In the figure below, the black axis would be the coordinate frame, with the unit vectors,, and each 90 degrees apart. To be valid, Newton’s laws must be based on an inertial, or non-accelerating, coordinate frame.Ī reference frame is a collection of unit vectors, or vectors with a magnitude of one, at right angles to each other. THE GEOCENTRIC EQUATORIAL COORDINATE SYSTEMĪs we discussed in Chapter 2 when the two-body equation of motion was derived, we found that it was based on Newton’s Second Law. We will first introduce the coordinate frame used for most earth-orbiting satellites, the geocentric equatorial coordinate system, then introduce each of the Classical Orbital Elements (COEs) relative to that fixed coordinate frame. The location of the satellite within its orbit, or true anomaly, which was also introduced in Chapter 2 The orientation of the orbit within its orbital planeĦ. Its orientation, or swivel, locating the orbital plane in spaceĥ. Its orbital tilt, or how it is oriented relative to the earth’s equatorĤ. Its shape, e, or eccentricity, which was also introduced in Chapter 2ģ.
Its size, a, or semi-major axis, which was introduced in Chapter 2Ģ.We will then learn how these can be used to understand the COEs, six parameters, that completely describe an orbit and a satellite’s location in it. In this chapter we will reference these vectors to an approximate inertial coordinate frame. Elliptical Orbit Position, R and Velocity V However, these are constantly changing as a satellite moves around its orbit and it is difficult to actually “visualize” where it is. So far, we have learned to describe where satellites are in orbit by it position, and velocity, vectors. In this chapter, we will introduce, describe, and present mathematical equations to find the Classical Orbital Elements (COEs), which are used to locate a satellite in orbit. 3 Chapter 3 – The Classical Orbital Elements (COEs)
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