Lunar Motions – Definition of the sidereal month Which statement best defines a sidereal month in terms of the Moon’s orbital motion relative to the fixed stars?

Introduction / Context:
The Moon’s motion can be described with different month definitions depending on the reference frame. Two key ones are the sidereal month (relative to the stars) and the synodic month (relative to the Sun, governing phases). Distinguishing these is fundamental in astronomy and calendar studies.

Given Data / Assumptions:

• The question focuses on the sidereal reference frame—fixed stars.
• We ignore rotation period and phase cycle unless directly relevant.
• We assume an idealized celestial sphere background.

Concept / Approach:
A sidereal month is the time the Moon takes to complete one 360-degree orbit around Earth relative to the fixed stars and thus return to the same apparent position against that starry background. This is about 27.3 days. By contrast, the synodic month (new Moon to new Moon) is about 29.5 days because Earth advances in its orbit around the Sun during that interval.

Step-by-Step Solution:
Identify the key phrase: “returns to the same position in the sky” relative to stars.Match with the sidereal definition (not the synodic, which references the Sun and phases).Select the option stating completion of an orbit and return to same sky position.

Verification / Alternative check:
Star charts confirm that after approximately 27.3 days the Moon appears near the same background stars, even though phases differ because the Sun–Earth–Moon geometry has changed.

Why Other Options Are Wrong:

• the period in which the moon completes an orbit around the earth: ambiguous unless specified relative to stars; (b) states this precisely.
• the period of rotation of moon: the Moon is tidally locked; not what “sidereal month” refers to.
• None of the above: incorrect because (b) is exact.

Common Pitfalls:
Confusing sidereal with synodic month; the latter governs phases and is longer because Earth moves around the Sun during one lunar orbit.

Final Answer:
the period in which the moon completes an orbit around the earth and returns to the same positions in the sky