Sky and Telescope - October 2017 - 19

LE AH TISCIONE / S&T, SOURCE: CAMBR ID GE DICTIONARY OF ASTR ONOMY

Our basic simulations showed this planet would need to lie
beyond a couple hundred a.u. and be larger than a few Earth
masses to shepherd the extreme objects. Its strong gravitational
inﬂuence would create some sort of dynamical resonance
behavior, similar to the stable resonance between Pluto and
Neptune that forces Pluto to go around the Sun twice for every
three orbits Neptune completes. This 2:3 resonance also keeps
Pluto and Neptune safely separated, even though their orbits
cross. Even if we never saw Neptune, we would still know it
exists because of the hundreds of known objects, called plutinos, with very similar orbits to Pluto's. This is also true with the
Jupiter and Neptune Trojans, which are in a 1:1 resonance with
their respective planets (S&T: June 2016, p. 16).
We also saw hints of a second trend, which Konstantin
Batygin and Michael Brown (both at Caltech) conﬁrmed two
years later in 2016: The orbital planes of the most extreme
objects are also aligned in ecliptic longitude. Just as locations
on Earth can have the same latitude but different longitudes,
orbits with similar arguments of perihelion can still have
various orientations with respect to each other. But if the
orbital planes have similar latitudes and longitudes, then they
line up in physical space (see facing page).
Using this alignment, the team was able to calculate a
rudimentary orbit for a distant, massive planet that would
cause these two geometric clusterings. The planet needed to
have a highly elongated orbit, with a perihelion that lies on
the opposite side of the Sun as the extreme objects' perihelia.
This arrangement allows the planet to spend most of its time
well away from the other, smaller objects and thus keeps
their orbits stable over the age of the solar system, somewhat
analogous to how Pluto stays away from Neptune.
Although statistically it was still unclear if the longitude
alignment was real, this work took me from some 70% sure
in 2014 to 80% sure that a massive planet much larger than
Earth exists beyond a couple hundred a.u.
Since then, Renu Malhotra (University of Arizona), Sarah
Millholland and Gregory Laughlin (both at Yale), and others
have shown that some of the extreme objects could be in
orbit period resonances with the much larger world. An orbital
period for the planet of around 17,000 years seems to work well.

Orbital Elements

c
e=a

t
1
P

Plane of
ecliptic

N
Direction of
vernal equinox

P = perihelion

Astronomers describe the shape, orientation, and timing of orbital
motion using a set of parameters called orbital elements. Six orbital
elements - a, e, i, Ω, ω, and T - specify everything you need to
know to locate an object in an elliptical orbit at any time. The ascending node, N, denotes where the body passes from below the
ecliptic to above it. Dotted lines belong to the underlying plane.

Orbital Elements for Solar System Objects
Name

Symbol

Deﬁnition and Function

Semimajor axis

Distance from elliptical orbit's
center to edge along the longest
axis. Deﬁnes the mean size of
the orbit.

Eccentricity

Distance between the ellipse's
center and one of its foci, divided
by a. Deﬁnes how elongated an
orbit is.

Inclination

Angle between the orbital plane
and the ecliptic plane.

Longitude of
ascending node

Angle drawn in the ecliptic plane
between the vernal equinox direction and the line where the orbit
intersects the ecliptic with the
object moving south to north.
Deﬁnes the direction in space of
the line where the orbit intersects
the ecliptic plane.

Argument of
perihelion

The ascending node-Sun-perihelion angle, measured in the
orbital plane in the object's direction of motion. Deﬁnes the
orbit's orientation with respect
to the ecliptic.

Time of perihelion
passage

When the object reaches perihelion. Sets the reference frame
for the orbital motion.

Curiouser and Curiouser
I'm now nearing the 90% level that this massive, distant
planet exists. Not only does our continuing survey now cover
most areas of ecliptic longitude on the sky, but we have also
discovered two more extreme objects, called 2013 FT28 and
2014 SR349. Amazingly, 2014 SR349 has all the same orbital
characteristics as the previously known extreme objects.
But while 2013 FT28 has a somewhat similar argument of
perihelion, its perihelion lies on the same side of the Sun as
the mystery planet's presumed perihelion, a 180° longitude
difference from the others. The existence of 2013 FT28 suggests that two clusters of objects exist, not just one, with the
ﬁrst group on the opposite side as the unseen, massive world
and the second on the same side, aligned with the planet

Orbital
plane

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Sky and Telescope - October 2017

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