...是月亮寶寶?🌛
The Moon’s Moon is a Moon?
月亮 -- 一個掛在夜空中獨一無二的存在，圍繞著地球並承載著故事。
The Moon - the one and only, orbiting the Earth and carrying the tales.
但其實天然衛星是一種很常見的物種，太陽系中就有超過200個，而且仍在增加。然而，儘管經過了幾個世紀的觀察，我們還沒有發現月亮有自己的月亮 – 亞月球。
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，亞月球真的是一個可能性嗎?
So, is sub-moon even a possible option?
圖來自NASA的火星及其兩個衛星被調色後的照片
Colour altered image of Mars and its two moons from NASA
星際管轄區
The Interstellar Jurisdictions
這知道答案，最重要的問題是物體與主宿星球之間的距離，也就是月球與地球的距離，或在這裡，月球與亞月球之間的距離。圍繞主宿的月球必須嚴格在主宿星球周圍的特定範圍內（希爾球內，洛希極限外）。
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.
希爾球是衛星與主宿星球距離的上限。在希爾球內時，影響衛星的主要引力來自主宿，而距離超過希爾球界限後的外殼被稱為零速度面。在那以後，在主宿軌道星球上的物體很可能被拋入太空，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-月關係而言，月球處於地球的希爾球內，因而受地球引力的控制。否則，它就會被太陽的引力控制，然後被甩到太空中的某個角落。
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.
另一邊的洛希極限，是衛星與主宿星球之間所需保持的最小距離。如果離得太近，衛星的命運會很快地走向盡頭，因為它會被主宿星球的潮汐力撕裂。潮汐力是因為物體近側的引力遠強於遠側而產生的。
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，如果踏過了界限，衛星內部的重力將不再能夠承受更強的外部拉力。土星周圍的光環很可能就是這樣形成的。
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.
圖為月球與地球的距離和它適合的區域，紅線代表希爾球，藍線代表洛希極限
The Moon within the red Hill sphere of Earth and outside of the blue Roche limit
距離產生美
Distance Creates Beauty
因為更大的物體往往能夠用它的引力影響到更遠的物體，它們希爾球的也就更大了，也就有更大的空間範圍來容納月球。這就是為什麼木星和土星都有那麼的追隨者了。
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.
圖為從NASA的卡西尼號飛船上看到正在發生季節性變化的土衛六在土星之前的自然顏色照片
The natural color view of Titan appearing before Saturn while undergoing seasonal changes, image from NASA's Cassini spacecraft
要讓月球有亞月球，月球自己需要與行星保持足夠大的距離，這樣行星的引力才不會過於強勢而『消滅』月球的希爾球。但可惜這正是天王星和海王星的衛星們所面臨的問題，因為它們的軌道都離行星太近了，以至於它們都沒有了自己的空間。
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.
就像我們人類一樣，我們需要給彼此足夠的空間，這樣我們才不會傷害到彼此；但同時，我們也要保持互相的關愛，這樣才能一家人和和睦睦。平衡是關鍵!
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!
圖為2001年NASA的伽利略號拍攝了木衛四的照片，是1995年開始繞木星運行的伽利略號獲得的唯一一張完整的木衛四彩色圖像。在木星最大的四顆月球中，木衛四的軌道是離這顆巨行星最遠。科學家們認為，圖中較亮的區域主要是冰，較暗的區域是被嚴重侵蝕的缺乏冰的物質。
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.
稀有的安全區
The Rare’s Safe Zones
了解了亞衛星的基本存在條件，美國和法國的兩位天體物理學家Juna A. Kollmeier和Sean N. Raymond對亞衛星的潮汐動力學穩定性進行了研究。換句話說，亞衛星的安全地帶。
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，他們為多個行星繪製了不同的月球-行星距離和衛星大小的關係圖，然後分析了不同大小亞月球適合的不同月球區域。
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.
這些區域是根據亞月球的固定質量和月球的各種關鍵特性計算出來的。其中最重要之一是月亮的潮汐質量因數- Qmoon，這個數字代表了不同密度的物體對潮汐力的反應;一般巖石天體的Qmoon值是100，而恆星的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.
研究小組發現，在太陽系所有的月球中，只有木衛四（木星月球之一）、土衛六（土星月球之一）和土衛八（土星月球之一）以及地球自己的月球具有為亞月球安家的能力。不過，在我們的太陽管轄範圍外，研究小組還發現，最近發現的系外行星克卜勒-1625b也有一顆能夠容納亞月球的月球。
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.
研究小組的數值模型還表明，較小的亞月球對主宿月球的大小和與行星的距離的要求都更寬容；更大的Qmoon值也代表了更寬泛的「宜居帶」。
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.
圖為不同衛星大小和它們與主宿星的距離的關係圖，灰色區域代表了月球可以穩定容納半徑為10km的亞月球的區域，段線和點線分別代表了20km和5km半徑的亞月球。只要在線的右上角，月球就有機會擁有亞月球。
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
有人可能會問，如果亞月球在理論上是可以存在的，那亞月球是否也可能有它們的月亮 – 亞次月亮？
One might wonder, if sub-moons are theoretically possible, can sub-moons also have their moons – subsubmoons?
根據之前的多個研究，亞月球通常要比它們的主宿星球小1萬倍左右。因此在太陽系中，最大的亞月球半徑只有10公裡，而它們最大的亞次月球半徑會在1公裡以下。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!
另一個問題是：如果有些月球是能夠擁有自己的月球的，為什麼它們現在都沒有呢？
One other question is: if some moons are capable of hosting sub-moons, why aren’t they?
有幾種可能的原因。首先，兩位物理學家這次的研究只考慮了穩定的亞月球的可能性，可能導致亞月球偏離軌道的因素不全在考慮範圍內。比如，我們月球的軌道就會受到太陽和地球微擾。
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.
還有一種可能就是，先前存在的亞月球由於各種原因被移除了。有一種理論認為，土星的土衛八在赤道上有一個明顯的脊，它是由自身與其他物體碰撞後形成的。碰撞中形成了一顆亞月球和一些碎片，然後這顆亞月球被推入太空了，而碎片落了下來形成了山脊。
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.
儘管我們還沒有找到任何亞月球，
但這並不意味它們不存在。
那就讓我們在亞月球最有可能出現的
大型月球旁繼續我們的探索吧！
希望在不久的將來我們能遇見這些新物種!
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!
圖為木星及其兩個最大的衛星 -- 木衛一和木衛二的彩色增強圖，這是NASA的朱諾號飛船在第八次飛過這顆氣態巨行星時拍攝的。
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.
長按關注 勿裡補說 公眾號，
了解物理點滴
圖片來自 NASA官網以及以下論文
文中部分英文信息參考來自美國和法國的Juna A. Kollmeier和 Sean N. Raymond的 「Can Moons Have Moons?" 論文
其餘中英文內容為原創
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