# A moon that is hard to orbit

I had a dream last night where I was coordinating a space program for an Earth-like planet, with a Moon much like our own. The Moon in the dream had an annoying quirk...

The space program kept sending hundreds of probes to try and orbit the Moon. Each probe managed to complete no more than a handful orbits around the Moon (each orbit taking a few hours). But the orbits quickly destabilized. For every one hundred probes:

• Ninety would end up escaping the Moon and going into a solar orbit;
• Eight would escape the Moon and stay orbiting the Earth. Of these eight, one would have a periapsis low enough to eventually burn in Earth's atmosphere;
• One would go suborbital and crash against the Moon;
• And finally, only one would managed to stay orbiting the Moon.

Outside of dreams, is there any scenario for an Earth-like planet in which this could happen? If this is not possible with an Earth-like planet and a Moon like our own, would this be possible with if the Moon had other combination of mass, size and distance to Earth?

I am aware of this question:

How can you make a stable configuration including a moon that has a moon?

But in my case I am thinking of probes, not natural satellites.

• Maybe if the moon has a very unbalanced gravitational field and the Space Program doesn't know/realize it. – RonJohn Apr 30 '18 at 13:51
• Our very own Moon is a good example. When humans began sending probes to the Moon they noticed that almost all orbits are unstable. It took decades until space exploration agencies discovered the only four possible inclinations for a stable Lunar orbit. – AlexP Apr 30 '18 at 14:44
• Well, if the probes kept crashing I would say the Moon Men were shooting them down. But if they are going off at crazy angles that doesn't make as much sense. – Hot Licks May 1 '18 at 1:02
• The moon has a molten core that isn't in the center of the moon, and as the moon spins it does so off axis. The core interacts with the Earth's gravity causing the position of the core to shift over time, and change the axis of spin. Since the core is inside the moon. The shifts can't be predicted as they are unseen. – Reactgular May 1 '18 at 14:02

That's plenty possible.

In fact, if you're willing to fudge your requirements just slightly, it could easily be the case for Earth's moon.

Let's look at the equation for orbital speed, also known as the vis-viva equation

$$v = \sqrt{\mu \left( \cfrac{2}{r} - \cfrac{1}{a} \right)} \approx \sqrt{\cfrac{\mu}{r}}$$

where $\mu$ is the standard graviational parameter, $r$ is the orbital radius at the moment you're calculating the orbital speed, and $a$ is the semi-major axis of the orbit. For any practical orbital calculations, the standard gravitational parameter $\mu$ is a constant for any given body, because it is the multiplicative product of a constant and the mass of the body being orbited. For the special case of a perfectly circular orbit (eccentricity = 0; you're unlikely to come across this in real life, but lots of orbits have eccentricities pretty close to zero), we have $a = r$, leading to the simplified, approximate expression.

Notice that in both cases, we're treating the body being orbited as a point source of a gravitational field of a magnitude described by $\mu$.

That's good enough if the body we're orbiting has an essentially uniform gravitational field, but there are bodies that don't. Earth's moon is one good example of a rather large body with a non-uniform gravitational field:

Look at that variance! We're seeing significant variance already in the third significant digit. Between dark blue and white on that scale is a difference in surface gravitational accelleration of over 1.5%.

In fact, the perturbation effects resulting from this are enough to make it difficult to attain a frozen orbit (a long-term stable orbit that minimizes station-keeping requirements) around Earth's moon. When the Apollo missions flew to the Moon in 1968-1972, these were unknown, so active orbital corrections and estimations of orbital degredation were used instead. The estimations turned out to be wrong, and active orbital correction requires fuel, which limits the useful life of the spacecraft in orbit. The frozen orbits were discovered (or perhaps rather, determined) only in 2001, almost 30 years after our first bout of manned exploration of the Moon ended.

While I'm not sure you could actually put a spacecraft into a lunar orbit and end up with it in solar orbit with no further powered maneuvers, you could put the one spacecraft that stays in its intended orbit into an orbit at inclination 27°, 50°, 76° or 86°, and the rest in other orbits, around a body exactly like Earth's moon, and you'll mostly get what you're after. Also, make sure to have your scientists in-story have frustrated discussions about mascons.

A lumpy moon has a lumpy gravitational field and orbits are, well, lumpy also and frequently not stable.

This has been an issue in putting satellites in orbit around comets and asteroids, and even around our own Moon, though there it's only an issue for very low orbits. (Unsurprisingly, the solution is to actively correct the orbit.)

For a moon to be significantly lumpy, it needs to be small (like an asteroid) or otherwise gravity would soon make it spherical.

• "gravity would soon make it spherical." - This is true, but this "soon" is geological soon, not human soon and could take significant time. Put the lump on the dark side and that's it ;) – Mołot Apr 30 '18 at 14:07

Our moon has a very weak magnetosphere, but it does have magnetic rocks, which surprised scientists because it suggests a time when it had a stronger magnetic field. That issue is discussed here.

With that as inspiration, let's assume a younger solar system with a younger moon with a highly viscous fluid outer core sloshing around an abnormally dense iron core. Let's also assume that this confuration has kept the moon from becoming tidally locked to the planet, so that it can rotate much faster.

This would give it a much stronger magnetic field, which could cause all kinds of havoc with probes: from yanking their magnetic frames around to messing with the navigation electronics and power system.

(For the record, I like Mark's answer better as I believe it would be much harder to detect and, therfore, harder to compensate for.)

• How could civilization arise on a planet after billions of years and send space probes to that planet's moon that was significantly younger than Earth's Moon? – M. A. Golding Apr 30 '18 at 19:07
• @M.A.Golding, I edited the answer to clarify. However, considering two of the three prevailing theories about lunar history require our own moon to be younger than our own planet, the answer to your question is, "easily." – JBH Apr 30 '18 at 19:17

If moon's Hill sphere is less that moon's radius, then it would be impossible to have stable orbit around it.

Our Moon has its Hill sphere with a radius of 60,000 km. If you bring it near Roche limit(20x times closer to Earth) then moon's Hill sphere would be 3,000 km - less than Moon's radius.

If you can make Moon less dense then you can place it father away.

• Wouldn't it also be impossible for the moon to hold itself together in the case you're describing? – a CVn May 1 '18 at 8:40
• Inside the Roche limit a moon would indeed be pulled apart, but very near the limit the moon itself would still be stable, but high orbits would be impossible. Very low orbits would be made unstable by a non-uniform gravity field. – JanKanis May 1 '18 at 13:08
• @JanKanis:, Or set it just within its own hill sphere; radius 60,000km; hill sphere 59,900km. Attempting to place an object in lunar orbit results in that object being ejected or deorbited into earth. Rock has some integrity; the moon won't break up. – Joshua May 1 '18 at 15:10