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Chapter 1: Problem 11

The time it takes the Moon to return to a given position as seen against the background of fixed stars, \(27.3\) days, is called a sidereal month. The time interval between identical phases of the Moon is called a lunar month. The lunar month is longer than a sidereal month. Why and by how much?

Short Answer

Expert verified
The lunar month is longer than the sidereal month by about 2.23 days because the Moon needs to travel more than 360 degrees to show the same phase due to the Earth's movement around the Sun.

Step by step solution

01

Understanding Sidereal Month

A sidereal month is the time it takes for the Moon to return to the same position against the fixed stars. This is basically the Moon's orbit around Earth, which is about 360 degrees and takes 27.3 days.
02

Understanding Lunar Month

A lunar month, however, is the time it takes for the Moon to return to the same phase, like from full moon to full moon. During one sidereal month, the Earth has moved along its orbit around the Sun, and the Moon needs to travel more than 360 degrees to catch up and return to the same phase.
03

Comparing the Two

This extra distance that the Moon needs to travel takes about 2.2 extra days, which makes the lunar month longer than the sidereal month. To calculate this precisely, subtract the duration of the sidereal month (27.3 days) from the average length of the lunar month (29.53 days).
04

Calculation

The exact duration can be computed as follows: \(29.53 - 27.3 = 2.23\) days. Therefore, the lunar month is longer than a sidereal month by about 2.23 days.

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