Synchronous Orbits

8 Key excerpts on "Synchronous Orbits"

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  Remote Sensing Physics

  An Introduction to Observing Earth from Space

  • Rick Chapman, Richard Gasparovic(Authors)
  • 2022(Publication Date)
  • American Geophysical Union

    (Publisher)

  Figure 2.11 shows the specific periods and inclinations required for a sun-Synchronous Orbits as a function of altitude. These can be computed directly from equations (2.17) and (2.19). A sun-synchronous orbit requires an incli-nation of more than 90 ∘ , so it is in a retrograde orbit. At an altitude of 825 km, a satellite in a sun-synchronous orbit will have an inclination of 98.71 ∘ and a period of 101.3 minutes. Note that a satellite in this type of orbit will not 130 120 110 100 90 Period (min) 2000 1500 1000 500 Altitude (km) 106 104 102 100 98 Inclination (deg) 8000 7500 7000 Semimajor axis (km) ← Period Inclination → Figure 2.11 Dependence of inclination and nodal period for sun-Synchronous Orbits. pass over the poles, leading to gaps in the polar coverage depending on the extent of the ground swaths of the sensors on the satellite, as shown in Figure 2.12. The ground tracks for three orbits of the sun-synchronous NOAA-20 satellite are illus-trated in Figure 2.13. The times are given in UTC, not local solar time. During each 101.3-minute orbital period, the point of solar noon on the Earth rotates 25.5 ∘ to the west, so on each orbit the satellite ground track must 20 Remote Sensing Physics Figure 2.12 Gap in polar coverage for an orbit with an inclination of 98.86 ∘ . move this much to keep at the same solar time. This is exactly what is shown. Another type of common orbit is a repeat-ing orbit, which is an orbit that exactly repeats its ground track after a certain interval of time. This type of orbit allows data to be collected at the same locations on the Earth with the same viewing geometry many times during the satel-lite’s lifetime. For the track to repeat, the Earth must make an integral number of rotations in the time required for the satellite to make an integral number of orbits.

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  Solar System Dynamics

  • Carl D. Murray, Stanley F. Dermott(Authors)
  • 2000(Publication Date)
  • Cambridge University Press

    (Publisher)

  5 Spin–Orbit Coupling This common body, Like to a vagabond flag upon the stream, Goes to and back, lackeying the varying tide, To rot itself with motion. William Shakespeare, Anthony and Cleopatra, I, iv 5.1 Introduction In the last chapter, we considered the effect of tides raised on a satellite by a planet where we assumed that the satellite was in a synchronous spin state (i.e., that the rotational period of the satellite was equal to its orbital period). As mentioned in Sect. 1.6 , most of the major natural satellites in the solar system are observed to be rotating in the synchronous state. How did this situation arise and what determines the spin–orbit state of a given satellite or planet? In this chapter, we start by further examining the effects of a tidal torque on a satellite’s rotation. This analysis reveals why, for example, in order to maintain its synchronous spin–orbit resonance, the Moon must have a permanent quadrupole moment. The consequences of this extra torque on the system are then examined and this leads to a general approach to the concept of spin–orbit resonance in the solar system. The origin and stability of these resonances are also discussed. 5.2 Tidal Despinning Consider the case of a satellite orbiting a planet in an elliptical orbit. Those parts of the orbit in which the satellite’s spin rate, which we denote by ˙ η + n , is less (or greater) than its angular velocity or the rate of change of its true anomaly ˙ f , are shown in Fig. 5.1a . If we transform to a reference frame that is centred on the satellite and rotates with the satellite’s mean motion n , then in this rotating frame the planet moves about its guiding centre in a 2:1 ellipse (cf. Sect. 4.5 ) as 189 190 5 Spin–Orbit Coupling satellite planet planet empty focus satellite (a) (b) r r ˙ η + n ˙ η ϕ Fig. 5.1. (a) The path of a rotating satellite in an inertial reference frame centred on a planet.

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  Dynamics and Control of Autonomous Space Vehicles and Robotics

  • Ranjan Vepa(Author)
  • 2019(Publication Date)
  • Cambridge University Press

    (Publisher)

  To achieve a polar orbit of Earth requires more energy, thus more propellant, than does a direct orbit of low inclination. To achieve the latter, the initial launch is normally accomplished near the equator, where the rotational speed of the surface contributes a significant part of the final speed required for orbit. Once in a polar orbit, the satellite will not be able to take advantage of the “free ride” provided by Earth’s rotation, and thus the launch vehicle must provide all of the energy for attaining orbital speed. 2.3.5 Walking Orbits It is possible to choose the parameters of a spacecraft’s orbit to take advantage of some or all of the gravitational influences to induce precession, which causes a useful motion of the orbital plane. The result is called a walking orbit or a precessing orbit, since the orbital plane moves slowly with respect to fixed inertial space. 2.3.6 Sun Synchronous Orbits A sun synchronous orbit is a particular type of walking orbit whose parameters are chosen such that the orbital plane precesses with nearly the same period as the planet’s solar orbit period. In such an orbit, the spacecraft crosses periapsis at about the same local time every orbit. This can be useful if instruments on board depend on a certain angle of solar illumination on the surface. Mars Global Surveyor’s orbit is a 2 pm Mars Local Time sun-synchronous orbit, chosen to permit well-placed shadows for best viewing. It may not be possible to rely on use of the gravity field alone to exactly maintain the desired synchronous timing, and occasional propulsive maneuvers may be necessary to adjust the orbit. 2.4 Impulsive Orbit Transfer The whole point about orbit transfers is to be able to change the orbit if a satellite by applying the minimum possible input to the satellite. One approach is to apply an 48 Space Vehicle Orbit Dynamics impulse to the satellite. Thus, the satellite experiences an impulsive change to its velocity vector.

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  Mobile Satellite Communication Networks

  • Ray E. Sheriff, Y. Fun Hu(Authors)
  • 2003(Publication Date)
  • Wiley

    (Publisher)

  Mobile Satellite C o ~ u n ~ c a t i o n Networks change in the node-to-node period of revolution is [ where a is the se~-major axis and T is the mean Keplerian period. However, the oblateness of the Earth sometimes can be used for good cause. For Earth resource and su~eillance missions where c o n s t ~ t illumination conditions are desirable, a ~un-sync~onous orbit can be used to make use of the advanta~e that the ascendi drifts Eastw~d at 0.~856' per day. This is the rate at which the Earth orbits around this case, the orientation of the orbital plane with respect to the E and a constant illumination condition can be met. Sun line r e m ~ n s fixed 3.3.4 A ~ ~ o ~ ~ ~ ~ r i c Drag ~tmospheric drag affects the rate of the decay of an orbit and the satellite lifetime as a result rce from the atmosphere on the satellite. This is due to the frictional force and ted on a satellite caused by collision the atoms and ions present in the Et has a more prominent egect on satellites below 800 h. The drag force on the satellite is expressed as [JEN-62]: 1 = -f d p (3.100) where CD is the drag coefficient; A is the cross-sectional area; p is the a t ~ o s ~ h e ~ c density; and v is the satellite velocity. y rewriti~g equation (3.4) in terms of the unit vectors er and e,, it can be shown that equation (3.4) can be expressed in component form: into account the atmosphe~c drag, equation (3.101) becomes: (3.101) (3.102) W = ~ C ~ ) / 2 ~ is called the ~~llistic c o e ~ ~ i e ~ t and rn is the mass of the satellite. circular orbit, the orbital decay causes no change on the shape of the orbit, i.e. it will owever, for an elliptical orbit, the orbital shape will become more circular. ~onstellation ~haracteristics and Orbital Parameters instantaneous coverage area of a satellite is at its maximum. Any point located within this coverage area will be within the geometric visibility to the satellite.

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  Geodesy

  • Wolfgang Torge(Author)
  • 2011(Publication Date)
  • De Gruyter

    (Publisher)

  Satellites may reflect incident light only (passive satellites), or they may carry on board subsystems such as transmitters/receivers, different type sensors, clocks, and computers (active satellites). In the latter case, an energy supply is required, and lifetime is rather limited. The mean orbital velocity of a satellite moving in an approximately circular orbit (r = a) is given from (5.29) by (5.37) For a satellite close to the earth (h = 1000 km), we obtain, with r = R + h= 7370 km, a velocity of 7.4 km/s. Kepler's third law yields the period of revolution U = 2xr/v = 104 min. The intersection of the orbital plane with a non-rotating earth represents a great circle on the earth's surface: subsatellite track. The rotation of the earth causes a western displacement of subsequent satellite orbits (Fig. 5.6), with a shift on the equator given by = 15 0 ·ί/Γη] = 0.25°·ί/Γπύη]. (5.38) sidereal day 5.2 Satellite Observations 137 Fig. 5.6. Subsatellite tracks The latitude range of the subsatellite tracks is determined by the inclination of the satellite. The following aspects have to be considered during the design (choice of orbital parameters) of satellite missions for geodetic applications: For positioning, the network geometry of the ground stations and the satellites plays a primary role. Simultaneous direction measurements from two ground stations to a satellite form a plane, and the intersection of planes provides positions. Range measurements utilize the intersection of spheres, whereas range differences, derived from Doppler-frequency shifts, use the intersection of hyperboloids. Satellites at high altitudes are less influenced by gravitational and air drag perturbations and therefore preferred. Low altitude satellites are required for the determination of the gravitational field. This is mainly due to the attenuation factor (ajr) in the spherical harmonic expansion of the gravitational potential ( a e = semimajor axis of the earth ellipsoid), cf.

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  Satellite Geodesy

  Foundations, Methods, and Applications

  • Günter Seeber(Author)
  • 2008(Publication Date)
  • De Gruyter

    (Publisher)

  3 Satellite Orbital Motion Precise time-dependent satellite positions in a suitable reference frame are required for nearly all tasks in satellite geodesy. The computation and prediction of precise satellite orbits, together with appropriate observations and adjustment techniques is, for example, essential for the determination of − geocentric coordinates of observation stations [12.1], − field parameters for the description of the terrestrial gravity field as well as for the determination of a precise and high resolution geoid [12.2] − trajectories of land-, sea-, air-, and space-vehicles in real-time navigation [12.3] − Earth’s orientation parameters in space [12.4]. Essentially, the accuracy of the final results depends on the accuracy of the available satellite orbits. This is increasingly true for tasks in applied geodesy, such as the determination of relative coordinates with the Global Positioning System [7]. The requirement for 1 cm relative accuracy in coordinates implies the requirement for the knowledge of satellite orbits on the few meter accuracy level or even better [7.4.3]. Those who apply satellite methods in geodesy, navigation and adjacent fields, must have a basic knowledge of satellite orbital motion, including the major perturbations, in order to assess the appropriate requirements for orbit determinations. Chapter 3 aims to provide this basic knowledge. Starting with the undisturbed Keplerian motion in a central force field [3.1] the major perturbations, as well as an elementary perturbation theory are discussed [3.2]. The effects of perturbations on satellite orbits are also treated [3.2.4]. A section on the integration and representation of orbits [3.3] follows because algorithms for orbit improvement are included in modern software packages for applied satellite geodesy. The appropriate use of satellite ephemerides is discussed together with the corresponding observation methods (e.g. [7.1.5]).

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  Digital Satellite Navigation and Geophysics

  A Practical Guide with GNSS Signal Simulator and Receiver Laboratory

  • Ivan G. Petrovski, Toshiaki Tsujii(Authors)
  • 2012(Publication Date)
  • Cambridge University Press

    (Publisher)

  The user is given a geometrical description of satellite motion and can determine satellite position for any moment of time. For a geodetic task, which requires significantly higher accuracy, we need to consider Newton’ s gravitational model. 40 Presentations and applications of GNSS orbits A gravitational force between two bodies is defined by Newton: ~ FðrÞ ¼  GMm r 2 ~ e r ; (2:1) where M is the mass of the Earth, m is the mass of a satellite, G is Newton’ s constant of gravitation, and ~ e r is the unit vector between centers of two bodies: ~ e r ¼ ~ r r : (2:2) For an Earth satellite we can assume that satellite mass is negligibly small with respect to the Earth’ s mass: m55M: (2:3) Consequently satellite motion can be described in inertial space by a differential equation system: d 2 ~ r dt 2 ¼ GM ~ e r r 2 : (2:4) The solutions of this equation can be elliptic, parabolic, or hyperbolic orbits, depending on the initial conditions, which are, in practical terms, the satellite initial velocity. We use Kepler ’ s laws here in the form derived by Newton and rephrase them for the case of satellites rotating around the Earth. In general Kepler ’ s laws describe any two point masses moving under mutual gravitational attraction. For the GNSS satellites we look only at elliptical orbits, though the orbits are conic sections in general. Keplers’ s first law. A satellite is moving around the Earth in an elliptical orbit, with the Earth’ s center of mass collocated with one of the focuses (see Figure 2.3). Keplers’ s second law. A line joining the centers of mass of a satellite and the Earth sweeps out equal areas in equal intervals of time (see Figure 2.3).

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  Fundamental Planetary Science

  Physics, Chemistry and Habitability

  • Jack J. Lissauer, Imke de Pater(Authors)
  • 2019(Publication Date)
  • Cambridge University Press

    (Publisher)

  In 1687, Newton showed that the relative motion of two spherically symmetric bodies resulting from their mutual gravitational attraction is described by simple conic sections: ellipses for bound orbits and parabolas and hyperbolas for unbound trajectories. However, the introduction of additional gravitat- ing bodies produces a rich variety of dynami- cal phenomena even though the basic interactions between pairs of objects can be straightforwardly described. In this chapter, we describe the basic orbital properties of Solar System objects (planets, moons, minor bodies and dust) and their mutual interactions. We also provide several examples of important dynamical processes that occur in the Solar System and lay the groundwork for describ- ing some of the phenomena that are considered in other chapters of this book. We begin in §2.1 with an overview of the two- body problem, i.e., the relative motion of an iso- lated pair of spherically symmetric objects that are gravitationally attracted to one another. Our dis- cussion introduces Kepler’s laws, Newton’s laws and the terminology used to describe planetary orbits. In the next three sections, we discuss the consequences of gravitational interactions among larger numbers of bodies. We consider the dynam- ics of spherically symmetric objects of finite size in §2.5. We relax the assumption of spherical sym- metry in §2.6 to analyze the dynamics of rotating planets and of orbits about them, and we consider the effects of tidal forces on deformable bodies in §2.7. Although gravity is the dominant force on the motions of large bodies in the Solar System, electromagnetic forces such as radiation pressure substantially affect the motions of small objects, which have larger surface area to mass ratios than do large objects; we discuss such forces in §2.8. We conclude the chapter with a brief overview of orbits about a mass-losing star, which may be important for very young and very old planetary systems.

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