Osculating Elements

In the near-circular case we have u f k const, and the osculating elements of Section 3.2 can be used. 

The osculating orbit (24) is an ellipse centered at v = 0, or u = F0/ljq. A more natural choice of orbital elements than vq, v 0 are four geometric parameters of the ellipse (24). We suggest to use the singular-value decomposition (SVD)... 

The considerations of Section 3.2., i.e. the introducing osculating harmonic elements by means of the singular-value decomposition, readily... 

For each planet, we may transform / , At, r, p into the elements a, e, A, zu employing the same transformations used to define the ordinary osculating heliocentric elements aosc, eosc, AOSc, wOSc of the two-body problem as functions of m, G(M + m), r, mi. However, the equations giving the osculating heliocentric elements depend on m only through fi. In order to use always the same routines, the above equations may be transformed. 

FIGURE 9.4 Torsion pendulum. Sample S in conditioning chamber C acts as the restoring element. The moment arm A with masses m, and mj is counterbalanced by weight W Amplitude of oscUlation can be recorded on drum D using thermal or hght-sensitive papers or stored and plotted on a computer. 

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