you will go immensly far from the sun before problems start arising. one rocket that was 700 trillion meters from the sun showed NaN m/s and NaN for the altitude. at the point you will need to run it on x100000 timewarp while piloting another craft
ive done the same thing with a rocket whose speed when entering Kerbol's SOI is around 45 to 46 km/s last time i saw the apoapsis was when it said around 6.8 quadrillion meters