# If Planet Nine indeed exists, how large a impact event there should be to be seen from Earth?

Recently I've found this news article, A meteorite crashed into the Moon during total lunar eclipse in January, about a collision into the moon that happened while a lunar eclipse was under way. According to a paper{1}, it produced a flash that peaked about 4.2 magnitude, what puts it in the range visible to the naked eye, assuming a threshold around magnitude 5:

Despite visible from Earth, it was caused by a pretty small object, about 45kg, with impact energy about 1.5 ton TNT equivalent:

That made me wonder, if we were lucky enough, could we pinpoint Planet Nine position just by looking in its general direction and waiting for a large enough impact with a KBO, able to produce a visible flash?

Or instead of a visible flash, perhaps we could at least hope to detect the infrared glow from the heat produced. For example, assuming a Planet Nine about twice Earth radius at 800 AU, I estimate the amount of energy received from the sun in a Earth day to be about $$10^{17}J$$:

Python 3.8.5 (default, Sep  4 2020, 07:30:14)
[GCC 7.3.0] :: Anaconda, Inc. on linux
>>> solar_constant_earth = 1362
>>> solar_constant_9th = solar_constant_earth * (1/800)**2
>>> solar_constant_9th
0.0021281250000000002
>>> 9th_cross_section = 3.1415 * (2 * 6350000)**2
File "<stdin>", line 1
9th_cross_section = 3.1415 * (2 * 6350000)**2
^
SyntaxError: invalid syntax
>>> cross_section_9th = 3.1415 * (2 * 6350000)**2
>>> daily_energy_input_9th = solar_constant_9th * cross_section_9th * 60 * 60 * 24
>>> daily_energy_input_9th
9.316555641045002e+16


This is about the estimated yield from the Tunguska event, so I think even a impactor as small as 100m across delivers the equivalent to a day worth of 9th total solar irradiation in a split second, so the infrared glow of the planet could be boosted a lot, briefly.

{1}. Madiedo, José M., et al. “Multiwavelength observations of a bright impact flash during the 2019 January total lunar eclipse”. Monthly Notices of the Royal Astronomical Society, vol. 486, no 3, julho de 2019, p. 3380–87. Silverchair, doi:10.1093/mnras/stz932. link

• Nice Question! A couple details: Total solar power delivered to the Earth in a day is $1.5 \times 10^{22} J$ according to this website: en.wikipedia.org/wiki/Orders_of_magnitude_(energy). Also, only a portion of the energy released in a meteor impact is light. Mar 14 '21 at 16:45
• @ConnorGarcia it's a lot more if you also consider thermal radiation from the hot impact to be light. Many surveys for asteroids are done in thermal IR so there is some chance of being seen that way.
– uhoh
Mar 15 '21 at 5:58
• Pretty sure you wouldn't, but it all depends on composition and energy. Stuff in the Kuiper Belt has <2 km/sec impact speeds, which is 10x smaller than at the Moon. Stuff in the Kuiper Belt is icy, not rocky, so impacts work differently, as do their accompanying flashes. We haven't see any impact flashes anywhere on any other bodies other than the Moon, so whether one would expect to see it on a hypothetical body that is literally >1000x farther away is pretty much a "no" to me, even if the flash in ice were as bright and even if it had the energy of an inner solar system impactor. Mar 15 '21 at 19:25
• @StuartRobbins , I think the impact speed would be dominated by P9 escape velocity, that should be quite high for a planet predicted to have up to 10 Earth masses. Mar 16 '21 at 16:02
• Slightly related: I believe people have been looking for the signature of matter getting eaten by 'planet 9' in the (unlikely I think!) case that it's not a planet but a primordial black hole. It might be worth looking for that work as they may have also done the maths for a planet.
– user38308
Mar 16 '21 at 19:30

We can compare the brightness of a comet hitting planet 9 with the 1994 impact of Shoemaker-Levy 9 / SL9 on Jupiter. It was seen by Hubble, and Galileo which was orbiting Jupiter at the time.

View from Galileo of SL9-W, a 49 second event involving a 350m comet fragment at 215,000km/h:

info from NASA:

• brightness of L-impact > that of G-impact by 20 percent * G impact about 15 percent of total light from Jupiter at maximum

_CCD (late 1980's tech, 800x800) time resolution 2.5 sec

• data returned for K, N, V and W impacts * W-impact clearly seen as light point with 1 percent of total luminosity of jupiter, and afterwards the fireball roughly constant during 49 secs at 15 percent of total Jupiter intensity.

_UV Spectrometer at 292 nm

• G-impact seen at 07:33:32; 20 percent increase in total Jovian brightness * secondary impact at 07:34:36, 1/4 as intensive as G itself

The fireball events from SL9 reached 3200km above the cloud deck the total energy released was 60,000,000 Megatons of TNT.

Jupiter is 5 Astronomical Units away and Planet 9 is estimated at ≈500AU away, so an SL9 equivalent impact would be 100 times further away and 100x100 times less bright than SL9 because of the inverse square law, corresponding to 13.6 apparent magnitude difference compared to SL9, which was 20% of Jupiter's brightness.

Perhaps i'm wrong, i'm suggesting a maximum visual magnitude of 13.4 / 11.2 for an SL9 event of comets ranging from 350m / 3.5km for planet 9.

Asteroids are probably very rare at 400AU, otherwise a processor could check historical records for matching flashes of light where Planet 9 would emit single or multiple flashes ranging from 5 to 20 apparent magnitude, conforming to a characteristic signal of a 5-10 second rise, a 30 to 120 second constant brightness and a fade.

• The last point would also be a good question, what is the collision rate in outer solar system. Thank you. I will wait a bit before accepting the answer, just in case other people want to weigh in. Mar 17 '21 at 13:17
• One of the reasons the SL9 impacts were so bright is due to the fact that they were Bolides, generating tremendous gas compression heat on atmo entry, which gives luminous efficiency of $\eta=0.12E_0^{0.115}$, where $E_0$ is the optical energy measured in kilotons, according to arxiv.org/abs/1009.1824, First Earth-based Detection of a Superbolide on Jupiter. So we may have to assume that Planet 9 has some kind of atmosphere for aliental's excellent answer to hold. Without an atmosphere, we would expect less of the kinetic energy emitted as light and more as heat. Mar 17 '21 at 16:00
• Also, we might expect impactor velocity to roughly correspond with planetary surface escape velocity, as they did for SL9. Jupiter's surface escape velocity is about 60 km/s, Neptune's is around 24, and Earth's is around 11. If we ball-parked Planet 9's at around 20, then 1/3 the velocity, means we need 9 times the impactor mass to generate the same kinetic energy as SL9 since $k_e=1/2mv^2$. Mar 17 '21 at 16:07
• What makes this question (and answer) so interesting is the possibility of mining previously observed data to look for impacts on Planet 9. If we found some, perhaps that could help direct our search. Of course, there is still some argument if good statistical evidence for Planet 9 exists, see: astronomy.stackexchange.com/questions/41455/…. Mar 17 '21 at 16:18
• I noticed perhaps there is a mistake in this part: "Jupiter is 5 Astronomical Units away and Planet 9 is estimated at >400AU away, so an SL9 equivalent impact would be 100 times less bright than SL9 was on Jupiter...". Did you assume the brightness drop is inverse linear with distance? I think there will be a inverse square relation. Mar 18 '21 at 12:37