Orbiting satellites are becoming more and more important to us. Satellites carry incredible volumes of television, telephone and digital data communications traffic. Satellites are also used to track ships, airplanes and transport trucks. Satellites provide imagery of wheat fields, rain forests, cloud cover and oil spills. And now, satellites provide the mechanism for the Global Positioning System (GPS). Now, everyday computer applications must know the whereabouts of satellites and what their sensors "see". Your clients must be able to reconcile the data observed from satellites with that obtained terrestrially, relating the two geographically.
The purpose of this chapter is to outline the special functions and considerations involved in the modeling of Earth satellite orbits and what their sensors may "see". Hipparchus provides powerful capabilities to correlate the position and sensor swaths of Earth satellites with Earth's surface features.
Some of the material in this chapter assumes that you have a little knowledge of orbital mechanics. However, even if you are totally unfamiliar with this subject, you might still want to skim through this chapter to get a feel for this very powerful component of Hipparchus. If you want to review some of the fundamentals, refer to the popular text Remote Sensing referenced in Appendix C: Bibliography.
Satellite orbits follow elliptical paths. Over time, an orbit traces an ellipse. You already know that Hipparchus works with the geometry of the ellipsoid. You also know that Hipparchus uses direction cosines and modern vector algebra to know what's where. These same techniques can be applied to the calculation of orbital positions. It should be no surprise then to learn that Hipparchus provides functions to permit you to work with orbits.
Now, not only will you be able to know the location of a satellite at any instant, you will be able to know what points on the ground can communicate with it and what areas on the ground its sensors "see". The ability to calculate the instantaneous relationships between a satellite and the ground provides you with an extremely powerful tool.
Defining the path of an orbiting satellite can be done in several ways. The most common method is to define the "Classical Orbit Parameters". These are parameters used to describe the orbit path. Hipparchus uses this standard. Your clients may provide this information in other ways. If so, you will first need to convert to the Classical form before attempting to initialize the Hipparchus Library orbit functions.
A common word associated with orbits is "period". Unfortunately, this word has two different meanings.
As one of the classical orbit parameters, "period" refers to the amount of time taken by an elliptically orbiting satellite to complete one full revolution. This is the definition used by Hipparchus.
Alternatively, "period" is sometimes used to refer to the time taken for successive crossings of the plane of the Earth's Equator. This is a different value from that described above, referring to the time taken to circle the Earth from a terrestrial point of view.
To caricature the difference, consider the orbit of a typical geo-stationary communications satellite. This is a high orbit in which the satellite sits continually over a single point on the Earth. Viewed from overhead the Earth, its period will be seen to be exactly one day (one sidereal day, that is). But, being stationary with respect to every point on the Earth, it will never cross the plane of the Equator and it's "period" might be forever! (As an aside, to be geo-stationary in the first place, it has to be orbiting directly over the Equator)!
It will be important that your clients check that the "period" they supply for a satellite is the classical one.
Applications that include orbital calculations are well supported by Hipparchus. You will find the relevant functions in section h4 of the Hipparchus Library.
To accommodate orbital applications, you will first have to initialize a control block, orbprms, with the specifications of the orbit. Orbits are defined using the h4_SetClassicalOrbit and h4_OrbitPrecession functions. These are used to initialize the orbprms control block (in memory). If your application works with multiple satellites, you will need to supply orbit specifications for each one. Please refer to the Hipparchus Library Reference Manual for a complete description of these functions and their arguments.
One important element of the orbprms control block is the "epoch". This is literally "a point in time". Using the supplied Hipparchus functions, you can set a starting epoch for an orbit and then successively apply a "delta" of time after that epoch to predict "future" positions of the satellite.
The instantaneous orbital position of the satellite is provided in terms of a location on its elliptical path. If required, your application can convert this position to a corresponding location on the surface in the Hipparchus sphere, typically using the functions in h4.
Orbital positions are calculated with the same high precision as surface positions. Precision is sub-millimetric, even for orbits as high as those of the geo-stationary communications satellites.
The Hipparchus orbit modeler is known as a "third order" modeler. This means that it accounts for the three most significant aspects of orbital motion: elliptical eccentricity, precession and the rotation of apsides. (Other less significant disturbances that can affect a satellite's orbital path are the uneven distribution of the Earth's mass, the influence of the Moon and Sun, atmospheric drag, and so on).
The orbit modeler calculates the path of an orbiting satellite in a manner largely transparent to both you and your client. You use the same set of functions to define its orbit and trace its path, regardless of its eccentricity. The orbit modeler is sufficiently precise that the orbit of most satellites can be accurately predicted for upwards of a month!
Many remote-sensing surveillance satellites have what is called a "viewing geometry". Their on-board sensors receive information about objects on or near the surface of the Earth. For example, some satellites observe weather patterns by sensing cloud cover, while others use side-looking radar to detect other specific features. Using Hipparchus, you can construct a two dimensional object that describes the sensor coverage (what the satellite sensor "sees") over a specific time interval. This coverage is often called the "sensor swath". An accurate definition of the swath pattern of a satellite can be critical to an application. In addition to tracing the surface points directly under an orbit (a nadir trace), Hipparchus permits the definition of side-looking swaths.
Using Hipparchus, you can easily perform the exacting calculations needed to select only the data seen by a satellite while overhead specific regions of interest. For example, if you are interested in data about ocean shipping lanes, data captured by the satellite while over the Sahara Desert will be of little interest, especially if the data acquisition and transmission costs are high.
Orbital modeling requires us to incorporate the concept of time. Dates and times used for orbital calculations are always expressed in terms of Universal Coordinated Time (GMT). Orbit times in seconds since epoch are easily expressed in the familiar terms of date and time. The Hipparchus Libraries include functions that perform common calendar arithmetic computations. All such time and date manipulations are "Year 2000 Compliant".
For a graphically animated illustration of the various satellite paths and operations possible on satellite orbits and their sensor objects, refer to Galileo for Windows 95 and the Orbits script in particular. Study of this animation and the Galileo script elements that produce it will provide immediate insight into the power of the Hipparchus orbit modeler.
One small proviso should be remembered when developing sensor swath objects. Keep the swath object to a single orbit. This is so that the object boundary does not cross itself and produce a computationally awkward object. You can best create an object that consists of multiple orbits by developing single objects for each orbit and then later taking the union of the collection to produce the single object you are looking for.
Satellite applications are increasingly important. Hipparchus provides an accurate means of knowing the exact position of satellites in relation to surface features. Remote sensor swaths can be converted to Hipparchus regions and intersected with other objects. Using the Hipparchus Library orbit functions in conjunction with the other Hipparchus Library functions, satellite applications are handled with relative ease.