Ephemeris Interpolation

THREE EPHEMERIDES FROM HORIZONS FOR THE PLANET MERCURY
  Ephemeris at 2000-01-01T00:00:00.000 TDB(TAI):
      a (au):         0.393637
      e (none):       0.197010
      i (°):          7.013140
      Ω (°):          48.121040
      ω (°):          25.956970
      ϖ (°):          74.078010
      τ (date/time):  1999-11-17T17:52:14.183 TDB(TAI)
        (time since): 3823665.816690 s
      T (days):       90.147069
      M (°):          176.732767
      n (°/day):      3.993474
      λ (°):          250.810777
  Ephemeris at 2000-02-01T00:00:00.000 TDB(TAI):
      a (au):         0.371523
      e (none):       0.209922
      i (°):          7.027295
      Ω (°):          48.503574
      ω (°):          35.274481
      ϖ (°):          83.778055
      τ (date/time):  2000-02-16T05:00:53.051 TDB(TAI)
        (time since): -1314053.051280 s
      T (days):       82.658116
      M (°):          293.760636
      n (°/day):      4.355289
      λ (°):          377.538691
  Ephemeris at 2000-03-01T00:00:00.000 TDB(TAI):
      a (au):         0.398776
      e (none):       0.224138
      i (°):          6.978935
      Ω (°):          48.312916
      ω (°):          31.146444
      ϖ (°):          79.459360
      τ (date/time):  2000-02-15T20:42:37.543 TDB(TAI)
        (time since): 1221442.456612 s
      T (days):       91.918093
      M (°):          55.368246
      n (°/day):      3.916530
      λ (°):          134.827606

FIRST INTERPOLATED EPHEMERIS (INTERPOLATED FROM FIRST TWO HORIZON EPHEMERIDES)
  Ephemeris at 2000-01-31T23:59:59.000 TDB(TAI):
      a (au):         0.371523
      e (none):       0.209922
      i (°):          7.027295
      Ω (°):          48.503574
      ω (°):          35.274477
      ϖ (°):          83.778051
      τ (date/time):  1999-11-17T17:52:14.183 TDB(TAI)
        (time since): 6502064.816690 s
      T (days):       82.658119
      M (°):          327.758931
      n (°/day):      4.355289
      λ (°):          411.536982

SECOND INTERPOLATED EPHEMERIS (INTERPOLATED FROM LAST TWO HORIZON EPHEMERIDES)
  Ephemeris at 2000-02-01T00:00:01.000 TDB(TAI):
      a (au):         0.371523
      e (none):       0.209922
      i (°):          7.027295
      Ω (°):          48.503574
      ω (°):          35.274479
      ϖ (°):          83.778053
      τ (date/time):  2000-02-16T05:00:53.051 TDB(TAI)
        (time since): -1314052.051280 s
      T (days):       82.658120
      M (°):          293.760689
      n (°/day):      4.355289
      λ (°):          377.538742

PARAMETERS "ϖ", "τ since", "M", "n", AND "λ" ARE CALCULATED FROM OTHER PARAMETERS FOR ALL EPHEMERIDES