Can a solar pulsation event be characterized by a low-dimensional chaotic attractor?

Using the theory of nonlinear dynamical systems a time-series analysis of a pulsation event in solar radio emission suggests that there exists a low-dimensional attractor. The power spectrum cannot be interpreted as a superposition of periodic components. Estimates of the maximum Lyapunov exponent and the Kolmogorov entropy give some hints to deterministic chaos. Consequences for the physical modelling of the event are discussed.     

J2 Invariant Relative Orbits for Spacecraft Formations

An analytic method is presented to establish J ₂ invariant relative orbits. Working with mean orbit elements, the secular drift of the longitude of the ascending node and the sum of the argument of perigee and mean anomaly are set equal between two neighboring orbits. By having both orbits drift at equal angular rates on the average, they will not separate over time due to the J₂ influence. Two first order conditions are established between the differences in momenta elements (semi-major axis, eccentricity and inclination angle) that guarantee that the drift rates of two neighboring orbits are equal on the average. Differences in the longitude of the ascending node, argument of perigee and initial mean anomaly can be set at will, as long as they are setup in mean element space. For near polar orbits, enforcing both momenta element constraints may result in impractically large relative orbits. It this case it is shown that dropping the equal ascending node rate requirement still avoids considerable relative orbit drift and provides substantial fuel savings.This revised version was published online in October 2005 with corrections to the Cover Date.