# Orbit Accuracy

Different conditions and considerations must be applied to a discussion about orbit accuracy. The term orbit accuracy may refer to the accuracy of the solution of the equations of motion with speciied parameters in the model of the forces acting on the satellite. In this case, little consideration is given to the accuracy of the parameters in the equations of motion. Instead the focus is simply on the accuracy of the technique used to solve the nonlinear ordinary differential equations given by Eqs. (2.3.46) and (2.3.47). If a general perturbation technique is used, the concern is usually with the small parameters, such as eccentricity, that are used to expand the forces and facilitate the solution. On the other hand, if a special perturbation technique is used, the concern will be with the step size of the numerical method chosen to solve the equations of motion. In either case, the solution technique is an approximation and will always introduce some error in the solution. To clarify this aspect, the terminology solution technique accuracy refers to the error introduced in the solution of the equations of motion by the solution technique, with no consideration given to the accuracy of the parameters in the equations. The solution technique accuracy can be controlled at different levels. For example, a numerical integration technique can be controlled by the step size and order of the technique.

Since the errors introduced by the solution technique can be controlled at some level, they are seldom the dominant error source. The parameters in the force models as well as the modeling of the forces are usually the most significant error sources. For example, all parameters in the force model have been determined by some means, usually as part of the orbit determination process. As a consequence, all parameters in the equations of motion contain some level of error. Such errors are crucial in the comparison of the solution to the equations of motion to physical measurements of some characteristics of the motion. In some cases, the error source may be embedded in the force modeling. In other words, the force model may be incorrect or incomplete. These errors will be described by the terminology force model accuracy.

In some cases, intentional mismodeling may be introduced to simplify the equations of motion. For example, the simple evaluation of the spherical harmonic terms in the gravitational force will require significantly greater computation time if the representation includes terms to degree and order 180 compared to degree and order 8. In this case, it may be acceptable to introduce a level of spherical harmonic truncation to reduce the computation time, though some error will be introduced into the solution by the omitted terms.

The most important consideration for the orbit accuracy is the specification of a requirement for the accuracy in each application. The requirement may be motivated by a wide variety of considerations, such as sensor accuracy, but the requirement will determine the selection of parameters for the solution technique, the accuracy of the force model parameters, the selection of force models, and the selection of a solution technique. The equations of motion are distinctly different if the orbit of a satellite must be known (and hence determined) with centimeter accuracy versus kilometer accuracy. Depending on these requirements, intentional model simplificat ions may be introduced. Identification of the accuracy to which the orbit must be determined is a vital aspect of the orbit determination problem.