Arguments for the presence of a distant large undiscovered Solar system planet

Aphelion distances of long-period comets show a slight excess around 30 000 to 50 000 au from the Sun. Positions of cometary aphelia within these dist ance limits are aligned along a great circle inclined to both the ecliptic and the Galactic plane. This paper examines one of the possible explanation s for this non-random clustering: that it is due to orbital perturbations b y an undiscovered object orbiting within the above-mentioned distances. A m odel consistent with the observations gives a retrograde orbit (inclination 120 degrees) for the object with a longitude of the ascending node at 77 d egrees +/- 13 degrees, a period of 5.8 x 10(6) yr and a radius of 32 000 au . The same model gives a present position for the undiscovered object of RA 20(h) 35(m), Dec. +5 degrees, with an error ellipse semimajor axis of 14 d egrees and a semiminor axis of 7 degrees. The magnitude is likely to be fai nter than 23. Such a distant object would almost certainly not remain bound for the age of the Solar system, and recent capture into the present orbit , although also of low probability, remains the least unlikely origin for t his hypothetical planet.