t) oscillates around zero because the effects of eccentricity and obliquity add and subtract through the year. The combined periodic components produce four dates when E(t) = 0, meaning a sundial and an idealized mean-time clock momentarily agree.

Step-by-Step Solution:
Recognize E(t) as a sum of annual and semi-annual terms tied to orbital geometry.Over one cycle, the function crosses zero at four distinct epochs.Therefore, the number of zero crossings per year is four.

Verification / Alternative check:
Almanacs list approximate dates (around mid-April, mid-June, early September, late December) where E(t) ≈ 0, confirming four events annually.

Why Other Options Are Wrong:
One, two, three, or five crossings do not match the well-documented annual behavior of E(t).

Common Pitfalls:
Confusing the dates of maxima/minima of E(t) with zero crossings; maxima/minima are when the discrepancy is greatest, not zero.

Final Answer:
Four times