Based on nominal orbital parameters, this is the result of a backward integration performed with Mercury6 (*) Bulirsch–Stoer run with a 0.05-day step, 1e-12 accuracy, and outputs every 100 days, integrating from JD 2461000.5 backward for 100 M days (~0.27 Myr)
(*) Chambers, J.E. 1999, “A Hybrid Symplectic Integrator that Permits Close Encounters between Massive Bodies,”
The following plot shows the relative velocity and distance at the time when the relative velocity was minimum (other previous minima might of course be present but the uncertainty is very high):
Best wishes,
Alessandro Odasso
Based on nominal orbital parameters, this is the result of a backward integration performed with Mercury6 (*) Bulirsch–Stoer run with a 0.05-day step, 1e-12 accuracy, and outputs every 100 days, integrating from JD 2461000.5 backward for 100 M days (~0.27 Myr)
(*) Chambers, J.E. 1999, “A Hybrid Symplectic Integrator that Permits Close Encounters between Massive Bodies,”
The following plot shows the relative velocity and distance following the time when the relative velocity was minimum (other previous minima might of course be present but the uncertainty is very high):
Alessandro Odasso
Based on nominal orbital parameters, this is the result of a backward integration performed with Mercury6 (*) Bulirsch–Stoer run with a 0.05-day step, 1e-12 accuracy, and outputs every 100 days, integrating from JD 2461000.5 backward for 100 M days (~0.27 Myr)
(*) Chambers, J.E. 1999, “A Hybrid Symplectic Integrator that Permits Close Encounters between Massive Bodies,”
The following plot shows the relative velocity and distance following the time when the relative velocity was minimum:
Best wishes,
Alessandro Odasso
Backward simulation performed with Mercury6 ``A Hybrid Symplectic Integrator that Permits Close Encounters between Massive Bodies''. Monthly Notices of the Royal Astronomical Society, vol 304, pp793-799.
Simulation based on nominal orbital paramters (21st March 2024)
Simulation parameters
)O+_06 Integration parameters (WARNING: Do not delete this line!!)
) Lines beginning with `)' are ignored.
)---------------------------------------------------------------------
) Important integration parameters:
)---------------------------------------------------------------------
algorithm (MVS, BS, BS2, RADAU, HYBRID etc) = BS
start time (days)= 2460309.50000
stop time (days) = -1e8
output interval (days) = 100
timestep (days) = 0.05
accuracy parameter=1.d-12
Backward simulation
Mercury6 package by J.E.Chambers (1999) ``A Hybrid Symplectic Integrator that Permits Close Encounters between Massive Bodies''. Monthly Notices of the Royal Astronomical Society, vol 304, pp793-799.
) Important integration parameters:
)---------------------------------------------------------------------
algorithm (MVS, BS, BS2, RADAU, HYBRID etc) = BS
start time (days)= 2460106.5
) stop time (days) = 102458000.5
stop time (days) = -1e8
output interval (days) = 100
timestep (days) = 0.05
accuracy parameter=1.d-12
Result
