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Nemesis - The Sun's dark twin.

According to Zetatalk, Planet X orbits between the sun and the
sun's dark twin, also known as Nemesis. There have been
several theories about a possible dark companion to the sun.
These theories predicted Nemesis to be 20,000 to 90,000 AU
from the sun.

Nemesis, the Sun's companion star, 1983-present

Zetatalk asks us to believe that Nemesis is 730 AU out or 18.7
times the Sun - Pluto distance as Zetatalk likes to state it. Even
more amazing is that Planet X is supposed to move  through
the inner solar system every 3600 years and return exactly on
course to orbit Nemesis again.

ZetaTalk: Comet Orbit

ZetaTalk: Equilibrium

ZetaTalk: Conflict

The first problem with this is that a companion star as close as
730 AU would have very obvious effects on the orbits of all the
planets. There would not have been searches for a 10th planet,
there would have been searches and theories about a companion
star from the profound effects we would see.

The second problem is that such an orbit, coming in from the
direction of Orion is very near the ecliptic and the orbit would
be altered on every pass thorough the solar system. Not only
would Planet X not line up for a return orbit around Nemesis,
even a comet like elliptical orbit would not survive long.

See:  Tom Van Flandern on the 3600 year orbit.

The third problem is that we are asked to believe that Planet X
spends most of it's time at the mid-point between the Sun and
Nemesis. Dithers between the 2 foci as Nancy likes to say.
Somehow it moves very slowly for many years, then
quickly accelerates at warp speed to make the next pass through
the solar system. Gravity would not give Planet X enough
acceleration to reach the solar system from it's early 2001
position at 360 AU (9 times the Sun - Pluto distance). If
somehow it could attain the speed necessary to arrive in 2003,
it would not orbit but fly right through the solar system never
to return.

See: The math, will it zoom by never to be seen again?

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