For a personal coding project, I'm trying to model orbits of satellites around the Earth. I take in some values from a user and use them to determine the shape of the orbit. I want to model the position in the orbit as a function of time so as time moves forward in the program, I can calculate the position at regular intervals and move the satellite around the earth. The user input includes, the apogee, perigee, inclination, and the longitude of the perigee. Currently from the user input, I'm able to determine the semi-major and minor axes, the eccentricity, and the orbital period. I believe I should be able to determine the mean anomaly, eccentric anomaly, and ultimately the true anomaly from this info but I'm unsure if I have enough data to do so.
Second, I am a bit confused about how I find the mean anomaly from this. I can determine the mean motion to use in the equation $M(t)=M(t_0)+n(t−t_0)$, but what do I use as $t_0$, and how do I calculate $M(t_0)$? Can anyone provide guidance on where to go from what I have started with?