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Table 2
Secular evolution of the satellite’s semi-major axis and eccentricity caused by its own tidal deformation.
| Tidal theory | From coupled model | |||||
|---|---|---|---|---|---|---|
| Satellite | without libration | with libration | ||||
| Satellite | ||||||
| da/dt [m/s] | de/dt [-/s] | da/dt [m/s] | de/dt [-/s] | da/dt [m/s] | de/dt [-/s] | |
| Eq. (58a) | Eq. (59) | Eq. (65) | ||||
| Moon | −8.75 ∙ 10−12 | −1.81 ∙ 10−19 | −8.76 ∙ 10−12 | −1.81 ∙ 10−19 | −8.84 ∙ 10−12 | −1.82 ∙ 10−19 |
| Phobos | −7.59 ∙ 10−12 | −2.76 ∙ 10−17 | −1.11 ∙ 10−11 | −4.03 ∙ 10−17 | −1.09 ∙ 10−11 | −3.93 ∙ 10−17 |
Notes. The secular rates extracted from our coupled propagation are in good agreement with expectations from the tidal theory (see Section 3.5), including the librational contribution for Phobos’ case.
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