e partly follow the previo nurical tegration of all ne psssan ≈ap;ap;ap; wisdo (1988， 72 d) and saha ≈ap;ap;ap; treae (1994， 225/32 d) we rounded the decial part of the their stepsizes to 8 to ake the stepsize a ultiple of 2order to reduce the auution of round-off errorthe putation processesretion to this， wisdo ≈ap;ap;ap; hon (1991) perford nurical tegrations of the outer five pary orbits g the syplectic ap with a stepsize of 400 d， 1/1083 of the orbital period of jupiter their result sees to be aurate enough， which partly jtifies our thod of deterg the stepsize however， sce the eentricity of jupiter (～005) is uch saller than that of rcury (～02)， we need so care when we pare these tegrations siplyters of stepsizes

the tegration of the outer five ps (f±)， we fixed the stepsize at 400 d

we adopt gas' f and g functionsthe syplectic ap together with the third-order halley thod (danby 1992) as a solver for kepler equations the nuber of axiu iterations we sethalle

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