Mission Design for the CubeSat OUFTI-1

CHAPTER 5- The squares of the orbital period of planets are directly proportional tothe cube of the semi-major axes of their orbit.The same laws can be applied to the motion of a satellite around a planet.In orbital mechanics, the spacecraft and the central body are considered aspoints with mass but without dimensions. As to describe the position and thespeed of a point in a tridimensional space we need six parameters, to completelycharacterize the motion of the satellite over an orbit we need the six so-calledorbital elements: the semi-major axis a, the eccentricity e, the true anomalyϑ or ν, the inclination i, the longitude or right ascension of ascending nodeΩ or RAAN and the argument of perigee ω. As shown in fig.5.8, the firsttwo describe the orbit shape and the last three the position of the orbit planerespect to the earth. The true anomaly, sometimes substituted by the time sinceperigee passage, introduces the position of the satellite on the orbit starting fromthe perigee: it’a the only parameter that varies along the orbit as long as wemaintain the hypothesis of ideal motion.Figure 5.8: Orbital ParametersThe motion is in fact considered to be ideal and determined only by thegravity force between the masses and the fictitious centrifugal force, withoutany perturbation as the aerodynamic drag and the presence of others bodies.Starting from the Newton’s laws and from the gravitational laws, we can definesthe orbital elements and some other parameters that can be useful for thecontinuation.We place ourself on the orbit plane and we call r p and r a the radius respectivelyof perigee and apogee and µ the earth gravitational constant. We definethen the following parameters that remain constant:Galli Stefania 34 University of Liège