<p>Answer: <strong>Yes</strong>, there are <strong>multiple</strong> no-eclipse orbits (other than the phase-shifted period solution by @woody) possible if we leverage various perturbation models of the two-body system.</p>
<ol>
<li><p><strong>The J2 effect.</strong> If you take into account the gravitational effects of Earth's equatorial bulge on the orbits of satellites, this causes a <a href="https://en.wikipedia.org/wiki/Sun-synchronous_orbit" rel="noreferrer">precession</a> of the any satellite's orbital plane around Earth's rotation axis. Satellites in polar orbits use this effect to rotate their orbital plane with a rate of one full rotation per year to view the Earth under the same solar angles permanently. We can use the same effect to keep the Moon's orbital plane from intersecting the Earth-Sun line indefinitely by placing the Moon in a polar low Earth orbit, at a range of altitudes with each a specific inclination which you can calculate with the approximating equation given in the <a href="https://en.wikipedia.org/wiki/Sun-synchronous_orbit" rel="noreferrer">Wikipedia article on Sun-sync orbits</a>.
However, as the Moon has a radius of 1736 km and we'd rather not have it scrape across our crust or burn up in the atmosphere, we should prefer orbital altitudes above 2000 km. As solutions to the combination of altitude and Sun-synchronous inclination exist only below 5981 km altitude, the longest orbital period that this kind of non-eclipsing Moon will have is 3.8 hours. Get ready for an Interstellar-like tsunami world!<sup>1</sup></p>
</li>
<li><p><strong>Lagrange Points.</strong> If we look beyond a strict Earth orbit towards the Sun-Earth two-body system, there are five locations where the gravitational attraction of both bodies and the centrifugal acceleration cancel out in the frame of reference rotating with the Earth around the Sun. In these so-called <a href="https://en.wikipedia.org/wiki/Lagrange_point" rel="noreferrer">Lagrange points</a> you could place the Moon to make it follow the Earth on its orbit around the Sun, without eclipsing it. Your best long-term choices are the stable L4 and L5 points, where the moon can sit still or <a href="https://en.wikipedia.org/wiki/Libration_point_orbit" rel="noreferrer">librate</a> in small loops around one of them. Unfortunately, L1, L2 and L3 are unstable, so if you tried placing the Moon in a halo orbit (to avoid the eclipse cases) around them, it would soon end up drifting off into the unknown. A disadvantage of L4 and L5 is that the Moon will appear rather small and create insignificant tides as it would be 389 times further away from Earth than it currently is.</p>
</li>
</ol>
<p><sup>1</sup> Your Moon won't last long in this orbit though, as <a href="https://en.m.wikipedia.org/wiki/Roche_limit" rel="noreferrer">tidal forces</a>  or centrifugal forces if you choose to let it rotate with a 3.8 hour period will rip it apart.</p>
<p><strong>Edit:</strong> props to @AJN and @Greg Miller, just saw that they had already proposed these ideas in the comments</p>
<p><strong>Edit2:</strong> added Roche Limit and clarified Lagrange case</p>
<p><strong>Edit3&amp;4:</strong> corrected Lagrange point formulation</p>

CC BY-SA 4.0
2023-09-12T08:37:53.483Z
Are there solutions for precessing orbits that are near the moon's orbit, not doing a full revolution of the plane per revolution, but a fraction of it? So the precession still is in resonance with the orbit, and eclipses can be avoided?
YPOC
CC BY-SA 4.0
2023-09-12T12:57:24.510Z
Thanks for the reply, @txp. Just so you're aware: When you reply to a comment on your own post, you need to tag that person or else they won't get a notification. Only on your own questions/answers you will receive comment notifications. :)
YPOC
CC BY-SA 4.0
2023-09-12T13:06:34.587Z
Gravity does not cancel our at _any_ of the Lagrange points; if it did, an object placed there would immediately depart them in a straight line. What it does is sum up in a way that allows the third object to orbit the first in a 1:1 resonance with the second that is partially stable on the case of L1,L2, or L3, and potentially long-term stable in the case of L3 and L5.
notovny
CC BY-SA 4.0
2023-09-11T21:24:54.077Z
2023-09-12T15:29:05.513Z
txp
<p>Answer: <strong>yes</strong>, a no-eclipse orbit is possible</p>
<p>The plane of the Earth-Sun orbit (the ecliptic) and the plane of the Earth-Moon orbit must intersect each other because they both contain at least one point in common: the CM of Earth. Two planes always intersect in a line, so there will always be two POTENTIAL positions for the three bodies to be aligned, as illustrated below.</p>
<p>However, that doesn’t mean the bodies MUST align: if a “month” was a proper fraction of a year, the Moon could always be above (or below) the ecliptic at times of potential eclipse.</p>
<p>For instance, consider an idealized Earth/Moon system with the Moon in a circular orbit of period 1/12 of a sidereal year and the Moon’s orbital inclination is 5* with respect to the ecliptic.</p>
<p><a href="https://i.sstatic.net/1VQOk.png" rel="noreferrer"><img src="https://i.sstatic.net/1VQOk.png" alt="enter image description here" /></a></p>
<p>Lunar eclipses occur when the moon is in positions A or D. Solar eclipses occur on positions B or C. The line A-D is the intersection of the ecliptic with the Moon’s orbital plane. Eclipses can only occur when all 3 bodies are on this line.</p>
<p>If the moon’s orbital period is a proper fraction of the Earth’s orbital period, the moon’s position in its orbit will be synchronized with the Earth’s orbit. For instance, if the moon's orbital period is 1/12 of a sidereal year and it starts in position E, a half year later it will have completed 6 orbits of the earth and be in position F. The moon has “missed” the only two opportunities in the year to have an eclipse. And since its orbit around Earth is synchronized with the Earth’s orbit around the sun, it will never get the chance in future years.</p>

CC BY-SA 4.0
2023-09-11T06:12:57.050Z
It is known that in the past the moon was closer to earth and hence had smaller orbital time period. Does that mean there was a time period in the history of the planet such that there were no eclipses ?
Dr. user44690
CC BY-SA 4.0
2023-09-11T06:15:00.903Z
@Dr.user44690 ...  sounds like you should post another question.
Woody
CC BY-SA 4.0
2023-09-11T09:54:20.983Z
If I understand correctly the moon's orbit will precess around Earth. Is it possible for this precession to be in resonance as well such that no explises occur?
YPOC
CC BY-SA 4.0
2023-09-11T20:16:51.857Z
@YPOC I don't think there is a physical mechanism that would synchronize the period of a moon around its planet with the period of the planet around its star, which is required to not have eclipses (contrast with tidal locking, which does eventually result in a stable, synchronized end state). If it did happen, I expect it would be an unstable chance occurrence that happened to line up but would not last.
Nuclear Hoagie
CC BY-SA 4.0
2023-09-11T20:24:21.903Z
@NuclearHoagie ... I'm sure you are right. In the long term, I doubt any n>2 body orbit is truly stable. Our solar system isn't. But the OP is "Is it mathematically possible to construct such an orbit?"
Woody
CC BY-SA 4.0
2023-09-30T22:10:17.470Z
it seems an eclipse free orbit would have a sidereal period of 30.438 days. What would the lunar orbit diameter be to get this period? I did an overly simplified calculation based on perfect circle orbit centered on earth (not barycenter) and must have got units really screwed up because my result was a few orders of magnitude off.
BradV
CC BY-SA 4.0
2023-09-10T20:54:18.137Z
2023-09-11T18:16:42.780Z
Woody
<p>Theoretically speaking, what orbit should the earth's moon must take so that there are never any eclipses - solar or lunar? Is it mathematically possible to construct such an orbit?</p>

CC BY-SA 4.0
2023-09-10T20:35:24.907Z
*Welcome to Space SE!* It's an interesting/instructive question but off-topic in Space SE. Possibly on-topic in Astronomy SE. I think if you give it a day this might be closed here and then migrated there, so don't double post in both places. I think the answer is "No" for the moon, but as AJN points out above, there are orbits that you have to manage using small station-keeping maneuvers that you can work to keep away from the Sun-Earth line. But a dumb rocky body would not stay there by itself.
uhoh
CC BY-SA 4.0
2023-09-10T21:26:02.723Z
I don't think the question is off-topic. There has been a lot of discussion about avoiding eclipses of JWST. I assume eclipse avoidance will continue to be a mission criteria for future space exploration.
Woody
CC BY-SA 4.0
2023-09-11T04:26:39.457Z
The if it were at either of the Lagrange pints L4, or L5, there would never be eclipses.  Though these aren't "orbits" in the traditional sense.
Greg Miller
CC BY-SA 4.0
2023-09-11T06:50:51.210Z
After reading everything in this thread, I realized that this is theoretically possible in at least two cases: 1) if the Moon's orbit never crosses the imaginary line connecting the Earth and the Sun and 2) If the Moon's orbit encircles Earth-Sun system, i.e. if the dimensions of the Moon's orbit exceed the dimensions of any of the orbits of the Earth and the Sun. In this case, the Moon will be a satellite of a system of two cosmic bodies. The search for stable orbits according to given criteria is probably studied within the framework of a numerical solution to the three-body problem.
ayr
CC BY-SA 4.0
2023-09-11T12:31:03.283Z
If the plane of the Moon's orbit is fixed relative to the earth-sun orbotal plane then if the earth-moon plane is at a greater angle than half the angle subtended by the disc of the sun THEN there will be no eclipses. || This is not essential for the above: Pluto rotates with its axis at (about?) 90 degrees to its orbit. If the Earth's Moon maintained its current orbit relative to earth AND the earth's plane was at 90 degrees to where it is now.the above would be very well satisfied. || Day and night on earth would be "totally different" :-)
Russell McMahon
<orbital-mechanics><solar-eclipse>
Orbit of the moon so that there are no eclipses
Dr. user44690
# Orbit of the moon so that there are no eclipses

(Asked by: username_0 on 2023-09-10)

Theoretically speaking, what orbit should the earth's moon must take so that there are never any eclipses - solar or lunar? Is it mathematically possible to construct such an orbit?

**Tags:** orbital-mechanics, solar-eclipse
> **Comments:**
> **username_1**: *Welcome to Space SE!* It's an interesting/instructive question but off-topic in Space SE. Possibly on-topic in Astronomy SE. I think if you give it a day this might be closed here and then migrated there, so don't double post in both places. I think the answer is "No" for the moon, but as AJN points out above, there are orbits that you have to manage using small station-keeping maneuvers that you can work to keep away from the Sun-Earth line. But a dumb rocky body would not stay there by itself.  
> **username_2**: I don't think the question is off-topic. There has been a lot of discussion about avoiding eclipses of JWST. I assume eclipse avoidance will continue to be a mission criteria for future space exploration.  
> **username_3**: The if it were at either of the Lagrange pints L4, or L5, there would never be eclipses.  Though these aren't "orbits" in the traditional sense.  
> **username_4**: After reading everything in this thread, I realized that this is theoretically possible in at least two cases: 1) if the Moon's orbit never crosses the imaginary line connecting the Earth and the Sun and 2) If the Moon's orbit encircles Earth-Sun system, i.e. if the dimensions of the Moon's orbit exceed the dimensions of any of the orbits of the Earth and the Sun. In this case, the Moon will be a satellite of a system of two cosmic bodies. The search for stable orbits according to given criteria is probably studied within the framework of a numerical solution to the three-body problem.  
> **username_5**: If the plane of the Moon's orbit is fixed relative to the earth-sun orbotal plane then if the earth-moon plane is at a greater angle than half the angle subtended by the disc of the sun THEN there will be no eclipses. || This is not essential for the above: Pluto rotates with its axis at (about?) 90 degrees to its orbit. If the Earth's Moon maintained its current orbit relative to earth AND the earth's plane was at 90 degrees to where it is now.the above would be very well satisfied. || Day and night on earth would be "totally different" :-)  

---

## 2 answers

### Answer by username_2 on 2023-09-10. Score: 20 | Accepted answer

Answer: **yes**, a no-eclipse orbit is possible

The plane of the Earth-Sun orbit (the ecliptic) and the plane of the Earth-Moon orbit must intersect each other because they both contain at least one point in common: the CM of Earth. Two planes always intersect in a line, so there will always be two POTENTIAL positions for the three bodies to be aligned, as illustrated below.

However, that doesn’t mean the bodies MUST align: if a “month” was a proper fraction of a year, the Moon could always be above (or below) the ecliptic at times of potential eclipse.

For instance, consider an idealized Earth/Moon system with the Moon in a circular orbit of period 1/12 of a sidereal year and the Moon’s orbital inclination is 5\* with respect to the ecliptic.

[![enter image description here](https://i.sstatic.net/1VQOk.png)](https://i.sstatic.net/1VQOk.png)

Lunar eclipses occur when the moon is in positions A or D. Solar eclipses occur on positions B or C. The line A-D is the intersection of the ecliptic with the Moon’s orbital plane. Eclipses can only occur when all 3 bodies are on this line.

If the moon’s orbital period is a proper fraction of the Earth’s orbital period, the moon’s position in its orbit will be synchronized with the Earth’s orbit. For instance, if the moon's orbital period is 1/12 of a sidereal year and it starts in position E, a half year later it will have completed 6 orbits of the earth and be in position F. The moon has “missed” the only two opportunities in the year to have an eclipse. And since its orbit around Earth is synchronized with the Earth’s orbit around the sun, it will never get the chance in future years.

> **Comments:**
> **username_0**: It is known that in the past the moon was closer to earth and hence had smaller orbital time period. Does that mean there was a time period in the history of the planet such that there were no eclipses ?  
> **username_2**: @Dr.user44690 ...  sounds like you should post another question.  
> **username_7**: If I understand correctly the moon's orbit will precess around Earth. Is it possible for this precession to be in resonance as well such that no explises occur?  
> **username_9**: @YPOC I don't think there is a physical mechanism that would synchronize the period of a moon around its planet with the period of the planet around its star, which is required to not have eclipses (contrast with tidal locking, which does eventually result in a stable, synchronized end state). If it did happen, I expect it would be an unstable chance occurrence that happened to line up but would not last.  
> **username_2**: @NuclearHoagie ... I'm sure you are right. In the long term, I doubt any n>2 body orbit is truly stable. Our solar system isn't. But the OP is "Is it mathematically possible to construct such an orbit?"  
> **username_10**: it seems an eclipse free orbit would have a sidereal period of 30.438 days. What would the lunar orbit diameter be to get this period? I did an overly simplified calculation based on perfect circle orbit centered on earth (not barycenter) and must have got units really screwed up because my result was a few orders of magnitude off.  

---

### Answer by username_6 on 2023-09-11. Score: 9

Answer: **Yes**, there are **multiple** no-eclipse orbits (other than the phase-shifted period solution by @woody) possible if we leverage various perturbation models of the two-body system.

1. **The J2 effect.** If you take into account the gravitational effects of Earth's equatorial bulge on the orbits of satellites, this causes a [precession](https://en.wikipedia.org/wiki/Sun-synchronous_orbit) of the any satellite's orbital plane around Earth's rotation axis. Satellites in polar orbits use this effect to rotate their orbital plane with a rate of one full rotation per year to view the Earth under the same solar angles permanently. We can use the same effect to keep the Moon's orbital plane from intersecting the Earth-Sun line indefinitely by placing the Moon in a polar low Earth orbit, at a range of altitudes with each a specific inclination which you can calculate with the approximating equation given in the [Wikipedia article on Sun-sync orbits](https://en.wikipedia.org/wiki/Sun-synchronous_orbit).
   However, as the Moon has a radius of 1736 km and we'd rather not have it scrape across our crust or burn up in the atmosphere, we should prefer orbital altitudes above 2000 km. As solutions to the combination of altitude and Sun-synchronous inclination exist only below 5981 km altitude, the longest orbital period that this kind of non-eclipsing Moon will have is 3.8 hours. Get ready for an Interstellar-like tsunami world!1
2. **Lagrange Points.** If we look beyond a strict Earth orbit towards the Sun-Earth two-body system, there are five locations where the gravitational attraction of both bodies and the centrifugal acceleration cancel out in the frame of reference rotating with the Earth around the Sun. In these so-called [Lagrange points](https://en.wikipedia.org/wiki/Lagrange_point) you could place the Moon to make it follow the Earth on its orbit around the Sun, without eclipsing it. Your best long-term choices are the stable L4 and L5 points, where the moon can sit still or [librate](https://en.wikipedia.org/wiki/Libration_point_orbit) in small loops around one of them. Unfortunately, L1, L2 and L3 are unstable, so if you tried placing the Moon in a halo orbit (to avoid the eclipse cases) around them, it would soon end up drifting off into the unknown. A disadvantage of L4 and L5 is that the Moon will appear rather small and create insignificant tides as it would be 389 times further away from Earth than it currently is.

1 Your Moon won't last long in this orbit though, as [tidal forces](https://en.m.wikipedia.org/wiki/Roche_limit) or centrifugal forces if you choose to let it rotate with a 3.8 hour period will rip it apart.

**Edit:** props to @AJN and @Greg Miller, just saw that they had already proposed these ideas in the comments

**Edit2:** added Roche Limit and clarified Lagrange case

**Edit3&4:** corrected Lagrange point formulation

> **Comments:**
> **username_7**: Are there solutions for precessing orbits that are near the moon's orbit, not doing a full revolution of the plane per revolution, but a fraction of it? So the precession still is in resonance with the orbit, and eclipses can be avoided?  
> **username_7**: Thanks for the reply, @txp. Just so you're aware: When you reply to a comment on your own post, you need to tag that person or else they won't get a notification. Only on your own questions/answers you will receive comment notifications. :)  
> **username_8**: Gravity does not cancel our at _any_ of the Lagrange points; if it did, an object placed there would immediately depart them in a straight line. What it does is sum up in a way that allows the third object to orbit the first in a 1:1 resonance with the second that is partially stable on the case of L1,L2, or L3, and potentially long-term stable in the case of L3 and L5.  

---

