你有想過住在第九行星上是什麼樣子嗎？（中英文）

06-01

自我鑒別、理性評論、切勿迷信

想必你已經聽過很多關於第九行星的資訊？若沒有的話，以下有幾項關於第九行星(Planet Nine)的重點：

古柏帶(穿越冥王星)中有許多天體。雖然古柏帶也是繞著太陽運行，但在某些程度上聚集在太陽系的一側。

古柏帶天體的運行可藉由未知的「第九行星」的引力影響來解釋。

第九行星可能不是最棒的名稱。我建議能用些更酷的名字像是屌行星，或是神奇寶貝行星。

依古柏帶天體的運行，可以推測第九行星的運行半軸長為700天文單位(一天文單位相當於地球與太陽的距離)，運行周期為10,000到20,000年。

據估計，第九行星的質量為6 x 1025 公斤( 質量較地球大)。行星半徑為13,000到26,000公里(地球半徑為6371公里)。

現在我們對於這個「理論上」存在的行星有一些初步的了解，接著就來思考一些問題吧！

NASA的新視野號需多久才能抵達第九行星？

雖然新視野號並不是以等速運行，我還是能以大約16公里/秒(16000公尺/秒)的速度估計。如果這個太空飛行器設定目標為第九行星與太陽最近距離的時候，那運行距離大約是200天文單位(2.99 x 1013 公尺)。現在我們也可以將這個平均速度用一般的定義理解(在一維空間里)。

我把1.87 x 109 秒換算成年(你可以在做課後作業時再計算)，得到59.3年。若是以第九行星離太陽最遠(1200天文單位)的可能性計算，我算得的運行時間為355.7年。喔！第九行星離太陽的距離大約和地球到第九行星的距離相等。不過我們若要真的發射一個太空飛行器飛越第九行星的話，我們可能得先找一個年輕的科學家，或是造一個更快的太空飛行器。

在第九行星上能行走嗎？

假設第九行星的表面為固體，除了覺得冷之外，行走在上面會是什麼感覺呢？這跟表面的重力場有關。在地球的表面，重力場為每公斤9.8牛頓。既然我們都知道身在地球表面的感覺，這個數據很適合拿來做對比。

一個行星的表面重力場跟兩項東西有關(恩，至少兩項)：行星的質量與行星的半徑。行星質量越大，重力場就越大。而當行星的半徑越長，重力場就越小(因為你離中心越遠)。表面重力場的大小可以這樣得到：

用第九行星的最大與最小半徑估算，我算得重力場大約為5.9到23.7牛頓/公斤。所以在第九行星上行走有可能和在地球上一樣(不過冷多了)。但重力場若真的是23.6牛頓/公斤的話，那走起路來可能就沒那麼容易了！

在第九行星的表面上有多冷？

讓我們假設第九行星沒有大氣。這個假設很重要，因為我們都知道一個行星的大氣對錶面溫度有非常大的影響(例子像是金星、地球、火星)。還有假設太陽是一個黑體(所有的輻射是從表面溫度而來)，那麼就能計算太陽的輻射能。如果輻射能量平均地從各個方向發出，光的強度會減少因為1除距離的平方。

當一行星接收太陽的輻射時，表面溫度會上升，同時也成為一個黑體輻射體。在接收到的輻射與放出的輻射相等時，行星的溫度會達平衡。這其中牽涉到一些數學計算，但大致上概念是這樣。以這個溫度模型與2000天文單位的距離，我算得的表面溫度是20.5克耳文(華氏-422.8度)。這比星際大戰中的霍斯(Hoth)星球還要冷。如果你假設第九行星不會吸收所有的輻射的話，那溫度就會更低一些。不過若是要接近實際值，還是得確知第九行星的屬性。

為了好玩，你也可以用同樣的模型計算地球表面溫度，你將會算得288 K的結果。但實際上，因為地球並不是完美的輻射吸收體，所以實際溫度比算出的結果低。如果沒有大氣，地球的溫度將會是約255Ｋ(華氏0度左右)。

作業

除了上述問題外，顯然還有其他的問題需要解答。下列問題是你的作業。是的，考試會考！

有些行星的發現起始於它們對其它行星運行的擾動。天王星運行軌道的改變受到海王星影響，也因此發現海王星的存在。如果我們只看冥王星的運行軌道，第九行星會偏離多遠？你應該用數值計算。你也可以把第九行星假定在任何地方。

地球的大氣層把溫度從255K加溫到288K。你能把足夠的二氧化碳加至第九行星，讓它的溫度更宜人嗎？這是個難以回答的問題，所以你需要一些估計。給你點暗示：沒有大氣的金星大約為300K，有大氣的話會超過700K。如果你能使第九行星的大氣厚度跟金星的大氣厚度一樣呢？假設溫度升高的增加係數相同，第九行星的溫度將如何？

技術上來說，以金星的大氣效應為模型並不容易，因為它的大氣層很厚。地球的大氣效應可以用單層模型(single layer model—via ACS)估算。估算是一件有趣的事。

第九行星真實存在完全解說

SURELY YOU HAVE heardall of the news about Planet Nine? If not,here are a few of the major points:

· There are many objects in the Kuiperbelt (the stuff past Pluto) that have orbits around the Sun but are sort ofbunched to one side of the solar system.

· The motion of these Kuiper beltobjects could be explained by the gravitational influence of an unknownplanet—Planet Nine.

· Planet Nine might not be the bestname. I would suggest something cooler like Planet Awesome or maybe PlanetPokemon.

· Based on the motion of the Kuiperbelt objects, Planet Nine would have an orbital period of 10,000 to 20,000years with a semi-major axis of 700 AU (1 AU equals the distance from the Sunto the Earth).

· The estimated mass of Planet Nine is6 x 10²⁵ kg(more massive than Earth) with a radius of 13,000 to 26,000 km (compared to6,371 km for the Earth).

Now that weknow at least something about this (theoretical) planet, let』s consider somequestions.

How Long Would it Take New Horizons to Get toPlanet Nine?

Really,there are two versions of this question. First you could ask how long it wouldtake New Horizons (the spacecraft that just flew past Pluto) to get to PlanetNine from its current location. I suspect the answer to this question is aninfinite amount of time. New Horizons doesn』t really have much fuel to messaround on any extra trips. In order to get to Planet Nine it would likely haveto make a huge course adjustment—and it probably doesn』t have enough fuel.

The second version of this question is 「how longwould a spacecraft like New Horizons take to get to Planet Nine?」 New Horizonsdoesn』t travel at a constant speed—however, I can still use an estimate of about 16 km/s (16,000 m/s). If this spacecraft targetedPlanet Nine during its closest approach to the Sun, that would be a distance ofabout 200 AU (2.99 x 10¹³ m).Now we can use the standard definition for average velocity (in one dimension).

I can convert 1.87 x 10⁹ secondsinto years (you can check the mathFORHOMEWORK)and I get 59.3 years. Doing the same thing for the case of Planet Nine beingthe farthest from the Sun (1200 AU), I get a travel time of 355.7 years. Oh,the distance from the Sun is approximately the same as the distance from theEarth to Planet Nine. But you can see that if we want to launch a spacecraft tofly past Planet Nine, we should either start with young scientists or find away to make a faster (much faster) spacecraft.

Could You Walk on Planet Nine?

Let』s assumethat Planet Nine has a solid surface. What would it be like to walk on it(other than being cold)? Really, this has to do with the surface gravitationalfield. On the surface of the Earth, the gravitational field is 9.8 Newtons perkilogram. We all know what it feels like on the surface of the Earth—so thiswill be a good number to use in a comparison.

The surfacegravitational field for a planet depends on two things (well, at least twothings): the mass of the planet and the radius of the planet. The more massivethe planet, the greater the gravitational field. The larger the radius of theplanet, the lower the gravitational field (because you are farther from thecenter). The magnitude of the gravitational field on the surface can be foundas:

Using the high and low estimates for the radiusof Planet Nine, I get a gravitational field between 5.9 and 23.7 N/kg. So, it』spossible that the field could be just likeon Earth (but much colder). Of course if the gravitational field is 23.6 N/kg,it』s going to suck trying to walk.

How Cold Is It on the Surface of Planet Nine?

OK, let』sstart off with the assumption that Planet Nine has no atmosphere. This isimportant because as we all know, the atmosphere of a planet can have a largeimpact on the surface temperature (see for example Venus, Earth, and Mars). Ifyou also assume that the Sun is a blackbody (all radiation is from surfacetemperature) then you can estimate the power radiated from the Sun. If all energyis radiated equally in every direction then the intensity of light willdecrease as one over distance squared.

As a planetreceives radiation from the Sun, the surface warms up. When this happens, theplanet also becomes a blackbody radiator. The equilibrium temperature of theplanet is the point at which the emitted and received radiation is equal.There』s a little bit of math, but that』s the general idea.

Using thistemperature model and a distance of 200 AU, I get a surface temperature of 20.5Kelvin (-422.8 Fahrenheit). That』s colder than Hoth. If you assume that PlanetNine doesn』t absorb all the radiation (which it wouldn』t), then the temperatureis a little bit lower—but you would have to guess at some properties of theplanet to get an actual value.

Oh, just forfun if you use that same model for the Earth you get a surface temperature of288 K—but it』s actually lower than that because the Earth isn』t a perfectabsorber. Without an atmosphere, the Earth』s temperature would be about 255 K(right around 0 Fahrenheit).

Homework

Clearlythere are other questions to answer. Here they are as homework questions foryou. Yes, these will all be on the test.

· Some planets were discovered afterfinding perturbations in other planet』s orbits. The changes in orbit of Uranuswas due to Neptune—that』s how it was discovered. Suppose we just watchedPluto』s orbit. How much of a deviation would be created by Planet Nine? Youshould try this as a numerical calculation. You can put Planet Nine whereveryou like.

· The Earth』s atmosphere warms it upfrom about 255 K to about 288 K. Could you add enough carbon dioxide to PlanetNine to give it a nicer temperature? This is a pretty tough problem, so youwill need to make some estimates. Here is a hint: Venus without an atmosphereis about 300 K and then with an atmosphere it is over 700 K. What if you put anatmosphere as thick as Venus on Planet Nine? Suppose it increased thetemperature by the same multiplicative factor—how hot would it be?

Technically, modeling the temperature effect ofVenus』s atmosphere isn』t so easy because it』s so thick. The Earth』s atmosphereeffect can be estimated with a single layer model—via ACS. Still, it』s fun to make estimations.