Picture of boy being examining by doctor at a tuberculosis sanatorium

Understanding our future through Open Access research about our past...

Strathprints makes available scholarly Open Access content by researchers in the Centre for the Social History of Health & Healthcare (CSHHH), based within the School of Humanities, and considered Scotland's leading centre for the history of health and medicine.

Research at CSHHH explores the modern world since 1800 in locations as diverse as the UK, Asia, Africa, North America, and Europe. Areas of specialism include contraception and sexuality; family health and medical services; occupational health and medicine; disability; the history of psychiatry; conflict and warfare; and, drugs, pharmaceuticals and intoxicants.

Explore the Open Access research of the Centre for the Social History of Health and Healthcare. Or explore all of Strathclyde's Open Access research...

Image: Heart of England NHS Foundation Trust. Wellcome Collection - CC-BY.

Analytical method for perturbed frozen orbit around an asteroid in highly inhomogeneous gravitational fields

Ceccaroni, Marta and Biscani, Francesco and Biggs, James (2012) Analytical method for perturbed frozen orbit around an asteroid in highly inhomogeneous gravitational fields. In: 2012 Analytical Methods in Celestial Mechanics, 2012-09-26 - 2012-09-29.

[img] PDF

Download (473kB)


This article provides a method for finding initial conditions for perturbed frozen orbits around inhomogeneous fast rotating asteroids. These orbits can be used as reference trajectories in missions that require close inspection of any rigid body. The generalized perturbative procedure followed exploits the analytical methods of relegation of the argument of node and Delaunay normalisation to arbitrary order. These analytical methods are extremely powerful but highly computational. The gravitational potential of the inhomogeous body is firstly stated, in polar-nodal coordinates, which takes into account the coefficients of the spherical harmonics up to an arbitrary order. Through the relegation of the argument of node and the Delaunay normalization, a series of canonical transformations of coordinates is found, which reduces the Hamiltonian describing the system to a integrable, two degrees of freedom Hamiltonian plus a truncated reminder of higher order. Setting eccentricity, argument of pericenter and inclination of the orbit of the truncated system to be constant, initial conditions are found, which evolve into frozen orbits for the truncated system. Using the same initial conditions yields perturbed frozen orbits for the full system, whose perturbation decreases with the consideration of arbitrary homologic equations in the relegation and normalization procedures. Such procedure can be automated for the first homologic equation up to the consideration of any arbitrary number of spherical harmonics coeffcients. The project has been developed in collaboration with the European Space Agency (ESA).