Lokasi planet ke-9?


34

Saya telah melihat sejumlah laporan berita yang mengindikasikan kemungkinan ada planet ke - 9 di Tata Surya kita , sesuatu dengan periode orbit antara 10k-20k tahun, yaitu 10 kali massa Bumi. Saya belum melihat indikasi nyata di mana objek ini mungkin. Jika saya memiliki akses ke teleskop yang cukup, dapatkah saya menemukan planet ini, dan bagaimana cara saya mengarahkan teleskop untuk menemukannya? Seberapa jauh kemungkinannya, atau apakah itu tidak dikenal?


1
Tidak-tidak, pertanyaannya valid. Planet hipotetis disimpulkan dari pengaruhnya terhadap benda lain. Bisa dibayangkan bahwa, dari pengaruh ini, posisi P9 dalam orbitnya dapat dihitung (dengan satu atau lebih solusi untuk persamaan). Jadi: dimana itu ???

Jawaban:


29

Terlalu suram untuk dilihat selama survei normal selama sebagian besar orbitnya.

Pembaruan: Para ilmuwan di Universitas Bern telah memodelkan sebuah planet 10 massa Bumi hipotetis dalam orbit yang diusulkan untuk memperkirakan kemampuan deteksi dengan lebih presisi daripada upaya saya di bawah ini.

Kesimpulannya adalah bahwa misi NASISE WISE mungkin akan melihat sebuah planet dengan setidaknya 50 massa Bumi dalam orbit yang diusulkan dan bahwa tidak ada survei kami saat ini yang memiliki kesempatan untuk menemukan satu di bawah 20 massa bumi di sebagian besar orbitnya. Mereka menempatkan suhu planet pada 47K karena panas sisa dari formasi; yang akan membuat 1000x lebih terang dalam inframerah daripada dalam cahaya tampak yang dipantulkan dari matahari.

Namun harus berada dalam jangkauan LSST setelah selesai (lampu pertama 2019, operasi normal mulai 2022); jadi pertanyaannya harus diselesaikan dalam beberapa tahun lagi bahkan jika cukup jauh dari orbit yang diusulkan Batygin dan Brown sehingga pencarian mereka dengan teleskop Subaru menjadi kosong.

Upaya awal saya untuk melakukan handwave estimasi kemampuan mendeteksi di bawah ini. The kertas memberikan parameter orbital potensi untuk sumbu utama semifinal, dan 200 - 300 AU untuk perihelion. Karena makalah tidak memberikan kasus yang paling mungkin untuk parameter orbital, saya akan membahas kasus ekstrim yang membuatnya paling sulit ditemukan. Mengambil nilai yang paling eksentrik dari yang memberikan orbit dengan sumbu semi-mayor 1500 AU dan perihelion 200 AU memiliki aphelion 2800 AU .4001500 AU200300 AU1500 AU200 AU2800 AU

Untuk menghitung kecerahan objek yang bersinar dengan cahaya yang dipantulkan, faktor penskalaan yang tepat bukanlah penurunan seperti yang dapat diasumsikan secara naif. Itu benar untuk objek yang memancarkan cahayanya sendiri; tetapi tidak untuk satu yang bersinar oleh cahaya yang dipantulkan; untuk kasus itu, penskalaan 1 / r 4 yang sama seperti pada pengembalian radar sesuai. Bahwa ini adalah faktor penskalaan yang benar untuk digunakan dapat diperiksa kewarasannya berdasarkan fakta bahwa meskipun ukurannya serupa, Neptunus 6 x lebih redup daripada Uranus meskipun hanya 50 % lebih jauh: 1 / r 41/r21/r46x50%1/r4 scaling gives a 5x dimmer factor vs 2.25 for 1/r2.

Using that gives a dimming of 2400x at 210 AU.8.516.5 magnitude. 500 AU gets us to 20th magnitude, while a 2800 AU aphelion dims reflected light down by nearly 20 magnitudes to 28 magnitude. That's equivalent to the faintest stars visible from an 8 meter telescope; making its non-discovery much less surprising.

Ini adalah sesuatu dari batas fuzzy di kedua arah. Energi residu dari formasi / bahan radioaktif pada intinya akan memberinya luminositas bawaan; pada jarak ekstrem ini mungkin lebih terang daripada cahaya yang dipantulkan. Saya tidak tahu bagaimana memperkirakan ini. Mungkin juga bahwa dingin yang ekstrim dari Oort Cloud mungkin telah membekukan atmosfernya. Jika itu terjadi, diameternya akan jauh lebih kecil dan pengurangan permukaan pantulan dapat meredupkannya satu atau dua urutan besarnya.

Tidak tahu penyesuaian seperti apa yang harus dilakukan di sini, saya akan mengasumsikan dua faktor tersebut membatalkan sepenuhnya dan meninggalkan asumsi asli bahwa itu memantulkan cahaya sebanyak Neptunus dan cahaya reflektif adalah sumber penerangan yang dominan untuk sisa perhitungan saya .

10,000 AU

Mungkin juga terlalu samar untuk dideteksi melalui gerakan yang tepat; meskipun jika kita bisa mengitari orbitnya dengan erat Hubble dapat mengkonfirmasi gerakannya.

Eksentrisitas orbital dapat dihitung sebagai:

e=rmaxrmin2a

Memasukkan angka-angka memberi:

e=2800 AU200 AU21500 AU=0.867

Plugging 200 AU and e=0.867 into a cometary orbit calculator gives a 58,000 year orbit.

While that gives an average proper motion of 22 arc-seconds/year, because the orbit is highly eccentric its actual proper motion varies greatly, but it spends a majority of its time far from the sun where its values are at a minimum.

Kepler's laws tell us that the velocity at aphelion is given by:

va2=8.871×108a1e1+e

where va is the aphelion velocity in m/s, a is the semi-major axis in AU, and e is orbital eccentricity.

va=8.871×108150010.8671+0.867=205 m/s.

To calculate the proper motion we first need to convert the velocity into units of AU/year:

205ms3600s1h24h1d365d1y1AU1.5×1011m=0.043 AUyear

To get proper motion from this, create a triangle with a hypotenuse of 2800 AU and a short side of 0.043 AU and then use trigonometry to get the narrow angle.

sinθ=0.0442800θ=8.799×104=3.17 arc seconds.

This is well within Hubble's angular resolution of 0.05 arc seconds; so if we knew exactly where to look we could confirm its orbit even if its near its maximum distance from the sun. However its extreme faintness in most of its orbit means that its unlikely to have been found in any survey. If we're lucky and it's within 500 AU, it would be bright enough to be seen by the ESA's GAIA spacecraft in which case we'll located it within the next few years. Unfortunately, it's more likely that all the GAIA data will do is to constrain its minimum distance slightly.

Its parallax movement would be much larger; however the challenge of actually seeing it in the first place would remain.


The proper motion is massive and easily detectable, but you would need JWST (or perhaps just HST) in order to measure it and they have small fields of view, so you'd need to know more-or-less where it was.
Rob Jeffries

Actually this is just at the faint end, and of course mabe its brighter in the IR. I read that the Subaru telescope is already looking.
Rob Jeffries

For anyone who read earlier versions, I made an ~60x error in calculating proper motion at aphelion; it would be readily observable in Hubble observations; but is probably too faint to have been picked out in any proper motion surveys.
Dan Neely

Such a great answer. At aphelion, how bright would the sun appear from Planet Nine? astronomy.stackexchange.com/questions/13282/…
joseph.hainline

2
Note here astronomy.stackexchange.com/questions/13280/… almost everyone (including me) forgot about the parallax, which is much bigger than the proper motion. It would be clearly identifiable by a large telescope within days. Gaia is all-sky, but limited to about 20th Mag.
Rob Jeffries

8

The position of the hypothetical object is not known with any certainty, so it's hard to know where to point your telescope.

The paper proposes a wide range of orbital distances anywhere from 400 to 1500 AU semi-major axis, with a perihelion (closest approach to the sun) of 200-300AU. This is 8 times as far as Neptune. (I didn't read the article closely enough to determine whether the body would be near perihelion or not at present; it could be over 1000 AU away, 30 times Neptune's distance.)

With a mass of 10 Earths, we would expect the body to be something like 2-5 times Earth's radius -- somewhat smaller than Neptune.

The combination of distance and size suggests the body would be far fainter than Neptune, no brighter than magnitude 16.5 at perihelion, and likely much dimmer.


1
If the orbital period is 30,000 years, then the proper motion on the sky will be a massive 40 arcsecs/yr. If it were as bright at V=16 I'm surprised this hasn't been picked up already in photographic surveys. It might be tricky because the proper motion is too big! Either way, a candidate could be confirmed in a matter of weeks if identified.
Rob Jeffries

I'm not much of an astronomer (I answered this Q when it was in space.sx rather than astronomy.sx). If you want to take a stab at reformulating the last paragraph, please do! I'm also not totally sure of the magnitude computation.
Russell Borogove

3
See my updated answer below. The problem you and I made was using a 1/r^2 falloff with distance; when since we are talking about reflected light 1/r^4 is the correct term. As a result, even at its closest it would be far fainter than your estimate.
Dan Neely

@DanNeely I had just figured that out myself. This is a serious error in the answer.
Rob Jeffries

Ah! Of course. Good catch.
Russell Borogove

4

Citing the original article:

We find that the observed orbital alignment can be maintained by a distant eccentric planet with mass ≥≈10 m⊕ whose orbit lies in approximately the same plane as those of the distant KBOs, but whose perihelion is 180° away from the perihelia of the minor bodies.

and

As already alluded to above, the precise range of perturber parameters required to satisfactorily reproduce the data is at present difficult to diagnose. Indeed, additional work is required to understand the tradeoffs between the assumed orbital elements and mass, as well as to identify regions of parameter space that are incompatible with the existing data.

So, finding out likely orbital parameters is work in progress.


2

Batygin and Brown made a website which describes the search for the 9th planet in clear terms. They specifically note the following:

perihelion (its closest approach to the sun) at around a Right Ascension in the sky of 16 hours, which means that the perihelion position is straight overhead in late May. Conversely, the orbit comes to aphelion (the furthest point from the sun) at about 4 hours, or straight overhead in late November.

So to look for it, one should look along the ecliptic, concentrating mostly on the area directly overhead in late November. Note that this is the part of the sky where the galactic center also appears. The inclination is estimated to be 30 degrees, plus or minus 20, so that distance from the ecliptic should be searched as well.


-1

If you had access to a sufficient telescope, you could theoretically see it, if you looked in the right place (although no one knows where the right place might be). But if it's anywhere near aphelion there are only a handful of sufficient telescopes in the world (let's say an 8m mirror or larger), so I think it highly unlikely that you have access to one of them.


6
While this is technically an answer to the question, it is sparse on the things that make good answers (citations, detailed explanations, and math).
Donald.McLean
Dengan menggunakan situs kami, Anda mengakui telah membaca dan memahami Kebijakan Cookie dan Kebijakan Privasi kami.
Licensed under cc by-sa 3.0 with attribution required.