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Motion of Celestial Bodies
Published in G.A. Gurzadyan, Theory of Interplanetary Flights, 2020
We can compare now all the constants determining the motion of a celestial body through its orbit. The six constants that we saw above are called elements of the elliptic orbit. These elements are the following.– the inclination of the orbital plane to the plane of the ecliptic. Numerically i is within ±90°.– the longitude of the line of nodes or the longitude of the ascending node of the orbital plane. It is counted in the direction from west to east and lies within the limits 0°-360°.– the longitude of the perigee from the line of nodes. It is also counted in the direction from west to east, and lies within the limits 0°-360°.– the semimajor axis of the elliptic orbit.– the eccentricity of the elliptic orbit: e < 1.– the time of transit of the celestial body through its perigee.
Satellite Optical Imagery
Published in Victor Raizer, Optical Remote Sensing of Ocean Hydrodynamics, 2019
The ideal elliptical orbit, with the earth at one node, is described by six Keplerian elements: α true anomaly (instantaneous angle from satellite to perigee)ω argument of perigee (twist)Ω longitude of the ascending node (pin)a semi-major axis of the elliptical orbit (size)e eccentricity of the orbital ellipse (shape)i inclination of the orbital plane (tilt).
Satellite Systems
Published in Jerry D. Gibson, The Communications Handbook, 2018
when an isotropic radiator is used to determine the gain of the antenna. Elevation: The angle at which a satellite is viewed from a site on Earth. Equatorial inclination: The angle that the orbital plane of a satellite makes with the equator. Equatorial orbit: A satellite is in an equatorial orbit when the orbital plane includes the equator. The
Fully distributed finite-time adaptive robust time-varying formation-containment control for satellite formation
Published in International Journal of Control, 2023
Pingli Lu, Qing Jiang, Ye Tian, Haikuo Liu, Changkun Du
The relative motion dynamics of satellite formation flying will be introduced in this section. In order to describe the relative motion dynamics of satellites conveniently, a local-vertical/local-horizontal (LVLH) coordinate system is defined in Figure 1. Thereinto, denotes the inertial coordinate system. The LVLH coordinate system is fixed on a reference satellite which moves along an ideal elliptical orbit around the Earth, where the origin is at the centroid of the reference satellite, the x-axis points from the centre of the Earth to this satellite, the z-axis is in the direction of angular momentum, that is, perpendicular to the orbital plane, and the y-axis represents the third axis of the right-handed frame.
Cooperative planning for multi-site asteroid visual coverage
Published in Advanced Robotics, 2021
Sumeet G. Satpute, Per Bodin, George Nikolakopoulos
An asteroid inertial coordinate frame is attached to the asteroid's center of mass, with -axis pointing along the orbit radius of the asteroid around Sun, the -axis perpendicular to the -axis in the orbital plane and the -axis completing the right-handed orthogonal coordinate frame. The orbital position of the asteroid and the spacecraft, with respect to the Sun, is provided by and , respectively, and denotes the spacecraft position with respect to the asteroid's center of mass. A body-fixed coordinate frame is attached to the asteroid's center of mass, while the geometric shape of the asteroid can be assumed as an ellipsoid, uniformly rotating with an angular velocity about its maximum moment of inertia axis (i.e. the z-axis in this case), as shown in Figure 2. The vector , denotes the ith landmark position on the asteroid surface, expressed in the body-fixed frame, denotes the surface normal at the respective landmark, whereas ϕ and represents the spacecraft's latitude and longitude position, respectively.
Using visualisations to develop skills in astrodynamics
Published in European Journal of Engineering Education, 2020
Lucinda Berthoud, Jonathan Walsh
The pedagogical design of the simulations was underpinned by variation theory. This theory was applied to the design of the simulations, for example when each of the orbital elements was given in an exercise, only one parameter was varied at a time. Each objective was chosen to be a gradual step-by-step building up of the critical concepts necessary to the understanding of the topic. To allow this to happen, the learning objectives were formulated as below, to: Explore the software interfaceCompare the differences between two orbital frames of referenceExplore, one by one, the difference that each Keplerian element makes to an orbitInterpret the ground track for each of the above variationsExplore several useful orbits such as Sun Synchronous, Geostationary and Molniya orbitsSee the process of rendezvous as a succession of burns to gain/lose altitude to match orbitsPerform an orbital plane change by varying the inclination of the orbitPerform a Hohmann transfer by varying the altitude of the orbit through burnsExplore an inclination change combined with a Hohmann transfer