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Table 1.
Displacement Xℒ3 − XL3, differences between the eigenvalues of ℒ3 and L3, and amplitude of the dynamical substitute (DS) along the Y axis for each planet.
| Body | Xℒ3 − XL3 |
 |
 |
DS amplitude |
|---|---|---|---|---|
| Mercury | −6.26 × 10−8 AU ∼ −9 km | −2.53 × 10−8 | 9.18 × 10−9 | 6.28 × 10−8 AU ∼ 9 km |
| Venus | −1.46 × 10−6 AU ∼ −218 km | −3.93 × 10−6 | 4.66 × 10−6 | 4.42 × 10−5 AU ∼ 6612 km |
| Mars | 2.85 × 10−8 AU ∼ 4 km | −1.99 × 10−7 | 2.77 × 10−7 | 1.07 × 10−5 AU ∼ 1595 km |
| Jupiter | 1.18 × 10−6 AU ∼ 176 km | −5.45 × 10−6 | 7.73 × 10−6 | 4.17 × 10−5 AU ∼ 6245 km |
| Saturn | 5.56 × 10−8 AU ∼ 8 km | −2.52 × 10−7 | 3.58 × 10−7 | 2.26 × 10−6 AU ∼ 338 km |
| Uranus | 1.03 × 10−9 AU ∼ 0.2 km | −4.66 × 10−9 | 6.61 × 10−9 | 5.47 × 10−8 AU ∼ 8 km |
| Neptune | 3.16 × 10−10 AU ∼ 0.05 km | −1.42 × 10−9 | 2.02 × 10−9 | 2.04 × 10−8 AU ∼ 3 km |
Notes. We use the Mathematica package AstronomicalData for the choice of the parameters.
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