The Experts below are selected from a list of 12 Experts worldwide ranked by ideXlab platform

Howard D. Curtis - One of the best experts on this subject based on the ideXlab platform.

  • The Two-Body Problem
    Orbital Mechanics for Engineering Students, 2020
    Co-Authors: Howard D. Curtis
    Abstract:

    This chapter presents the vector-based approach to the classical problem of determining the motion of two bodies due solely to their own mutual gravitational attraction. We show that the path of one of the masses relative to the other is a conic section (circle, ellipse, parabola, or hyperbola) whose shape is determined by the eccentricity. Several fundamental properties of the different types of orbits are developed with the aid of the laws of conservation of angular momentum and energy. These properties include the period of elliptical orbits, the escape velocity associated with parabolic paths, and the characteristic energy of hyperbolic trajectories. Following the presentation of the four types of orbits, the Perifocal Frame is introduced. This Frame of reference is used to describe orbits in three dimensions, which is the subject of Chapter 4.

  • Chapter 2 – The Two-Body Problem
    Orbital Mechanics for Engineering Students, 2020
    Co-Authors: Howard D. Curtis
    Abstract:

    Publisher Summary This chapter illustrates a vector-based approach to the classical problem of determining the motion of two bodies due solely to their own mutual gravitational attraction. The path of one of the masses relative to the other is a conic section (circle, ellipse, parabola, or hyperbola) whose shape is determined by the eccentricity. Several fundamental properties of the different types of orbits are developed with the aid of the laws of conservation of angular momentum and energy. These properties include the period of elliptical orbits, the escape velocity associated with parabolic paths, and the characteristic energy of hyperbolic trajectories. Following the presentation of the four types of orbits, the Perifocal Frame is introduced, and this Frame of reference is used to describe orbits in three dimensions. The chapter also presents a discussion of the restricted three-body problem to provide a basis for understanding the concepts of Lagrange points and the Jacobi constant.

  • Chapter 4 – Orbits in Three Dimensions
    Orbital Mechanics for Engineering Students, 2020
    Co-Authors: Howard D. Curtis
    Abstract:

    Publisher Summary This chapter explores the means of describing orbits in a three-dimensional space, which is the setting for real missions and orbital maneuvers and the orbits of earth satellites. This chapter discusses the ancient concept of the celestial sphere and the use of right ascension and declination to define the location of stars, planets, and other celestial objects on the sphere. This leads to the establishment of the inertial geocentric equatorial Frame of reference and the concept of state vector. The six components of this vector give the instantaneous position and velocity of an object relative to the inertial Frame and define the characteristics of the orbit. The chapter presents the six classical orbital elements that uniquely define the shape and orientation of an orbit and the location of body on it and how to transform the state vector into orbital elements and vice versa, taking advantage of the Perifocal Frame. The chapter also summarizes two of the major perturbations of earth orbits due to the earth's nonspherical shape that are exploited to place satellites in sun-synchronous and molniya orbits, and ground tracks along with the ways of computing them.

Konstantin V. Kholshevnikov - One of the best experts on this subject based on the ideXlab platform.

  • Manifolds and Metrics in the Relative Spacecraft Motion Problem
    Journal of Guidance Control and Dynamics, 2006
    Co-Authors: Pini Gurfil, Konstantin V. Kholshevnikov
    Abstract:

    This paper establishes a methodology for obtaining the general solution to the spacecraft relative motion problem by utilizing the Cartesian configuration space in conjunction with classical orbital elements. The geometry of the relative motion configuration space is analyzed, and the relative motion invariant manifold is determined. Most importantly, the geometric structure of the relative motion problem is used to derive useful metrics for quantification of the minimum, maximum, and mean distance between spacecraft for commensurable and noncommensurable mean motions. A number of analytic solutions as well as useful examples are provided, illustrating the calculated bounds. A few particular cases that yield simple solutions are given. Nomenclature a = semimajor axis E = eccentric anomaly E = follower orbit e = eccentricity F = follower Perifocal Frame f = true anomaly I = inertial Frame i = inclination Jk = Bessel function L = leader-fixed Frame M = mean anomaly n = mean motion n0 = fundamental frequency R = leader position vector R = relative motion invariant manifold r = follower position vector W = distance function α = normalized semimajor axis μ = gravitational constant ρ = relative position vector � = right ascension of the ascending node ω = argument of periapsis ω = angular velocity vector |·| = vector norm �·� = signal norm Superscripts � = leader ∗ = relative orbital element

Pini Gurfil - One of the best experts on this subject based on the ideXlab platform.

  • Manifolds and Metrics in the Relative Spacecraft Motion Problem
    Journal of Guidance Control and Dynamics, 2006
    Co-Authors: Pini Gurfil, Konstantin V. Kholshevnikov
    Abstract:

    This paper establishes a methodology for obtaining the general solution to the spacecraft relative motion problem by utilizing the Cartesian configuration space in conjunction with classical orbital elements. The geometry of the relative motion configuration space is analyzed, and the relative motion invariant manifold is determined. Most importantly, the geometric structure of the relative motion problem is used to derive useful metrics for quantification of the minimum, maximum, and mean distance between spacecraft for commensurable and noncommensurable mean motions. A number of analytic solutions as well as useful examples are provided, illustrating the calculated bounds. A few particular cases that yield simple solutions are given. Nomenclature a = semimajor axis E = eccentric anomaly E = follower orbit e = eccentricity F = follower Perifocal Frame f = true anomaly I = inertial Frame i = inclination Jk = Bessel function L = leader-fixed Frame M = mean anomaly n = mean motion n0 = fundamental frequency R = leader position vector R = relative motion invariant manifold r = follower position vector W = distance function α = normalized semimajor axis μ = gravitational constant ρ = relative position vector � = right ascension of the ascending node ω = argument of periapsis ω = angular velocity vector |·| = vector norm �·� = signal norm Superscripts � = leader ∗ = relative orbital element