Lunar Orbits and their potential uses

[redliox]

Most recently, NASA unveiled it was considering more than a Distant Retrograde Orbit for its first crewed Orion mission, EM-2.  More to the point though, since the Constellation days numerous (if not countless) orbits about the Moon and the Lagrange points furthermore have been suggested for staging points.  It seems more and more terms taken from the back of an orbital mechanics text book are being dredged and thrown out randomly; a lot of it seems excessive and arbitrary compared to Apollo's seemingly straightforward approach to orbiting Luna, but then again there is more than one way to literally approach the Moon...

There are several ways to define a Lunar orbit, but I'll narrow it down to 2 groups:
1) Parameter Based
2) Destination Based

Parameter Based orbits...basically are the literal classification of the orbit which can vary a lot, but I think they can be categorized roughly as follows:
-Lagrange Halo Orbits
-High Orbits
-Elliptical Orbits
-Low Orbits
Aside from their actual height above or placement relative to Earth-Luna, there's factors like whether they're "frozen" or "fixed" relative to Luna and the gravity anomalies in its crust, which destabilizes particularly the low orbits (assuming you don't have a large fuel supply).

Destination Based orbits would be the "political" interpretation of the above orbits.  There'd essentially be two main ways to classify them:
-Lunar-exclusive Staging Points
-Martian/Solar System Staging Points
A justification for Moon exploration is it serves as a precursor to Mars exploration (whether this is true is very debatable, but is extremely subject to political labeling).  However, the deeper your staging point is in the Lunar gravity well, the more of a hindrance it would be toward non-Lunar exploration.  Some orbits, however, could legitimately support both Lunar and Martian expeditions.

If you're knowledgeable about the intricacies of the Lunar gravity well and orbits, do post here.  Knowing what orbits make the most sense around the Moon seems a good idea, hence this thread.  I'll post my own opinions and what I know later.

[Steven Pietrobon]

With frozen orbits, one question I have is whether the orbital plane is fixed relative to the Lunar surface (that is the plane rotates relative to the stars with a 28 day period in the same direction as the Lunar surface), fixed relative to the stars, fixed relative to the Sun or moves in some other way. Anybody know and can give a reference?

[sdsds]

Pretty sure frozen orbits are fixed relative to the lunar mass concentrations; thus fixed relative to the surface.
https://science.nasa.gov/science-news/science-at-nasa/2006/06nov_loworbit

[sdsds]

 "Lunar Orbital Facility Location Options," at:
http://selenianboondocks.com/2016/04/lunar-orbital-facility-location-options/

Links to:
http://spirit.as.utexas.edu/~fiso/telecon/Whitley_4-13-16/Whitley_4-13-16.pdf

ISTM reading that makes a pretty good place to start.

[Steven Pietrobon]

Pretty sure frozen orbits are fixed relative to the lunar mass concentrations; thus fixed relative to the surface.
https://science.nasa.gov/science-news/science-at-nasa/2006/06nov_loworbit

That doesn't clarify if the orbits are Lunar synchronous. All it says is

"There are actually a number of 'frozen orbits' where a spacecraft can stay in a low lunar orbit indefinitely. They occur at four inclinations: 27º, 50º, 76º, and 86º"—the last one being nearly over the lunar poles."

That only gives the inclination of the orbits. With a Lunar synchronous orbit I think you would also need to specify the longitude at the Lunar equator the orbital plane crosses.

[Proponent]

Some lunar frozen orbits are nearly sun-synchronous.  In other words, the orbital plane rotates once per year with respect to the stars.  Such an orbit is obviously not lunar synchronous.

This doesn't prove that lunar-synchronous frozen orbits don't exist.  But such orbits would require precession rates 12 times greater.  My guess is that mascons can't do that.  But that's just a guess.

[redliox]

"Lunar Orbital Facility Location Options," at:
http://selenianboondocks.com/2016/04/lunar-orbital-facility-location-options/

Links to:
http://spirit.as.utexas.edu/~fiso/telecon/Whitley_4-13-16/Whitley_4-13-16.pdf

ISTM reading that makes a pretty good place to start.

Pretty sure frozen orbits are fixed relative to the lunar mass concentrations; thus fixed relative to the surface.
https://science.nasa.gov/science-news/science-at-nasa/2006/06nov_loworbit

That doesn't clarify if the orbits are Lunar synchronous. All it says is

"There are actually a number of 'frozen orbits' where a spacecraft can stay in a low lunar orbit indefinitely. They occur at four inclinations: 27º, 50º, 76º, and 86º"—the last one being nearly over the lunar poles."

That only gives the inclination of the orbits. With a Lunar synchronous orbit I think you would also need to specify the longitude at the Lunar equator the orbital plane crosses.

Some lunar frozen orbits are nearly sun-synchronous.  In other words, the orbital plane rotates once per year with respect to the stars.  Such an orbit is obviously not lunar synchronous.

This doesn't prove that lunar-synchronous frozen orbits don't exist.  But such orbits would require precession rates 12 times greater.  My guess is that mascons can't do that.  But that's just a guess.

Excellent findings!

During the Apollo era, flights 15 and 16 released subsatellites.  16's subsat was in an 11º orbit, and after only 35 days it crashed.  15's subsat was lucky, being in a 28º orbit (very close to the lowest inclined frozen orbit) and operated for a good year-and-a-half by comparison.  This would be an obvious example of choosing a good orbit (a frozen orbit more obviously).

A more modern example is the Lunar Reconnaissance Orbiter.  It's been circling the moon for over 7 years now in a low polar orbit with eccentricity that's brought it as low as 20 km.  Considering one frozen orbit inclination is at 86 degrees, I wouldn't be surprised if LRO occupies this slot closely (it was designed to last a year), given a 4 degree variation from a perfect 90 would still allow a thorough mapping of Luna (sadly only a listing of orbital altitude, not inclination, was on LRO's NASA websites).

The 2 inclinations that stand out the most to me would be 27º and 86º.  86, like with LRO, would allow for mapping and complete access to the whole Moon.  27, while primarily equatorial, is easier to access from Earth which would be vital for non-surface activity such as station construction or depot refueling (assuming, unlike LRO, the incoming spacecraft don't have reserves for extreme inclination adjustment).

As Steven pointed out (specifically on longitude), where a spacecraft would pass over the Moon is likely a big factor (especially if its a region with a large mascon anomaly).  I'm further curious how far the range of a frozen orbit could be.  The newly mentioned Near Rectilinear Orbits are near-polar as well but apparently range as far as 75,000 km; the article mentioned on Selenian Boondocks only specifies a "typical" frozen orbit ranging between 880 to 8,800 km but I'm under the impression now that frozen orbits can vary greatly including being either circular or elliptical, so long as their inclinations fall into a safe zone.

In regards to NASA's current decisions on orbits, it's clear the real limit is Orion itself...as well as politics.  The choice of distant or elliptical orbits aren't so much to take advantage of obscure math but to allow Orion close lunar encounters within SM's limited reserves.  During the initial "solo" missions this isn't a problem per say as it would grant the crew different views and even allow the deployment of new subsats (which nowadays we tend to call cubesats).  However, I don't think the extreme elliptical orbits are as practical to habitats/stations/depots; one large disadvantage of NROs or "frozen" polar ellipticals is access to the surface is difficult, even resulting in coverage of the pole opposite your landing/launch/base site (a railgun setup at the south pole ends up putting something into an orbit that favors the north pole in short).

[whitelancer64]

*SNIP*
A more modern example is the Lunar Reconnaissance Orbiter.  It's been circling the moon for over 7 years now in a low polar orbit with eccentricity that's brought it as low as 20 km.  Considering one frozen orbit inclination is at 86 degrees, I wouldn't be surprised if LRO occupies this slot closely (it was designed to last a year), given a 4 degree variation from a perfect 90 would still allow a thorough mapping of Luna (sadly only a listing of orbital altitude, not inclination, was on LRO's NASA websites).

The 2 inclinations that stand out the most to me would be 27º and 86º.  86, like with LRO, would allow for mapping and complete access to the whole Moon.  27, while primarily equatorial, is easier to access from Earth which would be vital for non-surface activity such as station construction or depot refueling (assuming, unlike LRO, the incoming spacecraft don't have reserves for extreme inclination adjustment).

As Steven pointed out (specifically on longitude), where a spacecraft would pass over the Moon is likely a big factor (especially if its a region with a large mascon anomaly).  I'm further curious how far the range of a frozen orbit could be.  The newly mentioned Near Rectilinear Orbits are near-polar as well but apparently range as far as 75,000 km; the article mentioned on Selenian Boondocks only specifies a "typical" frozen orbit ranging between 880 to 8,800 km but I'm under the impression now that frozen orbits can vary greatly including being either circular or elliptical, so long as their inclinations fall into a safe zone.
*SNIP*

"Sept. 15, 2009 the LRO orbiter spacecraft was moved into a polar-inclination of 89.7º circular 50 km mean altitude orbit"

https://directory.eoportal.org/web/eoportal/satellite-missions/l/lro

I can find no description of LRO's inclination after that date, so presumably it is still in a very similar orbit.

[redliox]

Pretty sure frozen orbits are fixed relative to the lunar mass concentrations; thus fixed relative to the surface.

Looking into that, the majority of Mascons are under the maria on the Near Side.  If the aim is to give the spacecraft (most likely a station or com sat) longevity, hugging the Near/Far terminator on the average Moon map would be the best strategy.  Mare Orientale and the South Pole-Aitken Basin are the next largest obstacles to be concerned about; regarding the later, if your spacecraft is meant to provide coverage of the south pole either its frozen orbit or NRO then its closest approach should be put over the north pole.

Outside of an orbit aligned with the terminator or accommodating the frozen orbital inclinations, L2 sounds like the best spot to utilize.  The main advantages are it can assist both Martian and Lunar ops and especially Far Side operations.  Biggest disadvantages are apparently travel time, not to mention a lander sent from any of the Lagrange points would require a larger fuel load (manageable depending on architecture).

[redliox]

"Sept. 15, 2009 the LRO orbiter spacecraft was moved into a polar-inclination of 89.7º circular 50 km mean altitude orbit"

https://directory.eoportal.org/web/eoportal/satellite-missions/l/lro

I can find no description of LRO's inclination after that date, so presumably it is still in a very similar orbit.

Oh thanks for finding that!  Apparently they can get very close to perfectly polar nowadays; presumably this wouldn't be a perfect frozen orbit but close enough that fuel meant for a year and be stretched to 7.

[redliox]

Ah...there is a limit to utilizing a polar frozen orbit like LRO: Lunar Prospector apparently found this out:

From https://science.nasa.gov/science-news/science-at-nasa/2006/06nov_loworbit

Alternatively, if there are mission reasons for choosing a non-frozen orbital inclination, plan to do frequent course corrections. Lunar Prospector had to do a maneuver every two months to keep itself in its initial circular orbit of 60 miles (100 km)—and more often than once a month when it was orbiting at only 20 miles (30 km) altitude

When I looked into Prospector's orbital inclination, it was cited at 90.5º.  Presumably the LRO would have a larger fuel supply not to mention flux back to 86 when it can.

[sdsds]

"Sept. 15, 2009 the LRO orbiter spacecraft was moved into a polar-inclination of 89.7º circular 50 km mean altitude orbit"

https://directory.eoportal.org/web/eoportal/satellite-missions/l/lro

I can find no description of LRO's inclination after that date, so presumably it is still in a very similar orbit.

I hope this is true! If Orion could park in that orbit a crewed lander should be able to get to the polar regions of interest with any-time abort capability.

My concern is that Orion can't get there (and back home) on its own.

[redliox]

"Sept. 15, 2009 the LRO orbiter spacecraft was moved into a polar-inclination of 89.7º circular 50 km mean altitude orbit"

https://directory.eoportal.org/web/eoportal/satellite-missions/l/lro

I can find no description of LRO's inclination after that date, so presumably it is still in a very similar orbit.

I hope this is true! If Orion could park in that orbit a crewed lander should be able to get to the polar regions of interest with any-time abort capability.

My concern is that Orion can't get there (and back home) on its own.

Pretty much.  Best bet, with current Orion capability specifically, would be to part it at a Lunar space station where there's a lander waiting.  It in turn would deliver a crew to/from the Moon and back to the station and Orion.  This is probably why there's all this emphasis on unusual yet distant orbits.

[Proponent]

The 2 inclinations that stand out the most to me would be 27º and 86º.  86, like with LRO, would allow for mapping and complete access to the whole Moon.  27, while primarily equatorial, is easier to access from Earth....

It's intuitively reasonable that reaching lunar polar orbit from LEO requires quite a bit more delta-V, but in fact it doesn't.  All you have to do is incline the trajectory outbound from Earth so that on arrival near the moon one is near a pole rather than the equator.  In other words, the trajectory need be inclined with respect to the moon's orbit by an amount equal to a couple of lunar radii divided by the distance between the Earth and the moon.  That's a few times (1800 km)/(380,000 km) = 0.00458 radians = 0.26^o. In other words, just do a plane change of a degree or so while doing the TLI burn, and you an reach polar orbit.

If, however, you want a free-return trajectory, then it gets more complicated (the attachment to this post has a nice analysis of free returns), and transit times increase.  I suppose that's why Constellation's plan for reaching high-latitude landing sites was to inject into a highly-elliptical, nearly equatorial orbit first and then chance inclination at the first apolune.

[redliox]

The 2 inclinations that stand out the most to me would be 27º and 86º.  86, like with LRO, would allow for mapping and complete access to the whole Moon.  27, while primarily equatorial, is easier to access from Earth....

It's intuitively reasonable that reaching lunar polar orbit from LEO requires quite a bit more delta-V, but in fact it doesn't.  All you have to do is incline the trajectory outbound from Earth so that on arrival near the moon one is near a pole rather than the equator.

So an orbit meant to support direct lunar activity could easily aim for the frozen inclinations of 76º and 86º or the NRO option.
 

If, however, you want a free-return trajectory, then it gets more complicated (the attachment to this post has a nice analysis of free returns), and transit times increase.  I suppose that's why Constellation's plan for reaching high-latitude landing sites was to inject into a highly-elliptical, nearly equatorial orbit first and then chance inclination at the first apolune.

If they can't do free-return that'd raise the need for either a space station or perhaps a surface base as a safe haven to aim for.  So an EM-3 flight that requires the free-return option would have to remain equatorial unless NASA/ESA feel reasonably confident about the ESM's propulsive (as well as ECLSS) capability.  We might better understand what to expect from the initial Orion visits.

[sdsds]

the attachment to this post has a nice analysis of free returns

Thanks for sharing that again! Of course what was true about orbital mechanics in 1963 is still true today!

The second class of free returns discussed in the paper is great. As you say they can pass by the Moon on what are very close to pole-to-pole trajectories. (That these exist is "easy" to see -- hah! -- based on the Theorem of Image Trajectories. Anybody could of thought of that! )

On a more general note: crew safety doesn't depend on outbound trajectories being truly "free return." Even if the main propulsion system fails Orion has (and likely any other Moon-bound spacecraft will have) an RCS capability that would provide "lots" of redundant delta-v. I think that might mean you wouldn't need the long delta-t to get safely to high inclination lunar orbits.

[redliox]

If, however, you want a free-return trajectory, then it gets more complicated (the attachment to this post has a nice analysis of free returns), and transit times increase.

Looking into the free trajectory info, there's apparently an option to do it at a high (polar-esque) inclination but at a distance of over 21,000 km.  Hard to interpret what they were saying but they implied there are 2 routes, one at a slight equatorial inclination and the second at a steeper polar one.  The former is what Apollo did.  The later would be of use to modern needs to explore the totality of the lunar surface.

[Proponent]

Here's a quick summary for those who have not waded through the paper.  Trajectories are analyzed in the rotating Moon-Earth frame, the moon's orbit being assumed circular.  Erect a rectilinear co-ordinate system in which the x-axis is the Moon-Earth line and the z-axis is normal to the Moon-Earth plane (MEP).  Only trajectories which are symmetric with respect to either the x-axis or the xz-plane are considered.   In the following discussion, inclinations are expressed with respect to the MEP, meaning that they'll differ by a few degrees from inclinations expressed with respect to the terrestrial or lunar equators. 

Free-return trajectories of the first kind are those for which perilune lies on the x-axis; the velocity vector at perilune will in general be inclined to the MEP.  The maximum lunar inclination possible is 10.8^o, and this requires a polar (with respect to the MEP) departure orbit from Earth.

Trajectories of the second kind are those for which the velocity vector at perilune is parallel to the MEP; perilune itself does not in general lie in the MEP.   These trajectories can have any inclination at the moon, but for each inclination only one perilune distance is possible.  Higher inclinations correspond to higher perilunes.  Reaching near-polar inclinations at the moon requires nearly polar departure orbits from Earth.

Co-planar trajectories (those which lie entirely in the MEP) are simultaneously of the first and second kinds.

Trajectories of either kind can be either circum-lunar (passing behind the moon) or cis-lunar (passing in front of it).  Trajectories can also be either co-rotating (departure orbit is eastward) or counter-rotating (departure orbit is westward).  I believe, though, that for current purposes there are no advantages to either cis-lunar or counter-rotating trajectories.  Apollo used co-rotating circum-lunar trajectories.

The paper shows transit times only for co-planar trajectories.  However, it does show that trip times increase significantly with increasing perilune distance, and I believe that will hold for non-co-planar trajectories as well.  A high-inclination free-return fly-by of the moon would entail a highly-inclined departure orbit and a round-trip lasting a few days longer than an equatorial fly-by.  In addition, perilune would be at a distance of about 30,000 km.

[sdsds]

MOSCOW, December 12. /TASS/. [...]the chief of the Manned Programs Center at the space industry’s main research institute, cosmonaut Oleg Kotov, has told TASS.

"The discussion over plans for creating an international station in the Moon’s orbit is in the initial phase. [...] Currently the station is seen as a small visitable orbiter consisting of three or four modules in the Moon’s polar highly elliptical orbit," he said.

This matches the description of an NRO.

http://tass.com/science/918631

[...]

In the Russian version of this TASS report, Roskosmos manned spaceflight department chief Sergei Krikalyov confirms that of the three orbits originally considered (low orbit, highly elliptical, libration point), the highly elliptical orbit is now the one being studied most closely.

[redliox]

MOSCOW, December 12. /TASS/. [...]the chief of the Manned Programs Center at the space industry’s main research institute, cosmonaut Oleg Kotov, has told TASS.

"The discussion over plans for creating an international station in the Moon’s orbit is in the initial phase. [...] Currently the station is seen as a small visitable orbiter consisting of three or four modules in the Moon’s polar highly elliptical orbit," he said.

This matches the description of an NRO.

http://tass.com/science/918631

[...]

In the Russian version of this TASS report, Roskosmos manned spaceflight department chief Sergei Krikalyov confirms that of the three orbits originally considered (low orbit, highly elliptical, libration point), the highly elliptical orbit is now the one being studied most closely.

NROs seem to be easy to access from Earth and have some stability, but from the perspective of either landing on the Moon or putting a space station in orbit around it I question their utility.  One advantage I can see is their long orbit would let a station/satellite/ect. loiter over one hemisphere and its pole, providing a steadfast relay; this would be especially useful for either polar or farside expeditions (presuming said-expedition is in the corresponding hemisphere).  The downside: during closest approach it would be screeching at blurring speeds over the Moon, making observations or deploying a lander difficult.