Long-Life Europa Geodesy Orbits Accounting for Navigation Uncertainties

Abstract

This work investigates the properties of phase space near a periodic orbit and their applications to orbit design and orbit determination. A low-altitude, near-polar periodic orbit is computed and an error covariance is generated by processing range-rate and altimetry measurements over seven days. The resulting covariance is used to disperse the orbit initial conditions in a Monte Carlo simulation. The distribution of the Monte Carlo run is biased toward longer orbit lifetimes, due to the stable and unstable manifolds associated with the periodic orbit. The orbit determination covariance is mapped into manifold coordinates and long lifetime orbits are shown to be aligned with the stable manifold. Periodic orbit continuation is used to generate a family of orbits with similar phase-space characteristics to understand the variation of manifold structure with orbit elements and Jacobi energy. The effect of Europa eccentricity on the phase-space location of long lifetime orbits is discussed and conclusions are given regarding the connection between orbit lifetime, design, and determination. Nomenclature a, e, i, Ω, ω, M = Keplerian orbital elements, km, [ ], deg, deg, deg, deg, respectively a s = stable manifold coordinate a u = unstable manifold coordinate C = Jacobi energy, km 2 ∕s 2 C = consider parameter state vector C nm ∕S nm = Stokes coefficients h 2 , k 2 = second degree tidal Love number n E = Europa mean motion, rad∕s R = inertial frame satellite position vector, km R e = Europa radius, km r = rotating frame satellite position vector, km t = time, s U = gravitational potential, km 2 ∕s 2 u = right eigenvector v = left eigenvector X = satellite state vector γ = center manifold phase, deg θ = manifold intersection angle, deg Λ = information matrix λ = eigenvalue μ = standard gravitational parameter, km 2 ∕s 2 ρ = center manifold magnitude Φ = state transition matrix

Systematic Orbital Design for a Jovian Moon Exploring Mission

“…They increased the lifetime of the orbit from 40 to 150 days. Boone and Scheeres 27,28) investigated the properties of the phase space near periodic orbits. Note that the aforementioned studies focused more on lowaltitude orbits and their stability.…”