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This topic may apply to Earth more than to other planets, but let's start with Earth.
Like so many things in this Universe, I've taken the behavior of the Earth-Moon system for granted.
Recently, I became interested in the times when the Moon rises, so I asked Google's Gemini to explain what seemed like short times. The answer would appear to involve the elliptical nature of the Moon's orbit, but the average time must become 48.8 minutes change over the course of some extended period of time.
In any case, Post #3 will contain an explanation by Gemini.
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This post is reserved for an index to posts that may be contributed by NewMars members.
I'm not expecting a lot of activity in this topic, but members are welcome to add posts with links, images or text that helps our readers to understand this natural phenomenon.
Index:
Post #3: Conversation with Gemini about Moonrise
Post #4: GW Johnson on variations of Moonrise, including topographical features
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This post contains a transcript of a conversation with Google's Gemini about Moonrise:
Conversation with Gemini
Moonrise question - Hi Gemini! I understand that (on average) the moon advances about 50 minutes per 24 hour Earth day. However, my local news provider says that Moon rise occurred at times less than 50 minutes apart over the past several days. Here is a list of the stated times:
4:30 PM 5:02 PM 5:32 PM and today will be 5:56 PM. The minutes separation are 32, 29, 25. Is there an explanation for the difference?
***
Google Search
That's an excellent observation! The reason the daily moonrise delay is less than the ∼50 minute average is due to the combined effect of the Moon's orbital tilt and your geographic latitude.The ∼50 minutes is just the average delay over the course of the Moon's ∼29.5-day cycle. The actual delay varies widely, from as little as ∼20 minutes to over ∼60 minutes, depending on the day. Your observed delays of 32, 29, and 25 minutes are all within this normal range of variation.
Why the Daily Moonrise Time Varies
There are two primary factors that cause the actual daily moonrise delay to fluctuate around the ∼50-minute average:1. The Angle of the Moon's Orbit to the Horizon (Most Significant Factor)
This is the main reason for the large variations you're observing.The Moon's orbit is tilted by about 5
∘
with respect to the Earth's orbit around the Sun. Furthermore, the Moon's path is also tilted relative to the Earth's equator (by a total angle that ranges from about 18 ∘ to 29 ∘ over an 18.6-year cycle).During certain times of the month, the Moon's orbital path makes a shallow angle with the eastern horizon at moonrise. When the angle is shallow, the Moon doesn't sink very far below the horizon after one Earth rotation. This means the Earth doesn't have to rotate as much to "catch up" to the Moon for the next day's moonrise. This results in a shorter-than-average delay (like the 25–32 minute delays you observed).
Conversely, when the Moon's orbital path makes a steep angle with the eastern horizon, the Moon sinks a considerable distance below the horizon after one day. The Earth has to rotate much further to bring it back into view, resulting in a longer-than-average delay (closer to or even over 60 minutes).
This effect is also highly dependent on your latitude. For observers at higher latitudes (further from the equator), this variation is more pronounced.
2. The Moon's Orbital Speed
The Moon's orbit around the Earth is not a perfect circle; it's an ellipse.When the Moon is at perigee (closest to Earth), it moves faster in its orbit (Kepler's Second Law). This greater movement means the Earth has to turn more to catch up, resulting in a longer daily delay.
When the Moon is at apogee (farthest from Earth), it moves slower, meaning the Earth doesn't have to turn as much to catch up, resulting in a shorter daily delay.
While this elliptical motion contributes to the variation, the orbital tilt and latitude effect (point #1) is typically the most dominant factor explaining why the daily delay can be so far from the ∼50-minute average.
***
Would I be correct in presuming that over the course of a year, I should see the moonrise intervals even out or average out to 50 minutes?
***Google Search
You are very close! Over the course of a year, the average daily delay in moonrise is about 50 minutes.This average is a great approximation and is based on the Moon's orbital period, but the actual delay from one day to the next can vary significantly, typically ranging from about 30 to 70 minutes.
Calculation of the Average Delay
The average daily delay is a result of the time it takes the Moon to complete a full cycle of phases, which is called the synodic month.Synodic Month: The average length of a synodic month (new moon to new moon) is approximately 29.53 days. This is the time it takes for the Moon to get back to the same position relative to the Sun and Earth.
Daily Angular Motion: For the Moon to cycle through all 24 hours of the day over 29.53 days, it moves an average of about 360
∘
in the sky during this time. The angular delay per day is approximately:29.53 days 360 ∘ ≈12.2 ∘ per day
Time Delay: The Earth rotates 360 ∘ in 24 hours, or 15 ∘ per hour. To find the time delay caused by the Moon's 12.2 ∘ daily movement, you calculate how long it takes for the Earth to rotate an extra 12.2 ∘ :15 ∘ per hour 12.2 ∘ ×60 minutes per hour≈48.8 minutes
This calculation gives a mean daily delay of about 49 minutes, which is commonly rounded to 50 minutes.Factors Causing the Daily Variation
While the average is around 50 minutes, the daily moonrise delay can vary because of two primary factors related to the Moon's orbit, which cause the 12.2
∘
value to fluctuate:1. The Angle of the Moon's Orbit (Latitude)
This is the most significant factor. The Moon's orbit is tilted about 5 ∘ relative to the Earth's orbit around the Sun (the ecliptic).Small Delay (Near the Equator): When the Moon's orbital path is nearly perpendicular to the eastern horizon, it moves a greater vertical distance from one night to the next. This means the Earth doesn't have to rotate as much to bring the Moon back into view, resulting in a shorter delay (as little as 30 minutes). This effect is most pronounced at higher latitudes but is generally less variable closer to the equator.
Large Delay (Near the Poles): When the Moon's orbital path is at a shallow angle to the eastern horizon, it moves a smaller vertical distance. The Earth must rotate significantly more to bring the Moon back into view, resulting in a longer delay (up to 70-85 minutes). This is most noticeable during certain seasons at high latitudes.
2. The Moon's Orbital Speed (Elliptical Orbit)
The Moon's orbit around the Earth is an ellipse, not a perfect circle.Near Perigee (Closest): The Moon moves faster in its orbit. This greater angular motion means the Earth has to rotate more to "catch up," which can increase the moonrise delay.
Near Apogee (Farthest): The Moon moves slower, which can slightly decrease the moonrise delay.
These two factors cause the actual daily moonrise delay to oscillate around the 50-minute average, but over many months (and definitely a year), they will cancel out, and the long-term average will indeed be close to 49-51 minutes.
***
Thank you for your careful and thorough explanation of something I've never had occasion to think about before. Does this behavior of the Moon-Earth system translate to tides as well? In other words, do tides also vary around this 48.8 minute average?
***Google Search
Yes, the daily difference in the time of high tide (the tidal interval) not only averages around the 48.8 to 50 minutes you described for moonrise but also varies significantly from this average.The average time for a point on Earth to "catch up" to the Moon is 24 hours and 50 minutes (a lunar day). Since most places have two high tides, they typically occur about 12 hours and 25 minutes apart, meaning high tide occurs about 50 minutes later each solar day compared to the day before.
However, this daily difference is just an average, and the actual delay varies due to several astronomical and geographic factors.
Factors Causing Variation in the Daily Tidal Interval
1. The Moon's Elliptical Orbit
The primary cause for the variation in the average 50-minute delay is the Moon's elliptical (oval-shaped) orbit around the Earth.The speed of the Moon varies as it orbits. When the Moon is closest to Earth (at perigee), it moves faster in its orbit, meaning the Earth has to rotate for a slightly longer time to "catch up" to it. This can increase the daily tidal delay.
When the Moon is farthest from Earth (at apogee), it moves slower, and the Earth has to rotate for a slightly shorter time to "catch up," which can decrease the daily tidal delay.
The 48.8 minutes you calculated is the theoretical average delay if the Moon moved at a constant speed in a circular orbit; the actual average of 50 minutes accounts for the non-circularity. The daily change can vary from as little as 16 minutes to as much as 86 minutes on different days of the lunar month.
2. Influence of the Sun
While the Moon is the main driver of tides, the Sun's gravity also creates a tide, and the two forces interact in a way that affects the timing of the ocean's response.The Sun's tidal force can influence the position of the high-tide bulges, causing them to precede or lag the Moon's position by a few hours, especially as the Moon changes its phase. This introduces another layer of variation to the timing.
3. Geographical and Hydrodynamic Effects
The time it takes for a tide to arrive at a specific location is also heavily influenced by local geography, which can accelerate or retard the tidal wave.Ocean Shape and Depth: Tides are essentially very long waves traveling through the ocean basins. The shape of the continental shelves, coastlines, and ocean floor greatly affects how these waves "slosh" and how quickly they move.
Local Resonance: The natural period of oscillation (sloshing) of a bay or basin can be a major factor. In some places, the local resonance can amplify or diminish the tide and dramatically change its timing relative to the Moon's position.
Topography: These local factors can cause the tidal interval to be very irregular, with the actual delay between high tides varying considerably from the 12 hour 25 minute average, and consequently, the daily delay changing from the 50-minute average.
In short, the 50-minute delay is a long-term average based on the Moon's orbital motion, but the Moon's varying orbital speed, the Sun's influence, and local geography cause the actual daily delay in high tide to fluctuate.
***
This is fascinating! Thank you for your clear exposition of the phenomena I've been taking for granted.
***That's wonderful! I'm glad you found the explanation helpful. Astronomy and oceanography are full of these fascinating cycles that govern our daily lives without us even realizing it. ??
If you have any other questions about the Moon, tides, or anything else, feel free to ask!
I think Gemini is quite possibly missing the importance of the elliptical nature of the Moon's orbit in the opening section above. It seems to me that if the Moon's orbit is highly eccentric, that would account for the change of interval between Moonrises. I don't think the location on Earth where the observation is made would be as significant a factor. However, this is the first time I've thought about this, so I'm looking forward to posts by members who have indeed thought about this previously.
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The moon's orbit about the Earth has a low, but nonzero, eccentricity. That eccentricity will overcome anything based on pure circles. But that effect at low eccentricity is still low.
There is also the issue of local topography. Few places on Earth are really an approximation to the "ideal sphere" used to estimate both sunrise and moonrise, and sunset and moonset, here on Earth. 1 degree of topographical deviation is a deviation of about 4 minutes in sunrise or moonrise, and in sunset and moonset.
Even the adjacent tree-line is a serious effect on this. Locally, the adjacent tree-line variations correspond to angle deviations up to 1.5 degrees (6 minutes) from the "ideal" horizon. Where I am, this is the central Texas prairie. But there really is topological deviation, plus the heights of adjacent tree-lines. Other locations with more pronounced deviations will have even larger time differences for sunrise, moonrise, sunset, and moonset. It is inherent.
Complicating that is some light refraction effects upon what you term sunrise and sunset. Even those definitions have a serious effect: about 2 minutes, whether you use tip-of-sun (or moon) at horizon, or the centerpoint of the disk. Both the sun and the moon are roughly half a degree in diameter as viewed from Earth.
Sorry, but that is the real-world stuff you have to deal with.
Now, who did a better job explaining it. Me, or ChatGPT?
I still say that the term "artificial intelligence" is an oxymoron. Precisely because no computer has any understanding of truth vs falsehood. If all you know is only what others have said, how can you possibly know what is right vs wrong?
Dare trust no machine, and very few real humans!
GW
Last edited by GW Johnson (2025-10-04 17:56:39)
GW Johnson
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"There is nothing as expensive as a dead crew, especially one dead from a bad management decision"
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For GW Johnson re #4
Thanks for contributing to this topic! It seems likely humans can go entire lifetimes without thinking about the variations in moonrise.
You've added new details to the variation.
The range of variation appears to be far greater than 2 minutes. Apparently, the range of variation can reach as low as 20 minutes and as high as 80, from an average of 48.8.
The key information I was looking for is eccentricity of the ellipse.
Your post describes the eccentricity as low, but that in itself doesn't help much to explain the reported variation.
It appears this topic has some room to grow, before we've (NewMars members) have arrived at a consensus of understanding of the variation of moonrise at a specific location.
Just to clarify.... the AI consulted in the opening of this series is built by Google. It's current name is Gemini, and it competes with ChatGPT and other systems.
This topic is available for contributions by NewMars members who can explain the wide variation of Moonrise observations from specific points on Earth. Since the average advance of Moonrise is 48.8 minutes. there has to be an explanation for variation to 20 degrees on the short side, to 80 degrees on the long side.
Important as trees may be, they would NOT account for variation of the location of the Moon it it's orbit.
To make a scientific observation, one would decide upon a condition that will be the same from one observation to the next, and then record the Moonrise time in accordance with that consistent rule. For example, one might decide that the rule is to wait for the bottom of the Moon to clear the horizon. On successive observations, any features of the landscape that are present would be accounted for, so the only variable would be the behavior of the Moon.
This topic is available for a post about how scientific observations of Moonrise are carried out.
When a member of this forum has demonstrated mastery of this particular knowledge set, that individual will be able to predict to the second when the Moon will rise as observed from a particular location on the Earth.
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The reference I propose for study of the Lunar cycle is timeanddate.com
In considering the information provided about Moonrise for a specific location on the surface of the Earth, time and date.com provided this display this morning:
2025 Moonrise/Moonset Meridian Passing
Oct Moonrise Moonset Moonrise Time Distance (mi) Illumination
1 - 12:52 am ↑ (235°) 4:30 pm ↑ (122°) 9:12 pm (26.1°) 240,814 70.2%
2 - 2:00 am ↑ (240°) 5:02 pm ↑ (116°) 10:02 pm (30.7°) 236,928 79.6%
3 - 3:11 am ↑ (247°) 5:31 pm ↑ (109°) 10:52 pm (36.5°) 233,023 87.9%
4 - 4:23 am ↑ (255°) 5:56 pm ↑ (100°) 11:40 pm (43.1°) 229,437 94.5%
5 - 5:35 am ↑ (264°) 6:20 pm ↑ (91°) Moon does not pass the meridian on this day.
I was surprised to see the text: Moon does not pass the meridian on this day.
That can be accounted for by the time of the last event: 11:40 PM. Since 24 hours plus (average of 48.8 minutes) must pass, it is clear that a passing will not occur on that specific day. Correction to earlier version of this post. The Moon is constantly advancing to the East, so skipped Meridian crossing events will occur regularly, and there will NEVER be two Meridian crossings in one day.
In the example of (presumably scientific) observations (or predictions) show above, we can see that elapsed times for meridian crossings are:
Meridian crossing appears to be a better measure of the Moon's progress than Moonrise...
The elapsed times for the given location, using Meridian Crossing are:
9:12 PM to 10:02 PM >> 50 minutes (compared to average of 48.8 minutes)
10:02 to 10:52 PM >> 50 minutes
10:52 PM to 11:40 >> 48 minutes
Meridian crossing appears to be a more reliable way of observing the Moon's travels than is Moonrise.
Interesting! Well, as I reported earlier, I've never had occasion to think about this before.
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In this post, Gemini will address the variations of Meridian crossing, which should be easier to understand than Moonrise, which can be obscured by trees.
Conversation with Gemini
Calculate Meridian Crossing Intervals - Hi Gemini! Thank you for your assistance with numerous previous requests! Today I'm hoping you might be willing to help with a bit of spreadsheet calculation. A website offers a table of data about Moon observations. www.timeanddate.com/Moon/USA/Columbus provides a table of predictions for Moon events as they will be observed at a specific location. Would you be willing to calculate the minutes elapsed between meridian crossings for the month of October, 2025? The numbers appear to be in the range of 48.8 plus or minus two minutes.
***Google Search
That's an excellent astronomical calculation request! It relates to the difference between the solar day (24 hours) and the mean lunar day (about 24 hours and 50 minutes). The variability is caused by the Moon's elliptical orbit and changes in its orbital speed.Based on the predicted Moon meridian crossing times for Columbus, USA, in October 2025, the calculated intervals between crossings are highly variable.
The minutes elapsed between consecutive Moon meridian crossings (the total interval) range from 1480 minutes to 1504 minutes.
However, given your reference to 48.8±2 minutes, you are asking for the daily delay in the crossing time—the minutes by which the Moon's transit occurs later each day compared to the previous day.
Here is the minute-by-minute calculation for the daily delay (Δt), which is the time elapsed in minutes in excess of 24 hours between consecutive meridian crossings.
Moon Meridian Crossing Daily Delay (Δt)
The daily delay in the Moon's meridian crossing time for October 2025, observed in Columbus, OH, is as follows:Interval (Date Range) Daily Delay (Δt) (Minutes) Total Interval (Minutes)
Oct 1 → Oct 2 50 1490
Oct 2 → Oct 3 50 1490
Oct 3 → Oct 4 48 1488
Oct 4 → Oct 5* 49 1489
Oct 5 → Oct 6 50 1490
Oct 6 → Oct 7 53 1493
Oct 7 → Oct 8 57 1497
Oct 8 → Oct 9 60 1500
Oct 9 → Oct 10 64 1504
Oct 10 → Oct 11 63 1503
Oct 11 → Oct 12 61 1501
Oct 12 → Oct 13 57 1497
Oct 13 → Oct 14 52 1492
Oct 14 → Oct 15 47 1487
Oct 15 → Oct 16 43 1483
Oct 16 → Oct 17 41 1481
Oct 17 → Oct 18 41 1481
Oct 18 → Oct 19 40 1480
Oct 19 → Oct 20 42 1482
Oct 20 → Oct 21 43 1483
Oct 21 → Oct 22 46 1486
Oct 22 → Oct 23 48 1488
Oct 23 → Oct 24 51 1491
Oct 24 → Oct 25 52 1492
Oct 25 → Oct 26 52 1492
Oct 26 → Oct 27 51 1491
Oct 27 → Oct 28 50 1490
Oct 28 → Oct 29 48 1488
Oct 29 → Oct 30 47 1487
Oct 30 → Oct 31 47 1487Export to Sheets
*Note: The online data for Oct 5 shows a "Moon does not pass the meridian on this day" entry. This is a common almanac anomaly when the transit time shifts just past midnight. The calculated delay of 49 minutes for the Oct 4 → Oct 5 crossing is based on the difference between the listed 11:40 PM transit on Oct 4 and the 12:29 AM transit on Oct 6, which represents the next sequential transit (one lunar day later).Summary of Intervals
The daily delay for the month ranges from a minimum of 40 minutes (Oct 18 → Oct 19) to a maximum of 64 minutes (Oct 9 → Oct 10).Average Daily Delay: 50.1 minutes (in line with your expected range of 48.8±2 minutes).
Average Total Minutes Elapsed: 1490.1 minutes (24 hours + 50.1 minutes).
***Thank you for your analysis and careful presentation! My plan is to post your presentation on a small international forum. My guess is that many of our members and readers have never thought about this before, so the variations may be of interest to some.
***
That's great to hear! I'm glad the presentation was helpful and that you plan to share it.The potential variations and different perspectives will likely make for interesting discussion on your international forum. I wish you the best with your post! ?
Where this discussion leads is to the eccentricity of the Lunar orbit, and (I would imagine) the angle of the Moon's orbital plane with respect to that of the Earth's plane of rotation.
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This post is a follow up on the hints about orbit eccentricity and orbit inclination we have seen in previous posts:
The post is up. Now I have a follow up ... There would be no variation in the meridian passage interval if the Moon were orbiting in a perfect circle, the Earth were a perfect sphere, and the orbital planes were aligned. As it happens, none of these is true. We can't (realistically) deal with the lumpy nature of the Earth, but we ** should ** be able to discover the orbital eccentricity and the angles between the Lunar orbital plane and the Earth's equatorial plane. Please report those, and (as a bonus) please look to see if there is an online animation service that allows the student to visualize the Lunar orbit.
***
That's an excellent follow-up question for your forum discussion. The variations you're seeing in the Moon's motion are indeed primarily due to the elliptical nature of its orbit and its inclination relative to the Earth's equator.
Here are the key orbital parameters you requested, followed by a suggestion for an online animation.
Key Lunar Orbital Parameters
Orbital Eccentricity
The Moon's orbit around the Earth is an ellipse, not a perfect circle. The degree of this oval shape is measured by its eccentricity (e).Eccentricity (e): ≈0.0549
Since this value is relatively small (close to 0), the orbit is only slightly elliptical. The Moon's distance from Earth varies throughout its orbit:
Point Description Distance (average)
Perigee Closest approach to Earth ≈363,300 km
Apogee Farthest point from Earth ≈405,500 kmExport to Sheets
The varying speed of the Moon as it travels between perigee (faster) and apogee (slower) is a major contributor to the variations in the meridian passage interval.Inclination of the Lunar Orbital Plane
The Moon's orbital plane is inclined with respect to two main reference planes:Earth's Ecliptic Plane: The plane of the Earth's orbit around the Sun.
Inclination to Ecliptic: ≈5.14
∘
(This is a relatively stable value).Earth's Equatorial Plane: The plane defined by the Earth's equator.
Inclination to Equator: This angle varies significantly because the Earth's equator is itself tilted relative to the ecliptic (by about 23.4 ∘ ). As a result, the Moon's orbit relative to the equator can range from a minimum of ≈18.3 ∘ up to a maximum of ≈28.6 ∘ . This cyclical variation takes about 18.6 years to complete (the Saros cycle/Nodal Precession period).
This inclination is what causes the Moon's apparent path across the sky to move north and south of the celestial equator, affecting when and where an observer sees it cross their local meridian.
Bonus: Online Visualization Tool
The best kind of tool for visualizing orbital mechanics is a planetarium program or a dedicated orbital simulator.A great free and powerful online option that allows students to visualize the Moon's orbit in three dimensions is:
The Solar System Scope or similar 3D interactive astronomy sites.
These often allow users to:
Select the Moon and zoom in.
Toggle on the orbital path (showing the elliptical shape).
Change the perspective to view the inclination of the orbit relative to the Earth's equator and the ecliptic plane.
While a simple "animation service" may be harder to find, these interactive tools offer the most robust visualization of the geometry contributing to the variations in meridian passage intervals.
***
Thank you for your research of this topic, and for your presentation, including the suggestions for sites able to help with visualization!
***You're very welcome! I'm glad the information and the visualization suggestions were helpful for your discussion.
If any new questions or topics arise from your forum's conversation, please feel free to ask! Happy to assist further.
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In this post, I report on a conversation with Gemini about the possibility of showing the distance of the Moon from Earth at various points in it's orbit, along with orbital velocity at the moment of crossing the Meridian. This information would help us to visualize the reasons for the changes we observe in meridian crossings. However, I don't think this would be the best use of Google's computing resources at this time.
In studying the table you provided, showing elapsed minutes between meridian crossings, it occurred to me that we still have two influences on the differences. One is the varying velocity of the Moon along it's orbit. We should see times greater than 48.8 when the Moon is closer and traveling faster, and we should see times less than 48.8 when the Moon is further away and traveling more slowly. Would it be difficult to add distance from Earth and rate of travel in km/s to the chart? Please don't proceed ... I'm just looking for an estimate of effort. What I'm trying to do is to see if we can separate the influence of orbital eccentricity from the inclination of the orbital plane.
***Google Search
That's an insightful next step in your analysis! You are correct that the varying orbital speed (governed by eccentricity) and the varying Right Ascension change (governed by both speed and orbital inclination) are the two primary causes of the differences in the meridian passage interval.Estimate of Effort
The effort required to add the Moon's distance and velocity to the chart would be Moderate to High, leaning toward high if the data is required for the exact times of the meridian crossings you used previously.Here is a breakdown of the effort:
1. Data Acquisition (Moderate Effort)
Need for Precise Ephemeris: Unlike the angular position (Right Ascension) needed to calculate the meridian crossing time, the distance and instantaneous velocity of the Moon are not readily available in simple online calculators for a series of specific dates/times.Specialized Software: To get the distance and tangential velocity (km/s) at each of your specific meridian crossing times, you would need to run a high-precision astronomical ephemeris calculator (like those provided by NASA JPL or a professional planetarium software) for each date and time. This is more complex than a simple table look-up.
2. Calculation and Validation (High Effort)
Velocity Calculation: The instantaneous orbital velocity is not constant. It is highest at Perigee (closest point) and lowest at Apogee (farthest point), following Kepler's Second Law (the law of areas).The Vis-Viva Equation is the standard way to calculate the instantaneous speed (v) at a given distance (r) in a two-body orbit:
v= GM( r2 − a1 )
where:
G is the gravitational constant.
M is the combined mass of Earth and the Moon.
a is the semi-major axis (average distance).
r is the instantaneous distance.
This calculation would need to be performed for every data point, or retrieved directly from a robust ephemeris, which is not a trivial operation.
3. Separating the Influences (Conceptual Effort)
Your goal is brilliant: separating the influence of eccentricity from inclination.Eccentricity's Influence: The Moon's instantaneous tangential speed (v) is directly correlated with its distance (r). When distance is low (Perigee), speed is high, and the meridian interval should be longer than the average.
Inclination's Influence: This effect is captured by the Moon's change in Right Ascension (RA). Even if the tangential speed were constant, the change in RA is smaller when the Moon is crossing the celestial equator, and larger when it is near its maximum declination (farthest north or south).
By plotting meridian interval against the Moon's distance (the eccentricity effect) and against the Moon's Declination (a proxy for the inclination effect), you could indeed visually and statistically attempt to isolate these two distinct cycles. The distance cycle (anomalistic month, ≈27.5 days) and the inclination cycle (tropical month, ≈27.3 days) are different, which allows them to be separated over a long enough period.
In short, while the idea is scientifically sound, acquiring the precise, time-stamped orbital velocity and distance data would require specialized ephemeris tools, making the effort level quite high.
***
Thank you for the estimate. I'm glad I asked. I think we should wait to see if there is enough interest to justify the request. That said, thank you for this series. I am hoping it will have value to future readers who may be interested in in the topic.
***That's a perfectly reasonable decision. Waiting to gauge the interest level is a smart way to allocate effort.
I'm very pleased that this series of analyses has been helpful to you and that you anticipate its value for other readers on your forum. It's a fascinating topic, and breaking down the orbital mechanics behind a seemingly simple observation like meridian passage time often leads to great educational discussions.
Please don't hesitate to reach out if the interest develops and you'd like to proceed with the more detailed analysis!
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Data on the moon's orbit about the Earth, from the "data" worksheet in the "orbit basics spreadsheet" file, part of the "orbits+" course materials available by links from the forums site.
Rmax = 405,506 km, Rmin = 363,299 km, Ravg = ellipse a = 384,403 km, eccentricity = 0.0549 (some 5.49%). speed V at apogee = 0.9632 km/s, V at perigee = 1.0751 km/s, avg V at R = a is 1.0176 km/s. Mean surf gravity 162.3 cm/s^2. Mean surface escape V = 2.376 km/s, mean surf circular orbit V = 1.680 km/s. Mean radius = 1738.3 km, polar radius = 1737.6 km, equatorial radius 1738.7 km. Mass = 7.354 x 10^22 kg.
GW
GW Johnson
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For GW Johnson re #10
Thanks for this valuable data about the Lunar orbit and related characteristics!
The change of times recorded for Meridian crossings varies over a range of minutes centered around 48.8 minutes. The excursions are observed in a day consisting of 1440 seconds plus 48.8 seconds, or a total of 1488.8 seconds. The variation of velocity you've reported in Post #10 is from 0.9632 km/s to 1.0751 km/s. The difference is .1119 km/s
My guess would be that there is likely to be an inverse correlation between velocity and meridian crossing time changes.
Any difference left over would then be due to the inclination of the orbit.
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