# Package org.orekit.orbits

This package provides classes to represent orbits.

See: Description

## Package org.orekit.orbits Description

This package provides classes to represent orbits.

It builds the base of all the other space mechanics tools. It provides an abstract class, Orbit, extended in four different ways corresponding to the different possible representations of orbital parameters. As of version 3.0, Keplerian, circular, equinoctial and Cartesian representations are supported.

## Design History

Early designs for the orbit package were much more complex than the current design. Looking back at these designs, they tried to do far too much in a single class and resulted in huge systems which were both difficult to understand, difficult to use, difficult to maintain and difficult to reuse. They mixed several different notions:

• representation (Keplerian, Cartesian ...)
• kinematics (parameters) and dynamics (propagation)
• physical models (complete or simplified force models, often implicitly assumed with no real reference)
• filtering (osculating and centered or mean parameters, related to some models)

They also often forgot all frames issues.

The current design has been reached by progressively removing spurious layers and setting them apart in dedicated packages. All these notions are now still handled, but all in different classes that are cleanly linked to each other. Without knowing it, we have followed Antoine de Saint Exupéry's saying:

It seems that perfection is reached not when there is nothing left to add, but when there is nothing left to take away.

The current design is not perfect, of course, but it is easy to understand, easy to use, easy to maintain and reusable.

## Current state versus evolving state

From the early design, the various orbit classes retained only the kinematical notions at a single time. They basically represent the current state, and serve as data holder. Most of methods provided by these orbits classes are getters. Some of them (the non-ambiguous ones that must be always available) are defined in the top Orbit abstract class (Orbit.getA(), Orbit.getDate(), Orbit.getPVCoordinates() ...). The more specific ones depending on the type of representation are only defined in the corresponding class (CircularOrbit.getCircularEx() for example).

It is important to note that some parameters are available even if they seem out of place with regard to the representation. For example the semi-major axis is available even in Cartesian representation and the position/velocity even in non-Cartesian representation. This choice is a pragmatic one. These parameters are really used in many places in algorithms, for computation related to period (setting a convergence threshold or a search interval) or geometry (computing swath or lighting). A side-effect of this choice is that all orbits do include a value for μ, the acceleration coefficient of the central body. This value is only used for the representation of the parameters and for conversion purposes, it is not always the same as the value used for propagation (but of course, using different values should be done with care).

Orbits also include a reference to a defining frame. This allows transparent conversions to other frames without having to externally preserve a mapping between orbits and their frame: it is already done. As an example, getting the position and velocity of a satellite given by a circular orbit in a ground station frame is simply a matter of calling orbit.getPVCoordinates(stationFrame), regardless of the frame in which the orbit is defined (GCRF, EME2000, ...).

Since orbits are used everywhere in space dynamics applications and since we have chosen to restrict them to a simple state holder, all orbit classes are guaranteed to be immutable. They are small objects and they are shared by many parts. This change was done in 2006 and tremendously simplified the library and the users applications that were previously forced to copy orbits as an application of defensive programming, and that were plagued by difficult to find bugs when they forgot to copy.

For orbit evolution computation, this package is not sufficient. There is a need to include notions of dynamics, forces models, propagation algorithms ... The entry point for this is the Propagator interface.

## Representations Conversions

All representations can be converted into all other ones. No error is triggered if some conversion is ambiguous (like converting a perfectly circular orbit from Cartesian representation to Keplerian representation, with an ambiguity on the perigee argument). This design choice is the result of many different attempts and pragmatic considerations. The rationale is that from a physical point of view, there is no singularity. The singularity is only introduced by a choice of representations. Even considering this, it appears that rather than having a parameter with no realistic value, there is an infinite possible number of values that all represent the same physical orbit. Orekit simply does an arbitrary choice, often choosing simply the value 0. In our example case, we would then get a converted orbit with a 0 perigee argument. This choice is valid, just as any other choice (π/2, π, whatever ...) would have been valid, in the sense that it does represent correctly the orbit and when converted back to the original non-ambiguous representation it does give the right result.

We therefore consider it is the responsibility of the user to be aware of the correct definition of the different representations and of the singularities relative to each one of them. If the user really needs to do some conversion (for example to provide an orbit as Two-Lines Elements later on, remembering than TLE do use Keplerian-like parameters), then he can do so.

The way conversion is handled in OREKIT is very simple and allows easy and transparent processing. All four parameters type extend the abstract class Orbit, and every propagation algorithm, be it analytical or numerical, use this abstract class as a parameter, even if internally it relies on a specific representation. As an example, the Eckstein-Hechler propagator is defined in terms of circular orbit only. So there is an implicit conversion done at propagator initialization time.

Author:
Luc Maisonobe, Fabien Maussion, Véronique Pommier-Maurussane