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Table 1.
Four Jacobi energies EJ in the bar potential.
| True | HO (Np = 2 × 105) | HO (Np = 107) | CylSP (Np = 2 × 105) | CylSP (Np = 107) | |
|---|---|---|---|---|---|
| L1, 2 | ±6.044056 | ±6.045628 | ±6.045613 | ±6.045552 | ±6.045552 |
| EJ, L1, 2 | −0.195471 | −0.195470 | −0.195473 | −0.195477 | −0.195475 |
| EJ, 1 = −0.41 | Stable | Stable | Stable | Stable | Stable |
| EJ, 2 = −0.39 | Stable | Stable | Stable | Stable | Stable |
| EJ, 3 = −0.37 | Stable | Stable | Stable | Stable | Stable |
| EJ, 4 = −0.35 | Unstable | Unstable | Unstable | Unstable | Unstable |
| EJ, 1/EJ, L1, 2 | 2.097498 | 2.097509 | 2.097476 | 2.097433 | 2.097455 |
| EJ, 2/EJ, L1, 2 | 1.995809 | 1.995191 | 1.995160 | 1.995120 | 1.995140 |
| EJ, 3/EJ, L1, 2 | 1.892864 | 1.892874 | 1.892844 | 1.892806 | 1.892825 |
| EJ, 4/EJ, L1, 2 | 1.7905469 | 1.790556 | 1.790529 | 1.790492 | 1.790510 |
Notes. Row (1): name of three methods. Row (2): position of the Lagrangian points L1, 2. Row (3): Jacobi energy at L1, 2. Rows (4)–(7): stability of the x1 orbit at these Jacobi’s energies. Rows (8)–(11): ratio of EJ/EJ, L1, 2.
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