The Orbit of Planet Nine (Part 4)

 March 4, 2026

only from m₉ = 5 to m₉ = 6 M_⊕ and from a₉ = 300 to a₉ = 310 AU. The orbital angles do not change substantially.

We conclude that the preference for smaller values of mass and semimajor axis is robust, and that the orbital angles (i₉, Ω₉, $₉) are largely unaffected by any contamination. While the posterior distributions for m₉ and a₉ have large tails towards larger values, the possibility of a closer brighter Planet Nine needs to be seriously considered.

An additional uncertainty worth considering is the diameter and albedo of Planet Nine. We have assumed values appropriate for a gas-rich sub-Neptune which, a priori, seems the most likely state for such a distant body. Given our overall ignorance of the range of possibilities in the outer solar system, we cannot exclude the possibility of an icy body resembling, for ex- ample, a super-Eris. Such an icy/rocky body

could be ∼50% smaller than an equivalent sub- Neptune in this mass range (Lopez & Fortney

2014), and while the large KBOs like Eris have high albedos, much of this elevated albedo could be driven by frost covering of darker irradiated materials as the objects move through very dif- ferent temperature regimes on very eccentric or- bits. An object at the distance of Planet Nine – which stays below the condensation tempera- ture of most volatiles at all times – could well lack such volatile recycling and could have an albedo closer to the ∼10% of the large but not volatile-covered KBOs (Brown 2008). Overall the effect of a smaller diameter and smaller albedo could make Planet Nine ∼ 3 magni- tudes dimmer. Such a situation would make the search for Planet Nine considerably more difficult. While the possibility of a dark super- Eris Planet Nine seems unlikely, it cannot be excluded.

Finally, we recall the affect of the choice of the prior on a₉. A prior assuming formation in a cluster would put Planet Nine more distant

than shown here, though it would also predict higher masses. Combining those effects we find that the magnitude distribution seen in Figure 8 would shift fainter by about a magnitude near aphelion but would change little close to peri- helion.

While all of these caveats affect the distance, mass, and brightness of Planet Nine, they have no affect on the sky plane position shown in Figure 8. To a high level of confidence, Planet Nine should be found along this delineated path.

1. CONCLUSION

We have presented the first estimate of Planet Nine’s mass and orbital elements using a full statistical treatment of the likelihood of detec- tion of the 11 objects with 150 < a < 1000 AU and q > 42 AU as well as the observa- tional biases associated with these detections. We find that the median expected Planet Nine semimajor axis is significantly closer than previ- ously understood, though the range of potential distances remains large. At its brightest pre- dicted magnitude, Planet Nine could well be in range of the large number of sky surveys being performed with modest telescope, so we expect that the current lack of detection suggests that it is not as the brightest end of the distribution, though few detailed analysis of these surveys has yet been published.

Much of the predicted magnitude range of Planet Nine is within the single-image detec- tion limit of the LSST survey of the Vera Rubin telescope, r ∼ 24.3, though the current survey plan does not extend as far north as the full pre- dicted path of Planet Nine. On the faint end of the distribution, or if Planet Nine is unexpect- edly small and dark, detection will still require

imaging with 10-m class telescopes or larger.

Despite recent discussions, statistical evidence for clustering in the outer solar system remains strong, and a massive planet on a distant in- clined eccentric orbit remains the simplest hy- pothesis. Detection of Planet Nine will usher in a new understanding of the outermost part of our solar system and allow detailed study of a fifth giant planet with mass common through- out the galaxy.

ACKNOWLEDGMENTS

This manuscript owes a substantial debt to the participants at the MATH + X Sympo- sium on Inverse Problems and Deep Learning in Space Exploration held at Rice University in Jan 2019 with whom we discussed the issue of inverting the observations of KBOs to solve for Planet Nine. We would also like to thank two anonymous reviewers of a previous paper whose excellent suggestions ended up being incorpo- rated into this paper and @Snippy X and @si- welwerd on Twitter for advice on notation for our likelihood functions.

Software: HEALPix (Gorski et al. 2005), as- tropy (Astropy Collaboration et al. 2013), scikit- learn (Pedregosa et al. 2011), emcee (Foreman- Mackey et al. 2013), corner (Foreman-Mackey 2016)

Table 2.

m9 (Mearth)	a9 (AU)	i9 (deg)	e9	a9 (deg)	Ω9 (deg)	l	∆l	num. particles
3	625	15	0.60	356	166	-182.1	-9.2	21100
4	230	10	0.15	250	108	-175.5	-2.6	30000
4	250	15	0.15	260	102	-175.3	-2.4	30000
4	500	20	0.33	224	86	-176.2	-3.3	120500
5	230	10	0.15	246	96	-174.3	-1.4	30000
5	250	5	0.15	250	126	-177.0	-4.1	30000
5	250	10	0.15	248	108	-174.4	-1.5	30000
5	260	15	0.10	246	94	-174.2	-1.3	25600
5	260	5	0.15	246	82	-177.0	-4.1	30000
5	280	10	0.10	246	96	-175.8	-2.9	25600
5	280	15	0.10	266	88	-175.0	-2.1	25600
5	300	10	0.15	234	108	-175.6	-2.7	25600
5	300	17	0.15	254	108	-172.9	0.0	25600
5	310	15	0.10	274	102	-175.1	-2.2	25600
5	356	17	0.20	252	88	-174.2	-1.3	25600
5	500	5	0.33	250	96	-179.2	-6.3	25600
5	500	10	0.33	244	86	-176.1	-3.2	25500
5	500	20	0.33	234	86	-176.2	-3.3	20200
5	720	20	0.65	234	96	-185.1	-12.2	30100
6	280	17	0.10	256	100	-173.2	-0.3	25500
6	290	17	0.15	250	108	-173.0	-0.0	25600
6	300	17	0.15	246	100	-173.4	-0.4	25600
6	310	10	0.10	252	96	-174.4	-1.5	25600
6	310	15	0.10	256	96	-174.6	-1.7	25600
6	310	17	0.10	244	108	-175.0	-2.1	25600
6	310	10	0.15	256	108	-173.0	-0.1	25600
6	310	15	0.15	252	116	-173.0	-0.1	25600
6	310	17	0.15	266	106	-173.5	-0.6	19900
6	310	5	0.20	244	108	-177.1	-4.2	25600
6	310	10	0.20	244	108	-173.9	-1.0	25000
6	310	15	0.20	252	92	-173.0	-0.0	25400

Table 2 continued

m9 (Mearth)	a9 (AU)	i9 (deg)	e9	a9 (deg)	Ω9 (deg)	l	∆l	num. particles
6	310	17	0.20	260	122	-173.2	-0.3	13600
6	310	20	0.20	242	96	-173.2	-0.3	23700
6	310	25	0.20	230	92	-174.7	-1.8	20000
6	310	30	0.20	238	88	-178.0	-5.1	25500
6	330	10	0.20	248	108	-174.6	-1.7	31300
6	330	15	0.20	252	92	-173.4	-0.5	14400
6	356	20	0.10	254	100	-175.3	-2.4	25600
6	356	20	0.15	250	110	-174.2	-1.3	25600
6	356	15	0.20	256	102	-174.1	-1.2	21200
6	356	17	0.20	262	100	-174.1	-1.2	25600
6	356	17	0.20	264	108	-173.9	-1.0	25600
6	356	19	0.20	238	100	-173.9	-1.0	48500
6	356	25	0.20	228	88	-176.2	-3.3	40200
6	356	30	0.20	238	96	-179.9	-6.9	16700
6	380	17	0.20	242	110	-174.1	-1.2	25600
6	380	17	0.25	246	92	-173.3	-0.3	25600
6	500	35	0.15	242	96	-181.8	-8.9	30000
6	600	40	0.15	260	94	-184.0	-11.1	30000
6	800	50	0.15	242	82	-188.4	-15.5	30000
7	356	17	0.20	246	92	-173.8	-0.9	25600
7	400	15	0.25	254	82	-173.9	-1.0	30900
7	400	20	0.25	246	102	-175.2	-2.3	52800
7	400	30	0.25	230	88	-177.5	-4.6	30800
7	450	25	0.15	248	108	-178.7	-5.8	30000
7	450	15	0.33	250	86	-175.8	-2.8	29700
7	450	20	0.33	236	80	-175.9	-3.0	25600
7	450	25	0.33	236	80	-176.2	-3.3	23500
7	500	20	0.15	256	94	-176.3	-3.4	25600
7	500	15	0.20	256	102	-175.6	-2.7	25600
7	500	17	0.20	268	96	-175.1	-2.1	25600
7	500	25	0.20	254	92	-177.6	-4.7	25600
7	500	20	0.25	260	94	-176.8	-3.9	25600
7	500	5	0.33	242	96	-178.2	-5.2	57300

Table 2 continued

Table 2 (continued)

m9 (Mearth)	a9 (AU)	i9 (deg)	e9	a9 (deg)	Ω9 (deg)	l	∆l	num. particles
7	500	10	0.33	252	92	-176.6	-3.7	41400
7	500	15	0.33	250	98	-175.5	-2.6	47700
7	500	17	0.33	250	100	-175.4	-2.5	17500
7	500	20	0.33	242	86	-176.1	-3.2	52400
7	500	25	0.33	234	86	-177.9	-5.0	54000
7	500	30	0.33	232	94	-179.0	-6.1	59600
7	500	35	0.33	230	86	-180.5	-7.6	41700
7	500	25	0.40	228	86	-179.7	-6.8	35000
7	500	25	0.45	226	74	-182.0	-9.0	27700
7	525	20	0.50	236	70	-179.6	-6.6	33000
7	550	17	0.40	244	88	-175.6	-2.6	25600
7	600	17	0.45	238	94	-174.9	-2.0	25600
7	640	17	0.50	240	102	-176.8	-3.9	16900
7	650	17	0.45	230	88	-174.6	-1.7	25500
7	800	50	0.15	310	50	-190.4	-17.5	30000
7	830	20	0.70	208	96	-184.7	-11.7	51200
7	1000	60	0.15	298	94	-191.2	-18.3	30000
8	400	20	0.15	248	108	-177.1	-4.2	30000
10	350	10	0.15	250	96	-176.3	-3.4	30000
10	400	20	0.15	242	84	-178.2	-5.3	30000
10	450	20	0.33	242	82	-177.8	-4.9	34300
10	525	20	0.15	264	106	-178.1	-5.2	30000
10	525	30	0.15	266	102	-184.6	-11.7	30000
10	525	40	0.15	304	138	-189.9	-17.0	30000
10	525	20	0.50	244	114	-180.8	-7.9	39700
10	525	20	0.65	242	90	-181.7	-8.8	20900
10	525	30	0.65	244	36	-187.1	-14.2	35600
10	700	20	0.35	244	108	-176.6	-3.7	25600
10	700	30	0.70	290	132	-190.0	-17.1	25600
10	750	10	0.35	234	106	-177.5	-4.6	19500
10	750	15	0.35	252	114	-176.1	-3.2	22400
10	750	20	0.35	244	100	-177.9	-5.0	25500
10	800	5	0.40	244	114	-177.5	-4.6	25600

Table 2 continued

m9 (Mearth)	a9 (AU)	i9 (deg)	e9	a9 (deg)	Ω9 (deg)	l	∆l	num. particles
10	800	10	0.40	240	112	-177.0	-4.1	25600
10	800	15	0.40	240	118	-177.8	-4.9	25600
10	800	15	0.45	240	120	-174.9	-2.0	25600
10	800	20	0.45	238	108	-176.0	-3.1	28600
10	800	25	0.45	234	100	-177.6	-4.7	23500
10	800	30	0.45	242	50	-184.0	-11.1	16800
10	800	60	0.45	182	114	-183.0	-10.1	30400
10	870	20	0.73	254	92	-185.4	-12.5	17900
10	1000	60	0.15	314	96	-192.8	-19.9	23600
10	1400	70	0.15	224	30	-190.0	-17.1	30000
12	500	15	0.20	256	94	-178.4	-5.5	25600
12	500	20	0.20	256	92	-181.2	-8.3	25600
12	500	25	0.20	266	102	-182.9	-10.0	25600
12	920	20	0.73	224	76	-182.1	-9.1	25800
12	960	20	0.79	242	54	-186.8	-13.9	24900
14	960	20	0.74	220	76	-185.6	-12.7	28000
16	1000	20	0.75	248	76	-183.2	-10.2	33600
20	900	60	0.15	306	66	-189.0	-16.1	30000
20	1000	15	0.65	242	122	-179.6	-6.7	30100
20	1000	20	0.65	240	118	-180.6	-7.7	33000
20	1000	25	0.65	246	70	-185.5	-12.6	32300
20	1070	20	0.77	240	124	-185.2	-12.3	64900
20	1400	70	0.15	264	0	-186.8	-13.9	30000
20	2000	80	0.15	260	152	-190.1	-17.2	30000

Note—Parameters used in the numerical simulations on the effects of Planet Nine (m₉, a₉, i₉, e₉) and the maximum ln(likelihood), l, which occurs at the listed value of a₉ and Ω₉. ∆l gives the difference in ln(likelihood) from the maximum value, which occurs at m₉ = 5, a₉ = 310, i₉ = 15, and e₉ = 0.10.

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