Thanks to fast, cheap computers, we members of the modern world can simply plug some initial conditions into a computer program and integrate the motion of the bodies numerically to follow their motio...Thanks to fast, cheap computers, we members of the modern world can simply plug some initial conditions into a computer program and integrate the motion of the bodies numerically to follow their motion as a function of time. If the orbit is circular, then this is easy: the fraction of a complete orbit is equal to the fraction of a complete period which has elapsed since the last perihelion passage.
The reader might like to refer back to Section 2.3, especially the part that deals with the polar Equation to an ellipse, to be reminded of the meanings of the angles θ, ω and v, which, in...The reader might like to refer back to Section 2.3, especially the part that deals with the polar Equation to an ellipse, to be reminded of the meanings of the angles θ, ω and v, which, in an astronomical context, are called, respectively, the argument of latitude, the argument of perihelion and the true anomaly.