By Gerhard Lang

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How can we describe the flight path or trajectory of the spacecraft? In this flight, the spacecraft experiences gravitational attraction from all the bodies of the universe plus non-gravitational forces (to be discussed in Chap. 5). This is a complicated problem. We will simplify the mathematical model to get the most important features and then add perturbations to the nominal or reference trajectory in Chap. 5. R. 2 Two-Body Problem Derivation of the Equation of Motion: The Mathematical Model We develop the equation of motion (the math model) for a satellite experiencing gravitational forces only.

The transit method looks for dips in a star’s brightness as orbiting planets pass by and block the light from the star. 3 Central Force Motion Another Simplifying Assumption For the problem of a spacecraft moving about a planet or a planet moving about the sun, one mass is much greater than the other. Hence, we assume 4. m2 > > m1. Then the motion of m1 is essentially the motion of a particle in an inertially fixed field centered at m2 because rc ¼ r2. Strictly speaking, this model is the “relative 2-body problem,” because we solve for the motion of the satellite relative to the central body.

Objective: Global coverage 3. : A geosynchronous orbit (GEO) is an earth orbit that has a period equal to one sidereal day. : A geostationary orbit (GEO) is a circular, geosynchronous orbit in the earth’s equatorial plane. A spacecraft that is in a geostationary orbit will hover over a fixed point on the earth’s equator. 4. Medium Earth Orbit (MEO) Examples: GPS (aka NAVSTAR) 24 active satellites in four planes of six satellites each Glonass (Russian System) 24 satellites with 8 satellites in each of 3 planes Galileo (European System) In development 5.