An Introduction to Celestial Mechanics

Cover An Introduction to Celestial Mechanics
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Another method that has been used is to consider all motion direct and the inclination as varying from 0° to 180°. The latter method avoids the use of double signs in the formulas and is adopted here.
[See Art. 86.] The node and inchnation define the position of the plane of the orbit in space.
The distance from the ascending node to the perihelion point counted in the direction of the motion of the body in its orbit is oi, and defines the orientation of the orbit in its plane. The longitude of
... the perihelion is denoted by tt, and is given by the equation W = Q> -\- CO.
This element is not a longitude in the ordinary sense because it is counted in two different planes.
The problem of relative motion of two bodies was of the sixth order (Art. 85), and in the integration six arbitrary constants were introduced. There are six elements, therefore, which are inde- pendent functions of these constants. They are a = major semi-axis, which defines the size of the orbit and the period of revolution, e = the eccentricity, which defines the shape of the orbit.


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