The orbital resonances between the asteroid Toro and the Earth and Venus

Among the very few tabulated asteroids with perihelion inside or closely outside the Earth's orbit some have periods nearly commensurable with the Earth's. The perturbed orbit of one of these, 1685 Toro, has been integrated over 1200 years. The results show that Toro is at present captured in resonance with the Earth and also that Venus has a drastic influence on the orbital elements. Toro's orbit is librating with a main period of 800 years and peak-to-peak amplitude of about 65°. The mechanism of libration is discussed.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978.