# How did scientists determine an estimate of the number of planets greater than Sedna's size to exist in the Inner Oort Cloud?

In the article, New Dwarf Planet Found at Solar System's Edge, Hints at Possible Faraway 'Planet X' (Wall, 2014) where they report on research and observations performed by astronomers that discovered the dwarf planet 2012 VP113 which is smaller than, but has an orbit severely elongated like that observed for Sedna.

The article reports the claim from the astronomers who discovered 2012 VP113 that

Based on the amount of sky the scientists searched, Trujillo and Sheppard estimate that about 900 bodies larger than Sedna may exist in this faraway realm, which the astronomers dub the inner Oort Cloud.

How was the estimate, in bold above, calculated?

• Wild guess: they surveyed approximately 1/900-th of the sky, found one such object, and concluded they can expect 900 total such things. If so, expect a large number of statisticians to collapse into black holes of anger as a result. – zibadawa timmy Sep 24 '14 at 10:01
• @zibadawatimmy best. comment. ever! The first sentence makes good sense, but of course I am looking for any papers etc about it. Your second sentence is just awesome! – user2449 Sep 24 '14 at 10:04

Unfortunately, the paper is not available on ArXiv (oh, what hardships we must overcome!), but I have found it here. In it, where the "900" figure is mentioned (2nd page, I believe), the authors (Trujillo and Sheppard) say that they ran simulations with the data already found and their additional findings, and found that 900$^{+800}_{-500}$ bodies larger than 1,000 km in diameter could exist. They also found that 430$^{+400}_{-240}$ relatively "bright" bodies could exist, as well. Notice that there is quite a lot of uncertainty there; they are rather cautious (and rightfully so) when announcing the results of their simulations.

Interestingly enough, they also mention a paper in that section, written partly by none other than Mike Brown (!) that also used simulation methods. The authors, Schwamb et al, concluded (in 5.4, as well as the conclusion) that 393$^{+1286}_{-264}$ and 74$^{+249}_{-47}$ objects greater than or equal to Sedna in brightness, not size, could exist (393 is for the "hot" population, while 74 is for the "cold" population). The reason Trujillo and Sheppard cited this paper is that their simulation results fit the results of the simulations by Schwamb et al., which is encouraging.

Summary: Trujillo and Sheppard arrived at 900 via simulations based on prior observations. There is a large amount of uncertainty in this number, but it does agree with prior simulations by Schwamb et al. While zibadawatimmy 's comment is perhaps the funniest I have seen, it is, fortunately, inaccurate. Those statisticians must be relieved.

I hope this helps.

• I hope you don't mind that I've edited in a reference. I had no idea who Mike Brown is and it is hard to Google for as there is a current news item about an unrelated man with the same name. – dotancohen Jan 11 '15 at 11:34
• @dotancohen That's a good idea. – HDE 226868 Jan 11 '15 at 14:21
• Noteworthy as Mike Brown is, Chad Trujillo was also on the Palomar team that discovered Eris. – Emilio Pisanty Aug 3 '15 at 13:50