Effect Of Atmospheric Drag Research Articles

Effects of plasma drag on low Earth orbiting satellites due to solar forcing induced perturbations and heating

The upper atmosphere changes significantly in temperature, density and composition as a result of solar cycle variations, which causes severe storms and flares, and increases in the amount of absorbed solar radiation from solar energetic events. Satellite orbits are consequently affected by this process, especially those in low Earth orbit (LEO). In this paper, we present a model of atmospheric drag effects on the trajectory of two hypothetical LEO satellites of different ballistic coefficients, initially injected at h=450km. We investigate long-term trends of atmospheric drag on LEO satellites due to solar forcing induced atmospheric perturbations and heating at different phases of the solar cycle, and during short intervals of strong geomagnetic disturbances or magnetic storms. We show dependence of orbital decay on the severity of both solar cycle and phase and the extent of geomagnetic perturbations. The result of the model compares well with observed decay profile of some existing LEO satellites and provide a justification of the theoretical considerations used here.

Analytical Model for the Propagation of Small-Debris-Object Clouds After Fragmentations

Current debris evolutionary models usually neglect fragments smaller than 10 cm because of the high computational effort they add to the simulation. However, small-debris objects can also be dangerous to operational satellites. This work proposes an analytical approach to describe the evolution of a cloud of small fragments generated by a collision in low Earth orbit. The proposed approach considers the cloud globally and derives its evolution analytically, in terms of the change in the spatial density under the effect of atmospheric drag. As a result, the analytical approach allows the representation of small fragments and noticeably reduces the computational time under 10% compared to the numerical propagation of all the fragment trajectories. For altitudes above 800 km, the relative error compared to the numerical method is lower than 10%.

A variable drag coefficient, spatially extended numerical model of hammer throws and new wind tunnel data on current hammers

The maximum distance a hammer can be thrown depends on its mass, length and aerodynamic drag, meaning that record hammer throws performed before and after a rule change (for example, if the minimum mass is changed) cannot be compared directly. However, if all factors affecting the flight of a hammer are fully understood, and the range travelled by a hammer thrown with a given initial speed, angle and release height can be predicted, records thrown under different rules can be compared. In this work, a numerical model is developed, which includes the effects of atmospheric pressure, altitude, Coriolis Effect, gravitational variation, wind speed, ambient temperature, linear drag, torsional drag, hammer size and hammer orientation. It is based on the model of Mizera and Horvath (J Biomech 35:785–796, 2002). Two refinements are made: the drag coefficient varies with Reynolds number, and the hammer is represented as a spatially extended object with nonzero moment of inertia. New wind tunnel data on the drag of the three main components of the hammer (ball, cable and handle) are presented. This data are incorporated into the model which is then used to predict throws made at the IAAF 2011 World Athletics Championships (Daegu, Korea). The model is shown to be capable of predicting to within 1 % the distance of hammer throws where the air density, latitude, release height, release angle and release velocity are known. It is more accurate than numeric and analytic models which assume a constant drag coefficient. This may be because it does not require the user to choose the drag coefficient and automatically uses an appropriate drag coefficient regardless of conditions. With a good biomechanical model or good assumptions about release speeds, throws with different implements can be compared to compare records thrown before and after rule changes. Further work is needed to develop a biomechanical model capable of predicting the release speed an athlete can achieve with a range of different implements.

Effects of Geopotential and Atmospheric Drag Effects on Frozen Orbits Using Nonsingular Variables

The concept of frozen orbit has been applied in space missions mainly for orbital tracking and control purposes. This type of orbit is important for orbit design because it is characterized by keeping the argument of perigee and eccentricity constant on average, so that, for a given latitude, the satellite always passes at the same altitude, benefiting the users through this regularity. Here, the system of nonlinear differential equations describing the motion is studied, and the effects of geopotential and atmospheric drag perturbations on frozen orbits are taken into account. Explicit analytical expressions for secular and long period perturbations terms are obtained for the eccentricity and the argument of perigee. The classical equations of Brouwer and Brouwer and Hori theories are used. Nonsingular variables approach is used, which allows obtaining more precise previsions for CBERS (China Brazil Earth Resources Satellite) satellites family and similar satellites (SPOT, Landsat, ERS, and IRS) orbital evolution.

Optimal sliding mode control for spacecraft formation flying in eccentric orbits

In order to control the relative motion for spacecraft formation flying in eccentric orbits, an optimal sliding mode controller is presented. This controller is designed based on the linearized two-body relative motion dynamics and is applied to the nonlinear system that includes the effects of external disturbances. The optimal control design is based on a linear quadratic method that is supplemented by an integral sliding mode control technique to robustify the controller. It is assumed that the leader and follower spacecraft are in a low Earth orbit and subject to the perturbing effects of J2 and atmospheric drag. Using the Lyapunov second method, the stability of the closed-loop system is guaranteed. The performance of the proposed controller in tracking the desired reference trajectory is compared to a sliding mode controller, and simulation results show the effectiveness of the proposed controller.

Estimation of ballistic coefficients of low altitude debris objects from historical two line elements

This paper presents a new method for estimating ballistic coefficients (BCs) of low perigee debris objects from their historical two line elements (TLEs). The method uses the drag perturbation equation of the semi-major axis of the orbit. For an object with perigee altitude below 700km, the variation in the mean semi-major axis derived from the TLE is mainly caused by the atmospheric drag effect, and therefore is used as the source in the estimation of the ballistic coefficient. The method is tested using the GRACE satellites, and a number of debris objects with external ballistic coefficient values, and agreements of about 10% are achieved.The method is also applied to estimate the BC values of three low perigee debris objects, which were tracked optically in May 2012 by the EOS Space Debris Tracking System. The single-station sparse tracking data of the three debris objects is processed using the orbit analysis software developed at EOS Space Systems. When tracking data of only 2 passes over about 24h is available, the errors of orbit predictions for 24h are mostly smaller than 100arc seconds using the estimated BC values from the new method – significantly smaller than prediction errors obtained using other BC estimations.

Nanosatellite swarm missions in low Earth orbit using laser propulsion

Many missions could benefit from the exploitation of very low height orbits, including Earth observation, atmospheric measurement and space weather research missions. However satelliteʼs lifetime decreases very quickly when the mission requires to orbit into the dense layers of the atmosphere. The mission performance could be enhanced using innovative propulsion techniques, counteracting the effect of atmospheric drag. Among these, laser propulsion potentially offers great weight and power savings, obtained by separating the propulsion system energy source from the propelled satellite. The energy source for the propulsion system is a pulsed laser beam generated remotely, while only collecting mirrors and ablative material are necessary on the target spacecraft. A mission architecture for very low altitude nanosatellite swarms using a space-based pulsed laser propulsion is described. A simplified laser-sustained re-orbiting maneuver sequence is proposed, leading to a straightforward evaluation of the maneuver times, showing that the laser propulsion system is suitable for low altitude nanosatellite missions.

Orbit evolution, maintenance and disposal of SpaceChip swarms through electro-chromic control

The combined effect of solar radiation pressure, Earth oblateness and atmospheric drag on the orbital dynamics of satellites-on-a-chip (SpaceChips) is investigated for future swarm mission concepts. The natural evolution of the swarm is exploited to perform spatially distributed measurements of the upper layers of the atmosphere. The energy gain from asymmetric solar radiation pressure can be used to balance the energy dissipation from atmospheric drag. An algorithm for long-term orbit control is then designed, based on changing the reflectivity coefficient of the SpaceChips. The subsequent modulation of the solar radiation pressure allows stabilisation of the swarm in the orbital element phase space. It is shown that the orbit lifetime for such devices can be extended through the interaction of solar radiation pressure and atmospheric drag and indeed selected and the end-of-life re-entry of the swarm can be ensured, by exploiting atmospheric drag.

Orbit design for future SpaceChip swarm missions in a planetary atmosphere

The effect of solar radiation pressure and atmospheric drag on the orbital dynamics of satellites-on-a-chip (SpaceChips) is exploited to design equatorial long-lived orbits about the oblate Earth. The orbit energy gain due to asymmetric solar radiation pressure, considering the Earth's shadow, is used to balance the energy loss due to atmospheric drag. Future missions for a swarm of SpaceChips are proposed, where a number of small devices are released from a conventional spacecraft to perform spatially distributed measurements of the conditions in the ionosphere and exosphere. It is shown that the orbit lifetime can be extended and indeed selected through solar radiation pressure and the end-of-life re-entry of the swarm can be ensured, by exploiting atmospheric drag.

Orbital Dynamics of "Smart-Dust" Devices with Solar Radiation Pressure and Drag

This paper investigates how perturbations due to asymmetric solar radiation pressure, in the presence of Earth shadow, and atmospheric drag can be balanced to obtain long-lived Earth centred orbits for swarms of micro-scale 'smart dust' devices, without the use of active control. The secular variation of Keplerian elements is expressed analytically through an averaging technique. Families of solutions are then identified where Sun-synchronous apse-line precession is achieved passively to maintain asymmetric solar radiation pressure. The long-term orbit evolution is characterized by librational motion, progressively decaying due to the non-conservative effect of atmospheric drag. Long-lived orbits can then be designed through the interaction of energy gain from asymmetric solar radiation pressure and energy dissipation due to drag. In this way, the usual short drag lifetime of such high area-to-mass spacecraft can be greatly extended (and indeed selected). In addition, the effect of atmospheric drag can be exploited to ensure the rapid end-of-life decay of such devices, thus preventing long-lived orbit debris.

Formation flight of satellites in the presence of atmospheric drag

The subject of this paper is the investigation of the effects of aerodynamic forces on the formation flight of satellites and the assessment of using differential drag as a means for formation maintenance. In order to study spacecraft formation flight in low Earth orbits, it is essential to consider the effect of J2. Schweighart and Sedwick have presented a set of linearized differential equations of motion, an extension of the Clohessy-Wiltshire equations, which includes the J2 effects and are valid for circular orbits. In this paper, the Schweighart-Sedwick equations are modified to include the effects of atmospheric drag while maintaining their linearity and simplicity. These ideas are then extended to include reference orbits of small eccentricity. This results in a set of linear differential equations of motion which takes into account J2 and drag perturbations as well as the elliptic nature of the reference orbit. Numerical simulation results based on the model are presented which characterize the effects of drag on projected circular type formations in the context of two different formation flying missions. It is shown that it is feasible to use differential drag to maintain a projected circular formation through simple panel rotation schemes.

Satellite Skin-Force Modelling for Atmospheric Drag Calculations

Satellites in low Earth orbits are influenced by the Earth’s atmosphere. The interactions between the molecules and the spacecraft cause the highest non-gravitational force, which in magnitude is comparable to planetary disturbances. Therefore the modelling of atmospheric drag effects is important for many missions with a scientific background like STEP (Satellite Test of Equivalence Principle). With the STEP mission variations between gravitational and inertial mass shall be measured with an accuracy of 10−18. The results are of great interest for cosmological and gravitational theories. To achieve the aimed accuracy, a precise model of external disturbances is necessary. In this article the method of Ray-Tracing is used to quantify the atmospheric drag forces and torques for spacecrafts of arbitrary shape.

Accretion rates of planetesimals by protoplanets embedded in nebular gas

When protoplanets growing by accretion of planetesimals have atmospheres, small planetesimals approaching the protoplanets lose their energy by gas drag from the atmospheres, which leads them to be captured within the Hill sphere of the protoplanets. As a result, growth rates of the protoplanets are enhanced. In order to study the effect of an atmosphere on planetary growth rates, we performed numerical integration of orbits of planetesimals for a wide range of orbital elements and obtained the effective accretion rates of planetesimals onto planets that have atmospheres. Numerical results are obtained as a function of planetesimals’ eccentricity, inclination, planet’s radius, and non-dimensional gas-drag parameters which can be expressed by several physical quantities such as the radius of planetesimals and the mass of the protoplanet. Assuming that the radial distribution of the gas density near the surface can be approximated by a power-law, we performed analytic calculation for the loss of planetesimals’ kinetic energy due to gas drag, and confirmed agreement with numerical results. We confirmed that the above approximation of the power-law density distribution is reasonable for accretion rate of protoplanets with 1–10 Earth masses, unless the size of planetesimals is too small. We also calculated the accretion rates of planetesimals averaged over a Rayleigh distribution of eccentricities and inclinations, and derived a semi-analytical formula of accretion rates, which reproduces the numerical results very well. Using the obtained expression of the accretion rate, we examined the growth of protoplanets in nebular gas. We found that the effect of atmospheric gas drag can enhance the growth rate significantly, depending on the size of planetesimals.

Thermospheric density model blending techniques: Bridging the gap between satellites and sounding rockets

Uncertainty in the atmospheric density is a crucial error source in calculating orbits of satellites in low Earth orbit. As a result, establishing accurate thermospheric neutral density models is important for predicting the motion of these satellites. Unfortunately, since density data in the altitude range between 140 and 200 km are sparse, predicting the neutral density to estimate atmospheric drag effects on the motion of satellites operating in this altitude region is subject to relatively large errors. A previous study found that the Jacchia‐Bowman model (JB2006) is the most reliable thermospheric empirical neutral density model above 200 km and the Naval Research Laboratory's Mass Spectrometer Incoherent Scatter (NRLMSISE‐00) model, whose core formulation is based on incoherent scatter radar data, can be considered a more reliable neutral density model below approximately 140 km. We have developed a simple bridging technique to blend the two models between these two regions. A two‐body model with atmospheric drag was used to compare effects of various atmospheric density models. These preliminary tests are conducted by propagating the positions of satellites orbiting between 140 and 200 km, with various ballistic coefficients, using the JB2006, the NRLMSISE‐00, and the bridging technique.

Investigating suitable orbits for the Swarm constellation mission – The frozen orbit

Abstract This paper proposes a suitable orbit design for the lower pair of ESA's Swarm constellation mission, flying side-by-side in near-polar and circular orbits with a separation of only 1.4° at ascending node. Both orbits are suggested to be frozen orbits to minimize the evolution, and an along-track separation strategy is applied to avoid collision risk. The characteristics of the proposed orbit type are examined through numerical techniques including high-fidelity perturbation models. The prime change from the initial configuration is an along-track separation. The perturbations causing the along-track drift are analyzed by switching on/off certain perturbations. The results indicate that the tesseral harmonics and the atmospheric drag yield dominant effects. The atmospheric drag effect shows a dependence on the local time of the ascending node. From two months of orbit propagation for the altitude 300 km the maximum along-track drift we obtain is about 80 km, which is still within the measurement requirement range. Several maneuver strategies for maintaining the proposed orbit design are suggested. The results analyzed for the proposed orbit design show that collision risk can be avoided by along-track separation within the frozen orbit design. Consequently, this combination is considered as a suitable approach for Swarm's lower pair.

Altitude measurement for model rocketry

The simple, ballistic time-of-flight equation for the maximum altitude of a vertically launched rocket neglects the effects of atmospheric drag. We show that the error introduced by using this equation to estimate the maximum altitude is typically less than 1% because of the effective cancellations of timing errors during the ascent and descent of the rocket.

A model of relative translation and rotation in leader-follower spacecraft formations

In this paper, a model of a leader-follower spacecraft formation in six degrees of freedom is derived and presented. The nonlinear model describes the relative translational and rotational motion of the spacecraft, and extends previous work by providing a more complete factorization, together with detailed information about the matrices in the model. The resulting model shows many similarities with models for systems such as robot manipulators and marine vehicles. In addition, mathematical models of orbital perturbations due to gravitational variations, atmospheric drag, solar radiation and third-body effects are presented for completeness. Results from simulations are presented to visualize the properties of the model and to show the impact of the different orbital perturbations on the fl ight path.

Atmospheric drag effects on the KOMPSAT-1 satellite during geomagnetic superstorms

Abstract We examine the atmospheric drag on the low earth-orbiting satellite, KOMPSAT-1 in a sun-synchronous orbit at ~685-km altitude starting in 1999, during a 3-month (October-December) period in 2003. This 3-month interval includes the October 29-30 and November 20 magnetic superstorms and weak to moderate storms. We observed that the daily KOMPSAT-1 drag acceleration transiently responses to transient storm-time disturbances. That is, there is an one-to-one correspondence between the KOMPSAT-1 drag accelerations and the storm events. We find that the drag acceleration correlates strongly with the level of geomagnetic disturbance. This indicates that the trajectory of KOMPSAT-1 is significantly perturbed during extremely disturbed intervals because of atmospheric density increase. The main contributor to the density increase is Joule heating associated with the geomagnetic activity rather than the solar EUV radiation, as reported by previous studies. We suggest that understanding how the upper atmosphere responses to the geomagnetic-associated heating is important to predict space weather impacts on low earth-orbiting satellites.

Results and Issues of Atmospheric Density Correction

The unpredictable effects of atmospheric drag are the dominant error source in orbit determination and prediction of low altitude satellites. One prospective direction for increasing the accuracy of position prediction for these satellites is the organization of an upper atmosphere monitoring service. This would be the analog of the weather service in the lower atmosphere. For this purpose drag estimates associated with cataloged inactive payloads and debris were used. At any given time there are several hundred such drag-perturbed space objects. The element sets for these space objects are updated as an ordinary routine operation by the space surveillance systems a few times per day in near-real time. With the drag data operative corrections to the modeled atmosphere density can be constructed without significant additional costs. The drag data for the space objects used in this study were obtained by using Two Line Element (TLE) sets as the observational data. The density corrections are expressed as a linear function of altitude. The time series for the density corrections were obtained with a one-day grid over a four-year interval. The effectiveness of this density correction process was evaluated by comparison of the orbit determination and prediction results obtained with and without the estimated density variations.

Atmospheric effects on the dynamics of the MIMOSA satellite

To predict the orbital effects of atmospheric drag, it is necessary to know a satellite's effective area perpendicular to the orbital velocity and the drag coefficient for various heights and various levels of solar activity. The atmospheric density has to be determined as a function of the satellite's position and time; in addition, the effects of the atmospheric rotational velocity are introduced (depending on the height and geographical latitude). To calculate the acceleration components caused by atmospheric drag, it is also necessary to have knowledge of the zonal and meridional atmospheric streams (winds), as well as the streams (winds) in arbitrary directions. The lifetime of the MIMOSA satellite is presented according to a variety of orbital elements and for different launch dates.