Two coplanar Newtonian orbit examples fit nine TOI-4562 b transit times at outer periods of 4,589 and 5,335 days

We tested whether nine public TOI-4562 b transit times select one outer orbit under a fixed Newtonian model. We used seven printed times and two 2025 TESS times from a verified SCI publication. The star mass is 1.192 solar masses. The inner mass is 2.30 Jupiter masses and its initial eccentricity is 0.76. The two planets share one plane. We adopt three-minute errors for the two later times. Two explicit examples have outer periods of 4,588.5 and 5,335.0 days and masses of 4.687 and 4.954 Jupiter masses. Their sums of squared scaled residuals are 1.987 and 2.103. Every residual is below one adopted error scale. Both inner orbit arguments reach search bounds. The examples predict transit centers that differ by 6.86 minutes on 8 December 2026 and 6.57 minutes on 21 July 2027. An independent force integration agrees with the transit calculations within 0.008 seconds through January 2030. The sampled orbits remain bounded in a 1,000-year integration. This finite test does not prove long-term stability. Prior work already shows orbit ambiguity for this system. Our contribution is a set of complete initial states, conditional forecasts, and reproducible numerical checks for the stated nine-time set. We do not fit radial velocities, transit shapes, or the ten-epoch conference data set. The examples do not establish the true companion orbit, and their forecast spread is not a confidence interval.

TOI-4562 · transit timing variations · planetary dynamics · conditional transit forecasts · reproducible orbit models