Lunar Ephemeris

What can be learnt from Lunar Ephermeris?

Ephemeris tables contain predictions regarding the position of astronomical objects for specific times in the future. Therefore, ephemeris tables reflect a level of scientific sophistication and confidence because, with the passage of time, the published predictions can be verified or falsified.

The earliest know ephemeris tables are associated with the second millennium BCE Vedic period of Indian astronomy. However, in the modern era the accumulated knowledge from four millenniums has been incorporated into computer software so that the calculation of ephemeris can be automated.

Ephemerides [plural of ephemeris] only contain predictions. They do not include any formulae or calculations. They do not include any underlying theory. They just contain the results of applied scientific knowledge.

From my perspective there is a lot of embedded applied science in ephemeris that can be analysed so that we can better understand and evaluate theoretical science.

Therefore, the following analysis of Lunar Ephemeris aims to provide a reference point upon which further research and studies can be based. The analysis may not contain any startling revelations [or it may – read on] but, hopefully it will provide some new perspectives which just go to prove:
to travel hopefully is a better thing than to arrive [R. L. Stevenson].

The analysis is based upon data from two sources:
NASA: Phases of the Moon: 2001 to 2025
Fourmilab Switzerland: Lunar Perigee and Apogee Calculator

Lunar Phases

Image credit: Wikipedia

Wikipedia provides a good introduction to Lunar Phases:

The Moon exhibits different phases as the relative position of the Sun, Earth and Moon changes, appearing as a full moon when the Sun and Moon are on opposite sides of the Earth and as a new moon (dark moon) when they are on the same side. The phases of full moon and new moon are examples of syzygies, which occur when the Earth, Moon, and Sun lie (approximately) in a straight line.

The time between two full moons (a Lunar month) is about 29.53 days on average (hence, the concept of the time frame of an approximated month was derived). This synodic month is longer than the time it takes the Moon to make one orbit around the Earth with respect to the fixed stars (the sidereal month), which is about 27.32 days. This difference is caused by the fact that the Earth-Moon system is orbiting around the Sun at the same time the Moon is orbiting around the Earth.

The average 29.53 day Lunar [Full Moon] month is confirmed by the ephemeris and this same average applies equally to the periods between New Moon, First Quarter and Last Quarter. However, the average does mask the variability of the lunar orbit where the time between New Moons ranges from 28.84 to 30.26 days.

Wikipedia makes some attempt to explain the variability:

The actual time between two syzygies or two phases is quite variable because the orbit of the Moon is elliptic and subject to various periodic perturbations, which change the velocity of the Moon. When the moon is closer to the earth, it moves faster; when it is farther, it moves slower. The orbit of the Earth around the Sun is also elliptic, so the speed of the Earth also varies, which also affects the phases of the Moon.

Plotting the number of days between New Moon, First Quarter, Full Moon and Last Quarter [for the years 2000 through 2025] provides an initial impression of chaos.

However, looking at each station individually does provide some insight into the natural rhythms that converge to make the lunar orbit.

Lunar Phas Days - New Moon

Lunar Phase Days - First Quarter

Lunar Ohase Days - Full Noon

Lunar Phase Days - Last Quarter

Lunar Apogee and Perigee

The distance between and the Earth and the Moon is continually changing but it usually quoted as an average distance [centre to centre] of 384,400 kilometres.

Wikipedia provides the following explanation:

In astronomy, a lunar distance (LD) is a measurement of the distance from the Earth to the Moon. The average distance from Earth to the Moon is 384,400 kilometers (238,855 miles). The actual distance varies over the course of the orbit of the moon, from 356,700 kilometres (221,600 mi) at the perigee and 406,300 kilometres (252,500 mi) at apogee.

High-precision measurements of the lunar distance are made by measuring the time taken for light to travel between LIDAR stations on Earth and retroreflectors placed on the Moon.

The Moon is spiraling away from Earth at an average rate of 3.8 cm per year, as detected by the Lunar Laser Ranging Experiment. The recession rate is considered anomalously high. By coincidence, the diameter of corner cubes in retroreflectors on the Moon is also 3.8 cm.

The first person to measure the distance to the Moon was the 2nd-century-BC astronomer and geographer Hipparchus, who used simple trigonometry. He was approximately 26,000 km off the actual distance, an error of about 6.8%.

The ephemeris provides confirmation of the 384,400 kilometres average distance but further detail highlights the 50,193 kilometres range between maximum apogee and minimum perigee. Unsurprisingly, the average period between apogees [27.56 days] and perigees [27.55 days] is close to the lunar sidereal rotation period of 27.32 days.

Lunar Apogee and Perigee distances

Interestingly, lunar apogee is remarkably stable and displays a sine wave pattern. Conversely, lunar perigee is remarkably volatile.
Both observations warrant further research.

Lunar Apogee and Perigee distance boundaries

Lunar Apogee and Perigee periods in days

Lunar Phase Boundaries

An additional perspective can be gained from a subset of the data by combining Phase and Distance data. This is an indicative [not precise] approach [based upon tagging apogee or perigee data when a Lunar Phase occurs within +/- 12 hours].

This perspective demonstrates that when the two cycles [Phase and Distance] are in-sync then the associated lunar distances [from Earth] are remarkably stable.

Lunar Phase Boundaries in kilometres

However, there is one very curious observation regarding these fairly stable apogee and perigee boundaries [that are associated with the Lunar Phases].

The outer apogee boundary forms an ellipse [red line] with its major-axis directed towards the sun i.e. the major-axis runs New Moon to Full Moon.

Conversely, the inner perigee boundary forms an ellipse [blue line] with its major-axis not directed towards the Sun i.e. the major-axis runs First Quarter to Last Quarter.

From my perspective the major-axes of both boundary ellipses should have an identical alignment if they are determined by the same set of forces i.e. gravity and orbital velocity [as in the standard theory].

Therefore, the difference in major-axis alignment indicates that the forces controlling the apogee ellipse are not exactly the same as the forces governing the perigee ellipse.

Arguably, electro-magnetic attraction causes both the New Moon Perigee boundary and the Full Moon Perigee boundary to be about 13,000 kilometres closer to Earth [when compared to the First Quarter and Last Quarter perigees] and this provides a scientific observation supporting the anecdotal view that earthquakes are more frequent [and dangerous] during the New Moon and Full Moon periods.

Lunar Phase Boundary Rings in kilometres

Tim Cullen
September 2012

Gallery | This entry was posted in Moon. Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s