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AlexP
AlexP
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TL;DR

While a 5:1 resonance between the rotation of the Moon and its orbital period is possible (albeit quite unlikely), it won't help.

Long explanation

A lunar month, or a lunation, is the time between two consecutive new Moons, that is, the time it takes the Moon to come back into the same position with respect to the Sun as seen from Earth. This time is not equal with the time it takes the Moon to complete one revolution around the Earth.

  • The time it takes the Moon to complete one revolution around the Earth is called the sidereal month, because after one revolution around the Earth the Moon comes into the same position with respect to the fixed stars. (The Latin word for "stars" is sidera. One star is sidus.)

    A sidereal month is 27.321661 average Earth solar days, or 27 d 7 h 43 min 11.6 s.

  • The time between two consecutive new Moons, that is, the time it takes the Moon to come back into the same position with respect to the Sun, is of course longer than a sidereal month; that's because after the Moon has completed a full revolution around the Earth, the Earth itself has advanced about 26° 56′ on its orbit around the Sun, so that the Moon still has some catching up to do in order to get back into position.

    This period is called the synodic month; on the average, a synodic month is 29 Earth solar days, 12 hours, 44 minutes and 2.9 seconds.

    The word synodic is Greek for "same path", syn- + -hodos "road, path". From the same Greek word meaning "road", the English language has "odometer", a device for measuring the distance travelled.

  • From simple geometrical considerations, the relationship between Earth sidereal years $T_\text{Earth}$, sidereal months $T_\text{Moon}$, and synodic months $S_\text{Moon}$ is as follows:

    $$S_\text{Moon} = T_\text{Moon} \times \frac{T_\text{Earth}}{T_\text{Earth} - T_\text{Moon}}$$

    Note that what counts is Earth sidereal year, not the practically important tropical year.

Moreover, the duration of a synodic month is not constant, because of course Earth's orbit is not perfectly circular, but a little flattened into an ellipse, so that the angular speed of Earth as it moves on its path around the sun is variable. Practically, the duration of a synodic month varies from about 29 days 6 hours to about 29 days 20 hours in the course of a year.

The point of all this arithmetic is to show that a 5:1 rotation-to-orbital period resonance, while not absolutely impossible, won't help. What would be needed would be a to have the rotation of the Moon equal an integer fraction of the synodic month, and that is extremely unlikely, because the two durations do not have any particular relationship.

TL;DR

While a 5:1 resonance between the rotation of the Moon and its orbital period is possible (albeit quite unlikely), it won't help.

Long explanation

A lunar month, or a lunation, is the time between two consecutive new Moons, that is, the time it takes the Moon to come back into the same position with respect to the Sun as seen from Earth. This time is not equal with the time it takes the Moon to complete one revolution around the Earth.

  • The time it takes the Moon to complete one revolution around the Earth is called the sidereal month, because after one revolution around the Earth the Moon comes into the same position with respect to the fixed stars. (The Latin word for "stars" is sidera. One star is sidus.)

    A sidereal month is 27.321661 average Earth solar days, or 27 d 7 h 43 min 11.6 s.

  • The time between two consecutive new Moons, that is, the time it takes the Moon to come back into the same position with respect to the Sun, is of course longer than a sidereal month; that's because after the Moon has completed a full revolution around the Earth, the Earth itself has advanced about 26° 56′ on its orbit around the Sun, so that the Moon still has some catching up to in order to get back into position.

    This period is called the synodic month; on the average, a synodic month is 29 Earth solar days, 12 hours, 44 minutes and 2.9 seconds.

    The word synodic is Greek for "same path", syn- + -hodos "road, path". From the same Greek word meaning "road", the English language has "odometer", a device for measuring the distance travelled.

  • From simple geometrical considerations, the relationship between Earth sidereal years $T_\text{Earth}$, sidereal months $T_\text{Moon}$, and synodic months $S_\text{Moon}$ is as follows:

    $$S_\text{Moon} = T_\text{Moon} \times \frac{T_\text{Earth}}{T_\text{Earth} - T_\text{Moon}}$$

    Note that what counts is Earth sidereal year, not the practically important tropical year.

Moreover, the duration of a synodic month is not constant, because of course Earth's orbit is not perfectly circular, but a little flattened into an ellipse, so that the angular speed of Earth as it moves on its path around the sun is variable. Practically, the duration of a synodic month varies from about 29 days 6 hours to about 29 days 20 hours in the course of a year.

The point of all this arithmetic is to show that a 5:1 rotation-to-orbital period resonance, while not absolutely impossible, won't help. What would be needed would be a to have the rotation of the Moon equal an integer fraction of the synodic month, and that is extremely unlikely, because the two durations do not have any particular relationship.

TL;DR

While a 5:1 resonance between the rotation of the Moon and its orbital period is possible (albeit quite unlikely), it won't help.

Long explanation

A lunar month, or a lunation, is the time between two consecutive new Moons, that is, the time it takes the Moon to come back into the same position with respect to the Sun as seen from Earth. This time is not equal with the time it takes the Moon to complete one revolution around the Earth.

  • The time it takes the Moon to complete one revolution around the Earth is called the sidereal month, because after one revolution around the Earth the Moon comes into the same position with respect to the fixed stars. (The Latin word for "stars" is sidera. One star is sidus.)

    A sidereal month is 27.321661 average Earth solar days, or 27 d 7 h 43 min 11.6 s.

  • The time between two consecutive new Moons, that is, the time it takes the Moon to come back into the same position with respect to the Sun, is of course longer than a sidereal month; that's because after the Moon has completed a full revolution around the Earth, the Earth itself has advanced about 26° 56′ on its orbit around the Sun, so that the Moon still has some catching up to do in order to get back into position.

    This period is called the synodic month; on the average, a synodic month is 29 Earth solar days, 12 hours, 44 minutes and 2.9 seconds.

    The word synodic is Greek for "same path", syn- + -hodos "road, path". From the same Greek word meaning "road", the English language has "odometer", a device for measuring the distance travelled.

  • From simple geometrical considerations, the relationship between Earth sidereal years $T_\text{Earth}$, sidereal months $T_\text{Moon}$, and synodic months $S_\text{Moon}$ is as follows:

    $$S_\text{Moon} = T_\text{Moon} \times \frac{T_\text{Earth}}{T_\text{Earth} - T_\text{Moon}}$$

    Note that what counts is Earth sidereal year, not the practically important tropical year.

Moreover, the duration of a synodic month is not constant, because of course Earth's orbit is not perfectly circular, but a little flattened into an ellipse, so that the angular speed of Earth as it moves on its path around the sun is variable. Practically, the duration of a synodic month varies from about 29 days 6 hours to about 29 days 20 hours in the course of a year.

The point of all this arithmetic is to show that a 5:1 rotation-to-orbital period resonance, while not absolutely impossible, won't help. What would be needed would be a to have the rotation of the Moon equal an integer fraction of the synodic month, and that is extremely unlikely, because the two durations do not have any particular relationship.

Source Link
AlexP
AlexP
  • 92.2k
  • 16
  • 198
  • 343

TL;DR

While a 5:1 resonance between the rotation of the Moon and its orbital period is possible (albeit quite unlikely), it won't help.

Long explanation

A lunar month, or a lunation, is the time between two consecutive new Moons, that is, the time it takes the Moon to come back into the same position with respect to the Sun as seen from Earth. This time is not equal with the time it takes the Moon to complete one revolution around the Earth.

  • The time it takes the Moon to complete one revolution around the Earth is called the sidereal month, because after one revolution around the Earth the Moon comes into the same position with respect to the fixed stars. (The Latin word for "stars" is sidera. One star is sidus.)

    A sidereal month is 27.321661 average Earth solar days, or 27 d 7 h 43 min 11.6 s.

  • The time between two consecutive new Moons, that is, the time it takes the Moon to come back into the same position with respect to the Sun, is of course longer than a sidereal month; that's because after the Moon has completed a full revolution around the Earth, the Earth itself has advanced about 26° 56′ on its orbit around the Sun, so that the Moon still has some catching up to in order to get back into position.

    This period is called the synodic month; on the average, a synodic month is 29 Earth solar days, 12 hours, 44 minutes and 2.9 seconds.

    The word synodic is Greek for "same path", syn- + -hodos "road, path". From the same Greek word meaning "road", the English language has "odometer", a device for measuring the distance travelled.

  • From simple geometrical considerations, the relationship between Earth sidereal years $T_\text{Earth}$, sidereal months $T_\text{Moon}$, and synodic months $S_\text{Moon}$ is as follows:

    $$S_\text{Moon} = T_\text{Moon} \times \frac{T_\text{Earth}}{T_\text{Earth} - T_\text{Moon}}$$

    Note that what counts is Earth sidereal year, not the practically important tropical year.

Moreover, the duration of a synodic month is not constant, because of course Earth's orbit is not perfectly circular, but a little flattened into an ellipse, so that the angular speed of Earth as it moves on its path around the sun is variable. Practically, the duration of a synodic month varies from about 29 days 6 hours to about 29 days 20 hours in the course of a year.

The point of all this arithmetic is to show that a 5:1 rotation-to-orbital period resonance, while not absolutely impossible, won't help. What would be needed would be a to have the rotation of the Moon equal an integer fraction of the synodic month, and that is extremely unlikely, because the two durations do not have any particular relationship.