I'm modelling planetary orbits using a spreadsheet and Feynman's numerical method given here. I have put together a spreadsheet (10,000 rows) to model Mars' orbit in three $\left(x,y,z\right)$ dimensions. I'm using SI units with a time interval of 3600 seconds. I'm using initial state vector data from JPL Horizons. I believe Feynman's method is called leapfrog integration. I've also tried the Runge-Kutta method, but with no significant improvement in accuracy.
In terms of the orbit cycle, does it matter when I take the initial JPL Horizons data? Aphelion or perihelion, for example, or some other point in the orbit?
EDIT. Just to be clear what I'm asking. The first row of my spreadsheet uses state vector data $\left(\mathbf{x},\mathbf{y},\mathbf{z},\mathbf{v_{x}},\mathbf{v_{y}},\mathbf{v_{z}}\right)$ from JPL Horizons for an arbitrary date and time. I've chosen 2000-Jan-01 12:00:00.0000 TDB. Will I get more accurate results if I use a date and time for a specific point in Mars' orbit? Aphelion or perihelion, for example? If the answer is yes, an explanation would be useful.