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I have an initial position, velocity and acceleration (in x,y,z coordinates) for a certain orbit, and I need to compute the next position, velocity and acceleration after a certain time interval (I only have the true position, vel and acc with a 2h gap, and I would need it for each minute for example). In order to compute the position and velocity I've used the f and g Lagrange coefficients. But could I compute the acceleration using this approach as well? In the book "Orbital Mechanics for Engineering Students by Howard Curtis", the author shows the expressions for the 'f', 'g' and the first derivatives of 'f' an 'g' (which are used for computing the future position and velocity). These expressions are:

Lagrange coefficients for position and velocity estimation

Could I compute the derivative again of f and g, to obtain the second derivative and compute then the acceleration? Or the approach with the Lagrange coefficient is only valid for estimating the position and acceleration? If so there is an easy way to estimate the acceleration as well?

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