(B.23) |

in a frame of reference that is instantaneously aligned with the ecliptic plane, as described in Section 4.12. Let ( , , ) and ( , , ) be the Cartesian components of and , respectively, in this standard reference frame. It follows from Equations (4.38), and (4.72)-(4.74), that

(B.24) | ||||||

(B.25) | ||||||

and | (B.26) |

as well as

(B.27) | ||||

(B.28) | ||||

and | (B.29) |

where

Here, , , , , , and are the orbital true anomaly, major radius, eccentricity, inclination, argument of the perihelion, and longitude of the ascending node, respectively, of Mercury. Moreover, , , , , , and are the corresponding quantities for the perturbing planet.

It is helpful to define

(B.32) | ||||||

and | (B.33) |

Making use of Equations (B.25)-(B.30), we deduce that

and

Hence,

(B.36) |

which implies that

and