8
$\begingroup$

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?

$\endgroup$
6
  • $\begingroup$ related $\endgroup$
    – AJN
    Sep 10, 2023 at 17:04
  • 4
    $\begingroup$ 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. $\endgroup$
    – uhoh
    Sep 10, 2023 at 20:35
  • 5
    $\begingroup$ 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. $\endgroup$
    – Woody
    Sep 10, 2023 at 21:26
  • 1
    $\begingroup$ 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. $\endgroup$ Sep 11, 2023 at 4:26
  • $\begingroup$ 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. $\endgroup$
    – dtn
    Sep 11, 2023 at 6:50

2 Answers 2

20
$\begingroup$

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

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.

$\endgroup$
8
  • 3
    $\begingroup$ Can you give an example of an orbit that meets the criteria in the question? $\endgroup$
    – Organic Marble
    Sep 10, 2023 at 21:38
  • 6
    $\begingroup$ as a minor addition to this: in addition to an orbit where everytime the moon passes the Earth-Sun line, it's out of the Earth-Sun plane, if the moon were sufficiently/excessively far from Earth it could clear the Earth's umbra (hence no lunar eclipses) and it could also appear small enough that we'd regard the moon's passage across the sun as a transit, not an eclipse. $\endgroup$
    – Erin Anne
    Sep 10, 2023 at 23:51
  • 2
    $\begingroup$ @Dr.user44690 ... sounds like you should post another question. $\endgroup$
    – Woody
    Sep 11, 2023 at 6:15
  • 4
    $\begingroup$ 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? $\endgroup$
    – YPOC
    Sep 11, 2023 at 9:54
  • 1
    $\begingroup$ @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. $\endgroup$ Sep 11, 2023 at 20:16
9
$\begingroup$

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 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. 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 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 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 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

$\endgroup$
7
  • 3
    $\begingroup$ I think the question implies an orbit around the Earth, so Lagrange points wouldn't really count because then the Moon would technically be orbiting the Sun. If the question allows this then might as well just send the Moon into orbit around the Sun and be done with it. I think it's worth mentioning it because it's interesting, but you might want to clarify with the OP if the question is limited to Earth orbit, either that or just add something to your answer emphasizing that Lagrange points would be a solar orbit and not an Earth orbit, even though you did allude to this already $\endgroup$
    – Steve Pemberton
    Sep 11, 2023 at 22:09
  • $\begingroup$ Thanks for your feedback! Clarified it in the answer $\endgroup$
    – txp
    Sep 12, 2023 at 6:30
  • $\begingroup$ 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? $\endgroup$
    – YPOC
    Sep 12, 2023 at 8:37
  • 1
    $\begingroup$ The J2 precession effect is strongest for low earth orbits, but let's ignore other effects and assume that the nodal precession equation for the J2 effect is still significant for our case. The Moon is around 46 times further away from earth than the proposed low earth orbit at 2000 km altitude, so the nodal precession will be ≈46² > 2000 times slower than the original period of one year. You can then fine-tune the period and inclination of the Moon's orbit to achieve the phase shifted regular period solution, so yes it's possible but more difficult than the original solution by @woody $\endgroup$
    – txp
    Sep 12, 2023 at 9:12
  • $\begingroup$ 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. :) $\endgroup$
    – YPOC
    Sep 12, 2023 at 12:57

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .