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Title: Constraints on planet X/Nemesis from Solar System's inner dynamics
Authors: Lorenzo Iorio
(Version v4)

We put full 3D constraints on a putative planet X by using the dynamics of the inner planets of the solar system. In particular, we compute the minimum distance of X as a function of its heliocentric latitude and longitude for different values of its mass.

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Title: The perihelion precession of Saturn, planet X/Nemesis and MOND
Authors: Lorenzo Iorio

We show that the retrograde perihelion precession of Saturn \Delta\dot\varpi, recently estimated by different teams of astronomers by processing ranging data from the Cassini spacecraft and amounting to some milliarcseconds per century, can be explained in terms of a localized, distant body X, not yet directly discovered. From the determination of its tidal parameter K = GM_X/r_X^3 as a function of its ecliptic longitude \lambda_X and latitude \beta_X, we calculate the distance at which X may exist for different values of its mass, ranging from the size of Mars to that of the Sun. The minimum distance would occur for X located perpendicularly to the ecliptic, while the maximum distance is for X lying in the ecliptic. We find for rock-ice planets of the size of Mars and the Earth that they would be at about 80-150 au, respectively, while a Jupiter-sized gaseous giant would be at approximately 1 kau. A typical brown dwarf would be located at about 4 kau, while an object with the mass of the Sun would be at approximately 10 kau, so that it could not be Nemesis for which a solar mass and a heliocentric distance of about 88 kau are predicted. If X was directed towards a specific direction, i.e. that of the Galactic Center, it would mimic the action of a recently proposed form of the External Field Effect (EFE) in the framework of the MOdified Newtonian Dynamics (MOND).

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Ed ~ It should be noted that evidence, such as using pulsar timings, indicate that there is no PlanetX.

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Title: Constraints on Planet X and Nemesis from Solar System's inner dynamics
Authors: Lorenzo Iorio

The gravitational acceleration imparted on the solar system's rocky planets by a putative large body like a planet or a star located at hundreds/thousands AU from the Sun can be considered as a small constant and uniform perturbation A over the characteristic temporal and spatial scales of the inner planetary regions (P_b <= 1 yr, r <= 1.5 AU). We computed the variation of the longitude of the perihelion \varpi averaged over one orbital revolution due to A by finding a long-period harmonic signal which can be approximated by a secular precession over the typical timescales of the inner planets. We compared such predicted effects with the corrections \Delta\dot\varpi to the standard Newtonian/Einsteinian perihelion precessions of Venus, Earth and Mars recently estimated by E.V. Pitjeva by fitting almost one century of observations with the dynamical force models of the EPM ephemerides which did not include the force imparted by the aforementioned body.
We obtained A_x =(-0.3 ±1) X 10^-15 m s^-2, A_y = (2 ±5) X 10^-16 m s^-2 and A_z = (-0.6 ±3) X 10^-14 m s^-2 for the Cartesian components of the perturbing acceleration, so that A= (0.6 ±3) X 10^-14 m s^-2. Such a constrain is three orders of magnitude better than that recently obtained from the analysis of the timing data concerning the time derivative of the periods of a set of pulsars. As a result, the minimum distances at which putative bodies with the mass of the Earth, Mars, Jupiter and the Sun can be located are 250 AU, 750 AU, 13.5 kAU = 0.21 ly, 500 kAU = 7.9 ly, respectively. A brown dwarf with m\approx 75-80 m_Jup cannot orbit at a distance smaller than about 1.8-1.9 ly from the Sun, while the minimum distance for a red dwarf (0.075 Solar masses <= m <= 0.5 Solar masses) ranges from 2.1 ly to 5.6 ly.

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Is there a Planet X?
Any new object would have to be well clear of the Kuiper belt to qualify as a planet. Yet intriguingly, it is studies of the belt that have suggested the planet's existence. Some KBOs travel in extremely elongated orbits around the sun. Others have steep orbits almost at right angles to the orbits of all the major planets.

"Those could be signs of perturbation from a massive distant object" - Robert Jedicke, a solar system scientist at the University of Hawaii.

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Title: Mass Limit on Nemesis
Authors: Varun Bhalerao (1), M. N. Vahia (2) ((1) Indian Institute of Technology Bombay, (2) TIFR)

We assume that if the sun has a companion, it has a period of 27 Myr corresponding to the periodicity seen in cometary impacts on earth. Based on this assumption, it is seen that the inner Lagrengian point of the interaction between the Sun and its companion is in the Oort cloud. From this we calculate the mass -- distance relation for the companion. We then compute the expected apparent magnitude (visible and J band) for the companion using the models of Burrows (1993). We then compare this with the catalogue completeness of optical and infrared catalogues to show that the sun cannot have a companion of mass greater than 44 M_jup (0.042 M_sun)

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The Binary Research Institute (BRI) has found that orbital characteristics of the recently discovered planetoid, "Sedna", demonstrate the remote possibility that our sun might be part of a binary star system.

This of course runs counter to other evidence, such as using pulsar timings, that show that the Sun is a solitary star.

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Blast from the past

The astronomers looking at Pioneer 10's tracking data obtained with the Nasa Deep Space Network, an array of large radio telescopes designed to communicate with far-off space probes, discovered a new object orbiting the Sun after the probe was mysteriously knocked off course.

On 8 December, 1992, when Pioneer 10 was 8.4 billion km away, it was deflected from its predicted course for about 25 days by an unseen object.
This was only the second time in history that a Solar System object has been discovered by its gravitational effect alone.

The planet Neptune was discovered in 1846 after Its position was predicted because of its gravitational tug on the planet Uranus.

The new body, found by a team at Queen Mary and Westfield College in London, UK, and the Jet Propulsion Laboratory in California, is a Kuiper Belt object.
The scientists had been looking for such an effect for years and have analysed the data using several different methods to confirm their findings.

"We are quite excited that we have found one of these events. It is a very neat signal" - Dr Giacomo Giampieri, of Queen Mary and Westfield College.

Pioneer 10 is currently heading towards the stars of the constellation of Taurus, which it will reach in about two million years time.

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By means of high-precision timing thanks to pulsars astronomers now know what the solar barycentre is doing with respect to the rest of the cosmos.
And it is not being pulled around by Planet X.

So there is nothing out there within worrying distance.

The astronomers, Nadia Zakamska, Scott Tremaine, made use of the Australia Telescope National Facility pulsar database (http://www.atnf.csiro.au/research/pulsar/psrcat/)


Constraints on the acceleration of the solar system from high-precision timing
Authors: Nadia L. Zakamska, Scott Tremaine (Princeton University)

Many astronomers have speculated that the solar system contains undiscovered massive planets or a distant stellar companion.
The acceleration of the solar system barycentre can constrain the mass and position of the putative companion. In this paper we use the most recent timing data on accurate astronomical clocks (millisecond pulsars, pulsars in binary systems and pulsating white dwarfs) to constrain this acceleration.
No evidence for non-zero acceleration has been found; the typical sensitivity achieved by our method is a/c=a few times 10^{-19} s^{-1}, comparable to the acceleration due to a Jupiter-mass planet at 200 AU.
The acceleration method is limited by the uncertainties in the distances and by the timing precision for pulsars in binary systems, and by the intrinsic distribution of the period derivatives for millisecond pulsars.
Timing data provide stronger constraints than residuals in the motions of comets or planets if the distance to the companion exceeds a few hundred AU.
The acceleration method is also more sensitive to the presence of a distant companion (closer than 300-400 AU) than existing optical and infrared surveys. We outline the differences between the effects of the peculiar acceleration of the solar system and the background of gravitational waves on high-precision timing.

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