Аннотация:Since the work of Paul D. Jose (1965) it is known that the path of the Sun about the center of mass of the solar
system has a short retrograde intervals every 180 years, when the angular momentum of the Sun suddenly changes
its sign. Our investigation (2009) discloses, that such physically unreasonable peculiarities in motion of the Sun
may be excluded if we suppose existence of a distant planet X in our solar system. Calculations shows, that regular
barycentric motion of the Sun will take place with the following characteristics of 10-th planet (a planet X):
1) average distance of a planet from the Sun a = 508 ..;
2) period of revolution T=11435 years;
3) mass of planet M = 0.3 (in masses of the Earth) or 3 masses of Mars;
4) the orbit of a planet is close to circular and its plane lays near the plane of ecliptic;
5) angular speed of movement of a planet X on an orbit is 0.3" per day.
If we assume, that the average density of a planet X is equal 1.7 g/sm3 (like Pluto) its radius will be equal 6322
km - almost exact size of the Earth (6378 km). For such radius and geometrical albedo 0.2 (as for Sedna) the
hypothetical planet X will be observed from the Earth as a star of visible magnitude 19.7.