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In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.
For an ellipse, recall that the semi-major axis is one-half the sum of the perihelion and the aphelion. For a circular orbit, the semi-major axis (a) is the same as the radius for the orbit. In fact, Equation 13.8 gives us Kepler’s third law if we simply replace r with a and square both sides.
We examine the simplest of these orbits, the circular orbit, to understand the relationship between the speed and period of planets and satellites in relation to their positions and the bodies that they orbit. Circular Orbits.
The orbit equation describes conic sections, meaning that all orbits are one of four types, as shown in Fig. 30. The particular type of orbit is determined by the magnitude of the eccentricity: Circles: \(e = 0\) Ellipses: \(0 < e < 1\) Parabolas: \(e = 1\) Hyperbolas \(e > 1\) Fig. 30 The 4 types of conic section: 1. Circle; 2. Ellipse; 3 ...
A line joining a planet and the Sun sweeps out equal areas in equal time. The square of the sidereal period of a planet is directly proportional to the cube of the semi-major axis of the orbit. While laws 1 and 2 are statements, law 3 is presented as an equation: A semi-major axis is the full width of an ellipse.
Paraphrase needed: Objects can settle in an orbit around a Lagrange point. Orbits around the three collinear points, L1, L2, and L3, are unstable. They last but days before the object will break away. L1 and L2 last about 23 days. Objects orbiting around L4 and L5 are stable because of the Coriolis force.
25.2 Planetary Orbits and the Center of Mass Reference Frame. We now commence a study of the Kepler Problem. We shall determine the equation of motion for the motions of two bodies interacting via a gravitational force (two-body problem) using both force methods and conservation laws.
