GRAIL (the Gravity Recovery and Interior Laboratory) was performing some gravity measurements per this link and found some interesting features called mascons.
Apparently, to provide more resolution(?), they had to drop the orbits pretty low. The article implies that is they didn’t fire their thrusters, we just might get a splashdown in a mare.
Orbital decay around earth is pretty obvious–atmosphere causes drag, which eventually causes the orbit to become lower and lower to the point that it burns up. The moon, having no atmosphere (or a very tenuous one), should allow for an indefinite orbit (well, relative to earth anyway) even at low altitude. (Re: The orbit of Apollo 10’s LEM got down to roughly 10 miles above the moon, IIRC).
So what’s the dope on this? What would be the mechanism of lunar orbital decay?
There’s a concept called the “Hill Sphere” which signifies the volume around an object in which a satellite of that object will remain in orbit. The moon is in the Earth’s Hill Sphere, so the moon orbits the Earth and is not lost to the Sun. The Moon’s Hill Sphere is considerably smaller than the Earth’s, so to stay in orbit around the Moon (and not be ‘pulled away’ into Earth orbit) any satellite of the Moon would have to be orbiting pretty low. Unfortunately, this puts the satellite well into the area in which tidal forces cause orbital decay, so there are no long term stable orbits around the moon. And as you say, the mascons don’t help either.
There are four inclinations with stable orbits around the Moon. Compare the results for PFS-1 and PFS-2, small satellites placed in Lunar orbit in the early 1970’s by the Apollo program:
ETA: Here’s a direct link to the NASA site the Wikipedia page cites for the above.
Zenbeam - thanks. Looks like the existence of these orbits is based on the moon’s deviation from sphericity, which is an important factor I didn’t discuss in my earlier post. The closer to the Moon an orbit is, the more important the details of the shape of the Moon will be to the stability or instability of an orbit. This is probably a bigger factor for artificial satellites than the tidal effects I mentioned earlier.
The sun’s tidal forces on the earth/moon system, is considerably less by comparison. However I don’t know if it’s weak enough to dismiss when it comes to factoring stable, low lunar obits.
I was refering to the tides due to the moon’s gravity on the satellite, but as I said I think the effects of the moon’s non-spherical shape are more important than the tides.
When I think of tides, my heritage is the earth’s oceans being influenced being influence by the sun and moon. So, in other words, the result of forces *external *to the earth. You’re suggesting that there’s an *internal *one. That’s what I don’t understand: what is that? A gravity gradient the satellite traverses through during the orbit? Or is it something else?
The Earth’s ocean moves in response to the tidal forces from the moon and the sun, with the moon causing most of the movement. The moon would also exert tidal forces on any satellite that the Moon happened to have; these tidal forces would tend to align the satellite so that it was oriented pointing towards the moon (the more elongated and flexible the satellite, the more rapidly such alignment would occur) (see Gravity-gradient stabilization - Wikipedia and Tidal locking - Wikipedia).
Because the moon’s orbital motion is slower than the Earth is rotating, the tidal forces of the moon on the earth tends to transfer angular momentum from the Earth to the Moon, so that the Earth rotates more slowly, and the Moon moves outward from the Earth (orbiting more slowly, but with more angular momentum because of the increased distance between the Earth and Moon).
However, the moon rotates very slowly, and any satellite of the Moon that was anywhere near the moon would orbit more quickly than the Moon rotates. In that circumstance the tidal interaction between the moon and its satellite will result in the Moon gaining angular momentum (rotating faster) and the satellite orbiting lower (losing angular momentum) resulting in an eventual crash into the moon (this is what’s going to happen to one of Mars’ moons). But the angular momentum transfer between the Moon and an artificial satellite is likely to be very slow - because an artificial satellite will be low in mass and small in diameter. The Moon’s asymmetry will be a much bigger disturbance on low-Moon orbits than the tidal interaction will be (I think).
The typical ideal orbit is a nice ellipse around a point source of mass. However, the whole point of mascons was that the moon was not an ideal point-source gravitational body. As the satellite approaches the mascons it speeds up slightly, which can also change its trajectory slightly. As a result, the orbit is somewhat eratic. If your talking about lunar orbits 50 or 100 miles up, so what? If you get down to a few miles above the surface, there’s the risk this change could change the orbit and bring it close enough to impact some mountains or set it off center a bit.
Then there’s the effect that the earth keeps pulling on the satellite too. as a result, the orbit would be pulled out of shape, it might look more like the petals of a flower, constantly precessing the high point (apogee?) of the orbit as the direction of the earth changes wrt the orbit.
Again, as long as the orbit rattles around with 50 or 100 miles of clearance, does not matter. If you get down to a few miles altitude - possible problems. I kinda question the “rattled the spaceship” assertions; but a lunar lander on a very fast flat low trajectory does not suddenly need to find it is going down faster than expected as it goes over an area of higher density.
The energy lost to tidal action (sloshing the oceans) as mentioned, is taken from the energy of the moon’s motion around the earth; as a result, some of the energy bleeds off, the moon slows down, and eventually (eons hence) will crash into the earth. (Plus, some energy is lost from the earth’s rotation and it is slowing down.)
Orbital decay around earth is due to the tenuous but real atmospheric drag at those high altitudes; famously, even the SkyLab and Mir lost enough energy to fall to earth after a decade or more. Being a very light tin can with giant solar panel sails did not help the problem.
One way to look at it is the position of periapsis: the closest approach point to the Moon. In a non-uniform gravitational field, this point drifts. Most famously with Mercury around the Sun. Note that one of the lesser forces there is the oblateness of the Sun.
Due to the Moon’s non-ideal gravity, this point can drift all over, shifting eccentricity, tilt, etc. Small differences going in and out of the “gravity well” of an elliptical orbit add up over time, especially.
Yep. In fact, if the solar system lasted long enough, the Earth would end up with a “day” lasting about 1150 hours (about a month and a half) and the Moon would orbit about 40% farther from the Earth than currently with an orbital period of 1150 hours as well. That’s the lowest energy condition for the Earth-Moon system under the constraint of conserving angular momentum.
Though, strictly speaking, angular momentum isn’t perfectly conserved for the Earth-Moon system, either, as there are a few processes which can (very slowly) carry away angular momentum, too. There’s trace amounts of friction with the interplanetary medium, and “dynamical friction” due to gravitational interactions with other Solar System objects, and gravitational radiation, and electromagnetic radiation from the interaction of the Earth’s magnetic field with the Sun’s. All of these, of course, are extremely small compared to the angular-momentum-conserving effects, though.
Heh. I spent a good ten minutes crafting my one line post, deciding whether to mention gravitational radiation, pondering whether gravitational interactions with other bodies would slow the system, and how do I fit in the Sun becoming a red giant and probably swallowing the Earth (which, I’ll point out, Chronos completely ignored).
Of course, I would have totally missed EM radiation from interactions between the Earth’s and the Sun’s magnetic fields. But fortunately, I finally just said “fuck it”, and carefully limited my response to just tidal interactions between the Earth and Moon.
Agreed. What may be the biggest factor is the tides from the Sun which transfer angular momentum from the Earth-moon system (slowing the earth’s rotation, primarily) to the Earth’s orbit (making the Earth orbit further from the Sun).
On the contrary, I’ve worked on satellites as an avionics engineer*. So I do have a rudimentary understanding of the fore mention discussion. If I really want to dig into the topic, I’ll go to Amazon and download a textbook and work through the problems.
If I wanted to. I was looking for instant gratification.
*As an example of subtle problems involving orbits: the realization that a geosynchronous satellites broadcast beams asserts a small force (in the billionths of Newtons) away from earth; hence, the spacecraft orbit is raised (and thus slows down). So when performing a station-keeping maneuver in order to stay within a designated “slot”, (the satellites will drift in an increasingly elongating figure 8 fashion over time, eventually into another designated slot) part of the maneuver ameliorates this teeny weensy effect.
