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In astronomy, orbit determination means to predict the way objects in space orbit each other. There are several methods for making these predictions. Initial orbit determination method is the easiest method and requires two measurements to find the direction and speed of an orbiting body. The least squares method is more accurate but requires many estimations of the same orbit to produce a prediction of the direction, speed, and orbit error. The sequential processing method is the most accurate and requires many estimates of orbit error from previous models. This method produces new orbital models that take into account the several factors that cause orbit error, like small collisions with space dust.
The application of orbit determination ranges from global positioning satellites (GPS) to binary star orbits. Orbit error can cause major problems in the GPS system and needs to constantly be monitored. Objects scheduled to collide with Earth are expected to be predicted with orbital determination methods before impact.
Initial orbit determination has been used throughout history and developed independently by many astronomers. It was used by Johannes Kepler to derive his three laws of planetary motion. The first accurate orbit model for the planet Mars was also developed using initial orbit determination.
Since it was first developed by Carl Friedrich Gauss in 1801, the least square method has replaced the use of initial orbit determination. An orbital period is a complete loop of an orbit. The least square method shows that between complete orbital periods there are always errors that form due to unknown forces and interactions of the orbiting body during the trip. Initial orbit determination does not take into account previous data. It is only the first step in modern orbit determination because the least square method calculates orbit error.
The sequential processing method is most preferred because of computer modeling. With this method and Sherman’s Theorem, astronomers develop orbital models with the use of computers to find the future position, speed, direction, and orbital error with very limited data. Sherman’s Theorem requires another math step to the sequential processing method, called linearization.
The complex math and extensive data required for the use of sequential processing method is often not available, so astronomers produce estimates for the sequential processing method. This reduces the difficulty of the orbit determination but slightly increases orbit error. This process is called state estimate referencing. Astronomers use state estimate referencing and linearization only when the orbital data they are studying is too small to use the non-linear methods of sequential processing.