Changes In Orbital Inclination Research Articles

Lorentz Force Effects on Orbit and Lifetime of Micrometer-Size Space Debris

In this Paper, through an orbital calculation using a developed orbital model, the effects of the Lorentz force on micrometer-size debris are studied from two perspectives: orbital changes and lifetime changes. First, with respect to orbital changes, the effects of the actual geomagnetic field and charge variation during orbital motion are assessed. It is revealed that, under the condition of an actual geomagnetic field, the Lorentz force is likely to cause secular changes in the semimajor axis and eccentricity. When considering the charge variation during orbital motion, the Lorentz force is likely to cause secular changes in orbital inclination. Second, with respect to lifetime changes, the debris lifetimes of cases with and without the Lorentz force are compared. A comparison of simulation results shows that the Lorentz force generally causes the lifetimes of objects to decrease. In addition, the Lorentz force significantly decreases the lifetimes of debris in particular orbits. Therefore, it can be concluded that the Lorentz force can generate a region wherein micrometer-size debris cannot survive for a long time. In this regard, the Lorentz force can create a new trend of the distribution for micrometer-size debris in low Earth orbit.

The Effects of Barycentric and Asymmetric Transverse Velocities on Eclipse and Transit Times

Abstract It has long been recognized that the finite speed of light can affect the observed time of an event. For example, as a source moves radially toward or away from an observer, the path length and therefore the light travel time to the observer decreases or increases, causing the event to appear earlier or later than otherwise expected, respectively. This light travel time effect has been applied to transits and eclipses for a variety of purposes, including studies of eclipse timing variations and transit timing variations that reveal the presence of additional bodies in the system. Here we highlight another non-relativistic effect on eclipse or transit times arising from the finite speed of light—caused by an asymmetry in the transverse velocity of the two eclipsing objects, relative to the observer. This asymmetry can be due to a non-unity mass ratio or to the presence of external barycentric motion. Although usually constant, this barycentric and asymmetric transverse velocity (BATV) effect can vary between sequential eclipses if either the path length between the two objects or the barycentric transverse velocity varies in time. We discuss this BATV effect and estimate its magnitude for both time-dependent and time-independent cases. For the time-dependent cases, we consider binaries that experience a change in orbital inclination, eccentric systems with and without apsidal motion, and hierarchical triple systems. We also consider the time-independent case which, by affecting the primary and secondary eclipses differently, can influence the inferred system parameters, such as the orbital eccentricity.

Optimal Law for Inclination Change in an Atmosphere Through Solar Sailing

The aim of this paper is to devise a local optimal strategy for the orbital inclination change of solar sail spacecraft in low Earth orbit, combining the effects of the solar radiation pressure and atmospheric forces. The spacecraft is modeled as a reflective flat plate. The acceleration due to effects of atmospheric forces and solar radiation pressure is computed, depending on the orbital parameters and attitude of the sail. Then, the attitude that maximizes the instantaneous orbital inclination change is found through Gauss’ equations. When either one of these effects dominates over the other (and so, one can be neglected), the analytic expressions are found. When both effects are considered, a numerical optimization is used. An additional constraint is introduced to avoid a decrease in the orbital semimajor axis, and therefore prevent losses of orbital energy, while increasing the inclination. Different regions are identified, depending on whether the atmospheric effects dominate, the solar radiation pressure dominates, or the two are comparable. Arcs along the orbit are determined in which the optimal attitude can be found analytically, and the expression is derived. Numerical results show that a consistent increase of inclination can be achieved in a one-year mission, starting from different circular orbits, by applying the proposed control laws.

A consistent analysis of three years of ground- and space-based photometry of TrES-2

The G0V dwarf TrES-2A, which is transited by a hot Jupiter, is one of the main short-cadence targets of the Kepler telescope and, therefore, among the photometrically best-studied planetary systems known today. Given the near-grazing geometry of the planetary orbit, TrES-2 offers an outstanding opportunity to search for changes in its orbital geometry. Our study focuses on the secular change in orbital inclination reported in previous studies. We present a joint analysis of the first four quarters of Kepler photometry together with the publicly available ground-based data obtained since the discovery of TrES-2b in 2006. We use a common approach based on the latest information regarding the visual companion of TrES-2A and stellar limb darkening to further refine the orbital parameters. We find that the Kepler observations rule out a secular inclination change of previously claimed order as well as variations of the transit timing, however, they also show slight indication for further variability in the inclination which remains marginally significant.

The effects of dynamical interactions on planets in young substructured star clusters

We present N-body simulations of young substructured star clusters undergoing various dynamical evolutionary scenarios and examine the direct effects of interactions in the cluster on planetary systems. We model clusters initially in cool collapse, in virial equilibrium and expanding, and place a 1-Jupiter-mass planet at either 5 or 30 au from their host stars, with zero eccentricity. We find that after 10 Myr ∼10 per cent of planets initially orbiting at 30 au have been liberated from their parent star and form a population of free-floating planets. A small number of these planets are captured by other stars. A further ∼10 per cent have their orbital eccentricity (and less often their semimajor axis) significantly altered. For planets originally at 5 au the fractions are a factor of 2 lower. The change in eccentricity is often accompanied by a change in orbital inclination which may lead to additional dynamical perturbations in planetary systems with multiple planets. The fraction of liberated and disrupted planetary systems is highest for subvirial clusters, but virial and supervirial clusters also dynamically process planetary systems, due to interactions in the substructure. Of the planets that become free-floating, those that remain observationally associated with the cluster (i.e. within two half-mass radii of the cluster centre) have a similar velocity distribution to the entire star cluster, irrespective of whether they were on a 5 or 30 au orbit, with median velocities typically ∼1 km s−1. Conversely, those planets that are no longer associated with the cluster have similar velocities to the non-associated stars if they were originally at 5 au (∼9 km s−1), whereas the planets originally at 30 au have much lower velocities (3.8 km s−1) than the non-associated stars (10.8 km s−1). These findings highlight potential pitfalls of concluding that (a) planets with similar velocities to the cluster stars represent the very low mass end of the initial mass function and (b) planets on the periphery of a cluster with very different observed velocities form through different mechanisms.

Upper atmospheric rotation rate from orbit analysis

The rotation speed Λ of the upper atmosphere, mainly at heights of 180–360 km, was evaluated from the changes in orbital inclinations of GFZ. The results indicate that the value of Λ (in rev/d) decreases from 1.2 at 360 km to 0.9 at 180 km.

Limits to the planet candidate GJ 436c

We report on H-band, ground-based observations of a transit of the hot Neptune GJ 436b. Once combined to achieve sampling equivalent to archived observations taken with Spitzer, our measurements reach comparable precision levels. We analyze both sets of observations in a consistent way, and measure the rate of orbital inclination change to be of 0.02+/-0.04 degrees in the time span between the two observations (253.8 d, corresponding to 0.03+/-0.05 degrees/yr if extrapolated). This rate allows us to put limits on the relative inclination between the two planets by performing simulations of planetary systems, including a second planet, GJ 436c, whose presence has been recently suggested (Ribas et al. 2008). The allowed inclinations for a 5 M_E super-Earth GJ 436c in a 5.2 d orbit are within ~7 degrees of the one of GJ 436b; for larger differences the observed inclination change can be reproduced only during short sections (<50%) of the orbital evolution of the system. The measured times of three transit centers of the system do not show any departure from linear ephemeris, a result that is only reproduced in <1% of the simulated orbits. Put together, these results argue against the proposed planet candidate GJ 436c.

Asteroid orbit evolution due to thermal drag

Thermal drag, a variant of the Yarkovsky effect, may act on small asteroids with sizes from a few meters to a few tens of meters. Yarkovsky thermal drag comes from an asteroid's absorbing sunlight in the visible and reradiating it in the infrared. Since the infrared photons have momentum, by action‐reaction, they kick the asteroid when they leave its surface. The reradiation, which is asymmetric in latitude over the asteroid, gives a net force along the asteroid's pole. Due to the asteroid's thermal inertia, averaging this force over one orbital period produces a net drag if the spin axis has a component in the orbital plane. A regolith‐free basaltic asteroid 60 m in radius can shrink its semimajor axis by 2 AU (the distance from the asteroid belt to the Earth) over the age of the solar system. Regolith‐free iron asteroids evolve at about half the rate of basaltic ones. These calculations ignore planetary perturbations, collisions, erosion, etc. The rate of evolution varies inversely with the asteroid's radius for the size range considered here, so that smaller objects evolve faster than larger ones. The rate‐radius relation fails for objects smaller than a few meters because the thermal skin depth becomes comparable to the size of the asteroid. Basaltic asteroids covered by regoliths more than a few centimeters deep evolve much more slowly than regolith‐free ones. Thermal drag tends to circularize orbits. It can increase or decrease orbital inclinations. An object whose spin axis points in random directions over its lifetime displays little change in orbital inclination. Thermal drag appears to have little to do with the delivery of chondrites from the asteroid belt; the thermal drag timescale (108 years for meter‐sized objects) is long compared with their cosmic ray exposure ages, and aphelia in the asteroid belt are not expected for mature thermal drag orbits. However, Yarkovsky thermal drag may act on the recently discovered near‐Earth asteroids, which have radii of 10–30 m. Asteroid 1992 DA, for instance, might have its orbit shrunk by 0.1 AU in 3×107 years, removing it from an Earth‐crossing orbit. The near‐Earth asteroids also tend to have small to moderate orbital eccentricities, as expected for highly evolved thermal drag objects. However, the time needed to bring them in from the asteroid belt (about 109 years) is long compared with the collisional and dynamical lifetimes (both about 108 years) for Earth‐crossing objects, arguing against their emplacement by thermal drag.

Effect of rotating earth for analysis of aeroassisted orbital transfer vehicles

Aeroassisted orbital transfer vehicles operate both in the endo- and exo-atmospheres. Although an orbital trajectory is shaped by the inertia! state variables, the aerodynamic maneuvering that induces trajectory perturbation is dictated by the relative velocity. The difference in relative velocities between a nonrotating and a rotating earth produces a substantial difference in the entry dynamic pressure. The exit-condition errors introduced at the edge of sensible atmosphere by the dynamic pressure difference produce significant deviations in the final orbit transfer. Endo-atmospheric flight control laws that tend to minimize the orbit reinsertion propellent requirement for orbit transfer and plane change are also demonstrated. In conclusion, aeroassisted orbital transfer vehicle analysis with an operational altitude constraint and a stationary earth assumption tends to underpredict the final low-earth orbit altitude and to overpredict the orbital inclination change. Because the turning radius is on the Order of a global scale, latitude positions may influence the effectiveness of orbit plane-change analysis.

An improved theory for determining changes in satellite orbits caused by meridional winds

Meridional (south - to - north) winds in the upper atmosphere may be specified by the equivalent angular rotation rate, Ф and previous theories for the effect of meridional winds on satellite orbits have used Ф as the controlling parameter. In this report the theory is developed anew in terms of the parameter M = Ф Sec Ф, where Ф is the latitude. It is shown that in practice M is just as useful as Ф; and M has the advantage of leading to a much simpler and more accurate theory for expressing the changes in orbital inclination and right ascension of an orbit of any eccentricity (0 &lt; e &lt; 1) produced by meridional winds in an oblate atmosphere. The theory is developed in two parts: for high eccentricity ( e &gt; 0.05) and for low eccentricity ( e &lt; 0.05).

Analysis of 208 U.S. Navy orbits for the satellite 1970-47B at 14th-order resonance

The orbit of 1970-47B passed very slowly through 14th-order resonance, and the changes in orbital inclination and eccentricity have been analysed over a 4-year period, from January 1977 to January 1981, using 208 U.S. Navy orbits. The analysis has yielded values for three pairs of lumped harmonic coefficients of 14th order, which have accuracies equivalent to 0.4, 1.5 and 2.0 cm in geoid height. Three pairs of values of 28th-order lumped harmonic coefficients were also obtained, and the best of these has a standard deviation (S.D.) corresponding to an accuracy of 0.7 cm in geoid height. The lumped harmonic coefficients have been compared with the corresponding values from the latest geopotential models, and agreement is satisfactory.

Evaluation of 15th-order harmonics in the geopotential from analysis of resonant orbits

Satellite orbits contracting under the influence of air drag experience 15th-order resonance when the track over the Earth repeats after 15 revolutions. If the orbital decay rate is slow enough, an orbit passing through the resonance is appreciably perturbed by the effects of 15th-order harmonics in the geopotential. We have used the observed perturbations in 23 resonant orbits, at various inclinations to the equator, to determine the harmonic coefficients of order 15 and degree 15, 16, 17,... 35. Analysis of the changes in orbital inclination on the 23 orbits gives the harmonics of odd degree, while those of even degree are found from the changes in eccentricity on 16 of the orbits. The values derived are given in tables 6 and 8. The coefficients of degrees 15, 16, 17,... 23, should be more accurate than any previously obtained; their average s. d. is 1.4 x 10 -9 , equivalent to 1 cm in geoid height. Comparisons with comprehensive Earth models show the Goddard Earth Model 10B to be the best, and a standard deviation of about 3 x 10 -9 in the GEM 10B 15th-order coefficients is indicated.

Optimal three-burn orbit transfer

Abstract : This report presents an optimal three burn solution to a class of orbit transfer problems requiring large changes in orbital inclination. A nonlinear programming algorithm was used in conjunction with a simplified trajectory simulation, which used Keplerian orbit transfers and impulsive velocity increments. A number of parametric results were obtained using the simplified simulation. The validity of the simplified simulation was established for specific vehicle configurations with finite burns and oblate earth effects included. The effect of multiple stage rockets has also been treated.

Analysis of the orbit of 1970-65D, cosmos 359 rocket

Cosmos 359 rocket 1970-65D, was launched on 22 August 1970 into an orbit inclined at 51·2° to the Equator, with an initial perigee height of 209 km: it decayed on 6 October 1971 after a lifetime of 410 days. The orbit has been determined at 42 epochs during the lifetime, using the RAE orbit refinement program, PROP, with over 2600 observations. Observations from the Hewitt cameras at Malvern and Edinburgh were available for 10 of the 42 orbits. Ten values of density scale height, at heights between 185 and 261 km, have been determined from analysis of the variations in perigee height. Upper-atmosphere zonal winds and 15th-order harmonics in the geopotential have been evaluated from the changes in orbital inclination. The average atmospheric rotation rate, for heights near 220 km, is found to be 1·04 rev/day; but there are striking departures from the average, with well-established values of 1·30, 0·75, 1·35 and 0·95 over four successive 75-day intervals. The changes in inclination at the 15th-order resonance in November 1970 give values of lumped 15th-order harmonics, which will provide equations for evaluating coefficients of order 15 and even degree (16,18,…) and also show that useful results on the geopotential can be obtained from satellites with perigee as low as 200 km.

Equations for 15th-Order Harmonics in the Geopotential

BY analysing the orbit of Ariel 3, Gooding1 obtained two equations between 15th-order coefficients in the Earth's gravitational potential from the changes in orbital inclination as the satellite passed through 15th-order resonance (when the successive tracks over the Earth are exactly 24° apart). Gooding's equations, simplified by omitting terms which should be small, are: illustration where the quantities C and S are normalized coefficients in the infinite series expansion of the geopotential, as defined, for example, by Gaposchkin and Lambeck2. Open image in new window

The rotational speed of the upper atmosphere determined from changes in satellite orbits

Abstract Because the atmosphere rotates, a satellite is subjected to a small lateral aerodynamic force which has the effect of slightly changing the inclination of the orbit to the equator. For an eastbound satellite the inclination decreases, sometimes by as much as 0.1°, and the amount of the change is a measure of the angular velocity of the atmosphere at heights near that of the satellite's perigee. In this paper the angular velocity of the upper atmosphere is determined by examining the changes in orbital inclination of all suitable satellites. Although the orbital information is imperfect, useful values were obtained from 9 satellites, covering the years 1958–63, heights of 200–300 km and latitudes from 0–60°. If the angular velocity of the atmosphere is expressed as Λ times the angular velocity of the Earth, the values of Λ obtained all exceed 1, ranging between 1.1 and 1.9, with a mean of 1.46 and rms scatter of 0.28. This corresponds to a mean west-to-east wind speed in mid latitudes of over 100 m/sec. The results thus indicate that the upper atmosphere at 200–300 km height rotates faster than the Earth. A possible explanation is suggested.

The effect of atmospheric rotation on the orbital plane of a near-earth satellite

Besides the perturbations due to the gravitational field of the earth, the rotation of the earth’s atmosphere produces a perturbing force on a satellite which affects the motion of its orbital plane. Theoretical formulae are derived for the rotation of the orbital plane about the earth’s axis and the change in orbital inclination of a near-earth satellite of small eccentricity (&lt; 0.2) due to the influence of the atmosphere. It is assumed that the atmosphere is spherically symmetrical and has a density which varies exponentially with altitude. Comparison of the theoretical changes in orbital inclination show reasonably good agreement with those estimated from kinetheodolite observations, although the need for a slightly steeper theoretical curve is indicated. Although the rotation of the orbital plane is small, allowance must be made for it when making estimates of the harmonics of the earth's gravitational field.