月亮的月亮是月亮宝宝?🌛 The Moon’s Moon is a Moon?
月亮 -- 一个挂在夜空中独一无二的存在，围绕着地球并承载着故事。
The Moon - the one and only, orbiting the Earth and carrying the tales.
但其实天然卫星是一种很常见的物种，太阳系中就有超过200个，而且仍在增加。然而，尽管经过了几个世纪的观察，我们还没有发现月亮有自己的月亮 – 亚月球。
With more than 200 of them and still accounting, natural satellites are actually common species in the Solar System. However, despite centuries of observation, no moons have yet to be found with them own moon.
所以，亚月球真的是一个可能性吗?
So, is sub-moon even a possible option?
图来自NASA的火星及其两个卫星被调色后的照片
Colour altered image of Mars and its two moons from NASA
星际管辖区
The Interstellar Jurisdictions
这知道答案，最重要的问题是物体与主宿星球之间的距离，也就是月球与地球的距离，或在这里，月球与亚月球之间的距离。围绕主宿的月球必须严格在主宿星球周围的特定范围内（希尔球内，洛希极限外）。
The most important condition to consider is its distance to its host, so the distance between the moon and Earth, or in this case, the sub-moon to the moon. They have got to be within the delicate region, between host’s Hill sphere and Roche limit, which is a range of radii in space around the celestial body.
希尔球是卫星与主宿星球距离的上限。在希尔球内时，影响卫星的主要引力来自主宿，而距离超过希尔球界限后的外壳被称为零速度面。在那以后，在主宿轨道星球上的物体很可能被抛入太空，不再被主宿的引力所限制。
The Hill sphere acts as the outer most limit. When within the Hill sphere, the gravitational force on the satellite is dominantly from the host. The outer shell beyond the Hill sphere is called a zero-velocity surface, after which, the orbiting object is very likely to be flung into space rather than being constrained by the host.
就日-地-月关系而言，月球处于地球的希尔球内，因而受地球引力的控制。否则，它就会被太阳的引力控制，然后被甩到太空中的某个角落。
In terms of the Sun-Earth-Moon relationships, the Moon is within the Earth’s Hill sphere and therefore controlled by our gravitational pull. Otherwise, it would have been under Sun’s gravitational pull and who know where it might end up.
另一边的洛希极限，是卫星与主宿星球之间所需保持的最小距离。如果离得太近，卫星的命运会很快地走向尽头，因为它会被主宿星球的潮汐力撕裂。潮汐力是因为物体近侧的引力远强于远侧而产生的。
The Roche limit on the other side, is the minimal distance that needed between the two objects. Being too close would lead to the end of the moon’s lifetime, as it gets torn apart by the host’s tidal forces. The tidal forces are the results when the gravitational pull on the near side of the object is much stronger than the far side.
因此，如果踏过了界限，卫星内部的重力将不再能够承受更强的外部拉力。土星周围的光环很可能就是这样形成的。
So, if approached further, the satellite’s internal gravity would no longer be able to withstand the stronger outer pulls. Rings around Saturn are every likely to have been formed like this.
图为月球与地球的距离和它适合的区域，红线代表希尔球，蓝线代表洛希极限
The Moon within the red Hill sphere of Earth and outside of the blue Roche limit
距离产生美
Distance Creates Beauty
因为更大的物体往往能够用它的引力影响到更远的物体，它们希尔球的也就更大了，也就有更大的空间范围来容纳月球。这就是为什么木星和土星都有那么的追随者了。
Since larger objects are more likely to have gravitational influences over large distances, they also have larger Hill spheres, therefore larger range of space to host potential moon. Hence why Jupiter and Saturn having more followers.
图为从NASA的卡西尼号飞船上看到正在发生季节性变化的土卫六在土星之前的自然颜色照片
The natural color view of Titan appearing before Saturn while undergoing seasonal changes, image from NASA's Cassini spacecraft
要让月球有亚月球，月球自己需要与行星保持足够大的距离，这样行星的引力才不会过于强势而‘消灭’月球的希尔球。但可惜这正是天王星和海王星的卫星们所面临的问题，因为它们的轨道都离行星太近了，以至于它们都没有了自己的空间。
For moons to host sub-moons, they need to be at a large enough distance to the planet, so the planet’s gravitational force is not overpowering the moons’ Hill spheres. But unfortunately, this is the problem faced by Uranus and Neptune’s moons, as they are all orbiting too tightly for their mother planet to have their own space.
就像我们人类一样，我们需要给彼此足够的空间，这样我们才不会伤害到彼此；但同时，我们也要保持互相的关爱，这样才能一家人和和睦睦。平衡是关键!
Just like us humans, enough space needs to be given to each other, so we do not destroy each other, but at the same time also stay connected to still be together as a family. Balance is the key!
图为2001年NASA的伽利略号拍摄了木卫四的照片，是1995年开始绕木星运行的伽利略号获得的唯一一张完整的木卫四彩色图像。在木星最大的四颗月球中，木卫四的轨道是离这颗巨行星最远。科学家们认为，图中较亮的区域主要是冰，较暗的区域是被严重侵蚀的缺乏冰的物质。
NASA's Galileo captured this image of Callisto in 2001, and is the only complete global color image of Callisto obtained by the spacecraft, which began orbiting Jupiter in 1995. Of Jupiter's four largest moons, Callisto orbits the farthest from the giant planet. Scientists believe the brighter areas in the image are mainly ice, while the darker areas are heavily eroded ice-poor material.
稀有的安全区
The Rare’s Safe Zones
了解了亚卫星的基本存在条件，美国和法国的两位天体物理学家Juna A. Kollmeier和Sean N. Raymond对亚卫星的潮汐动力学稳定性进行了研究。换句话说，亚卫星的安全地带。
Knowing the basic existence conditions of the sub-moons, two astrophysicists from USA and France: Juna A. Kollmeier and Sean N. Raymond, investigated the tidal-dynamical stability of sub-moons. In another words, the safe zones for sub-moons.
首先，他们为多个行星绘制了不同的月球-行星距离和卫星大小的关系图，然后分析了不同大小亚月球适合的不同月球区域。
First plotting the different moon-planet distances and size of the moons for multiple planets, the physicists then found the region suitable for moons to have sub-moons of different sizes.
这些区域是根据亚月球的固定质量和月球的各种关键特性计算出来的。其中最重要之一是月亮的潮汐质量因数- Qmoon，这个数字代表了不同密度的物体对潮汐力的反应;一般岩石天体的Qmoon值是100，而恒星的Qmoon值是106。
Those regions were calculated with fixed mass of theoretical sub-moons and various key properties of the host moon. One of those being the moon’s tidal quality factor – Qmoon, which is a number for how a specific body with certain density reacts to tidal forces; general rocky bodies have Qmoon= 100, while stars are around 106.
研究小组发现，在太阳系所有的月球中，只有木卫四（木星月球之一）、土卫六（土星月球之一）和土卫八（土星月球之一）以及地球自己的月球具有为亚月球安家的能力。不过，在我们的太阳管辖范围外，研究小组还发现，最近发现的系外行星开普勒-1625b也有一颗能够容纳亚月球的月球。
Of all moons studied within the Solar System, the team found that only Callisto (Jupiter), Titan and Iapetus (Saturn), and Earth’s own Moon are capable to host sub-moons. However, outside our local star’s jurisdiction, the team found that the recently discovered exoplanet Kepler-1625b also have a moon capable of hosting sub-moons.
研究小组的数值模型还表明，较小的亚月球对主宿月球的大小和与行星的距离的要求都更宽容；更大的Qmoon值也代表了更宽泛的“宜居带”。
The team’s numerical modeling suggests that smaller sub-moons can exist over a broader range of moon sizes and distance to their planet; and larger Qmoon means more ‘habitable zone’ of sub-moons.
图为不同卫星大小和它们与主宿星的距离的关系图，灰色区域代表了月球可以稳定容纳半径为10km的亚月球的区域，段线和点线分别代表了20km和5km半径的亚月球。只要在线的右上角，月球就有机会拥有亚月球。
The relation between the radius of moon around different planets and its distance from that planet. The gray region shows where the moon could stably host a submoon with radius 10 km, while dashed line and dotted line shows 20km and 5km radius sub-moons respectively. Moons have the potential of hosting a sub-moon if its on the upper right hand side of the line
一切皆有可能
Everything is Possible
有人可能会问，如果亚月球在理论上是可以存在的，那亚月球是否也可能有它们的月亮 – 亚次月亮？
One might wonder, if sub-moons are theoretically possible, can sub-moons also have their moons – subsubmoons?
根据之前的多个研究，亚月球通常要比它们的主宿星球小1万倍左右。因此在太阳系中，最大的亚月球半径只有10公里，而它们最大的亚次月球半径会在1公里以下。太小了！
Using previous studies, sub-moons generally have to be roughly 10 thousand times smaller than their host. Therefore, with largest possible sub-moons in the Solar System having only ~10km in radius, their largest subsubmoons would be sub-km-sized. Too small!
另一个问题是：如果有些月球是能够拥有自己的月球的，为什么它们现在都没有呢？
One other question is: if some moons are capable of hosting sub-moons, why aren’t they?
有几种可能的原因。首先，两位物理学家这次的研究只考虑了稳定的亚月球的可能性，可能导致亚月球偏离轨道的因素不全在考虑范围内。比如，我们月球的轨道就会受到太阳和地球微扰。
There are several possible explanations. First of all, the study did by two physics only considered the possibilities of stable sub-moons, factors that could cause instabilities of the sub-moon’s orbit may not be considered. For example, the orbits around the Earth’s Moon are subject to perturbations caused by the Sun and Earth.
还有一种可能就是，先前存在的亚月球由于各种原因被移除了。有一种理论认为，土星的土卫八在赤道上有一个明显的脊，它是由自身与其他物体碰撞后形成的。碰撞中形成了一颗亚月球和一些碎片，然后这颗亚月球被推入太空了，而碎片落了下来形成了山脊。
There is also the possibility of sub-moons previously existing and for various reasons have been removed. One theory of Saturn’s Iapetus having a significant ridge along its equator is that it came from a collision of itself and something else, which formed a sub-moon and some debris. Later the debris fell back to from the ridge while the sub-moons got pushed away into space.
尽管我们还没有找到任何亚月球，
但这并不意味它们不存在。
那就让我们在亚月球最有可能出现的
大型月球旁继续我们的探索吧！
希望在不久的将来我们能遇见这些新物种!
Though we haven’t seen any sub-moons yet,
does not mean they are impossible.
With sub-moons most likely to appear
next to large moons,
we will continue our search,
hoping to see them in the near future!
图为木星及其两个最大的卫星 -- 木卫一和木卫二的彩色增强图，这是NASA的朱诺号飞船在第八次飞过这颗气态巨行星时拍摄的。
The color-enhanced image of Jupiter and two of its largest moons -- Io and Europa, which was captured by NASA's Juno spacecraft as it performed its eighth flyby of the gas giant planet.
图片来自 NASA官网以及以下论文
文中部分英文信息参考来自美国和法国的Juna A. Kollmeier和 Sean N. Raymond的 “Can Moons Have Moons?" 论文
其余中英文内容为原创
Images from official website of NASA and the below article
Parts are sited from “Can Moons Have Moons?" by Juna A. Kollmeier and Sean N. Raymond from USA and France
The rest of the Chinese and English content are original
