Numerische Untersuchungen Über Nicht-Periodische Transtrojaner-Bahnen

For 14 values of the mass parameter μ (from 0.0010 until 0.0150) the non-periodic Transtrojan orbits (aroundL ₄ and L₅) are investigated, which on the plane restricted problem of three bodies pass the point situated opposite to the body μ (looking from the main mass) with zero velocity in the rotating coordinate system. Results: The Transtrojan state contains a finite number of ‘double librations’ (aroundL ₄ and L₅); this number decreases with growing value of the mass parameter. Above a value of mass parameter between 0.010 and 0.015 no further double-libration takes place. Certain topologic properties of the Transtrojan state are found; for example this state has a phase of narrowing and a phase of widening of the single librations; thereby the amplitudes of the librations fluctuate in a characteristic manner. The investigations will be published inAstronomische Nachrichten in German language.