Open Access
Table 1
Symbol key.
| Notation | Explanation | Reference |
|---|---|---|
| M* | mass of the star | |
| Mp | mass of the planet | |
| Mm | mass of the moon | |
| ρm | density of the moon | |
| Rp | radius of the planet | |
| Rm | radius of the moon | |
| Cp | maximal moment of inertia of the planet | |
| Cm | maximal moment of inertia of the moon | |
| θp | rotation angle of the planet | |
| ap | semi-major axis of the planet | |
| am | semi-major axis of the moon | |
| ep | eccentricity of the planet | |
| em | eccentricity of the moon | |
| np | mean motion of the planet | |
| nm | mean motion of the moon | |
| Impq | integers used to number the tidal Fourier modes | Eq. (20) |
| Flmp(i) | inclination functions | Eq. (20) |
| Glpq(e) | eccentricity function | Eq. (20) |
| ωlmpq | Fourier modes of the tides in the planet | Eq. (21) |
| χlmpq≡|ωlmpq| | forcing frequencies excited in the planet | Eq. (22) |
| ϵ1=ϵ1(ωlmpq) | tidal phase lags in the planet | |
| k1=k1(ωlmpq) | dynamical Love numbers of the planet | |
| K1(ωlmpq)=k1(ωlmpq)sin ϵ1(ωlmpq) | quality functions of the planet | Eq. (23a) |
| Q1(ωlmpq)≡1/|sin ϵ1(ωlmpq) | tidal quality factors | Eq. (24) |
| rH | Hill radius of the planet | Eq. (1) |
 |
reduced Hill radius of the planet | Eq. (2) |
| rr | Roche radius of the planet | Eq. (6) |
 |
synchronous value of the lunar semi-major axis | Eq. (7) |
 |
solar polar tidal torque acting on the planet | |
 |
lunar polar tidal torque acting on the planet | |
| G | Newton’s gravitational constant |
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