Apogee Height Research Articles

Метод определения параметров движения космических аппаратов на основе радиоинтерферометрических измерений со сверхдлинной базой

The proposed method for measuring current navigational parameters of spacecrafts makes it possible to control them to a certain extent using a single ground-based automated station. With this the following specifics of a single-station control are taken into account: location of spacecraft spatial-time monitoring stations, geometrical interpretation of these measurements, difficulties in processing of the received information and proper selection of radio equipment required for performing such measurements. The proposed method for trajectory tracking is based on the ultra-long-baseline interferometry. Measuring base here is the distance between a ground-based radio complex and onboard radio complex of the reference spacecraft that is constantly visible by the ground-based monitoring station. Onboard radio complex can include an array of spacecrafts traveling either along elongated elliptical orbit with an apogee height of more than twenty thousand kilometers or along a 36000 km high geostationary orbit. Application of the proposed method will help extend capabilities of the space monitoring system in terms of prompt clarification of public and private catalogues of spacecrafts orbiting the Earth.

TEST OPTICAL OBSERVATIONS OF THE COSMOS 1408 FRAGMENTS

The non-functioning spacecraft COSMOS 1408 (NSSDCA/COSPAR ID: 1982-092A) was destroyed as a result of tests involving Russian anti-satellite weapons on 15 November 2021. This led to the creation of a significant debris cloud that poses a threat to other objects in low Earth orbit (LEO), particularly those in close orbits. More than 1500 of these fragments reached trackable sizes. Such events require rapid and immediate monitoring through all available ground tracking means, including radar and optical observation. The following study presents the results of optical observations of the selected fragments of COSMOS 1408 in Ukraine. These observations were carried out by the telescope OES30 from the National Space Facilities Control and Test Center of the State Space Agency of Ukraine and the Fast Robotic Telescope (FRT) of the Research Institute "Mykolaiv Astronomical Observatory" in February 2022. The observations demonstrated that Ukrainian optical sensors are capable of tracking LEO space debris objects with radar cross-sections (RCS) less than 0.1 square meters when relatively accurate ephemeris data is available. The astrometric reduction has been performed for the acquired frames with fragments of the satellite, which revealed that orbital parameters of a significant part of the targeting objects were close to the orbital parameters of the original satellite before the event. Furthermore, the results of processing the available observations indicated that the range of apogee heights significantly exceeds the range of perigee heights. These findings align with conclusions drawn by previous researchers. In the future, it will be essential to assess the capabilities of sensors for observing the aftermath of object destruction in LEO, especially during the initial hours and days following such events when precise debris orbit data may be lacking.

Optimization of the launch profile of geostationary spacecraft with electric propulsion system using Falcon-9 launch vehicle

A combined flight profile is being considered, in which the Falcon 9 launch vehicle launches the spacecraft into elliptical intermediate orbit from the Cape Canaveral launch site. In the process of analyzing the problem, the value of the height of the perigee and the inclination of the intermediate orbit are fixed, and the height of the apogee of the intermediate orbit varies. After separation from the last stage of the launch vehicle, the spacecraft carries out transfer to geostationary orbit using electric propulsion system. At the stage of insertion spacecraft from intermediate orbit to geostationary orbit using electric propulsion system, the problem of minimizing the mass of the propellant, multi-revolutionary transfer is considered. The number of revolution and the height of the apogee of the intermediate orbit vary in order to analyze the effect of these parameters on the duration of the transfer and the delivered mass of the spacecraft into geostationary orbit. The main purpose of this paper is to calculate the optimal values of the apogee height of the intermediate orbit and the optimal number of revolution that ensure the delivery of the maximum mass of the spacecraft to the geostationary orbit in a given time delta(t)*. To solve the optimization problem, the Pontryagin maximum principle is applied. After apply ing the maximum principle, the optimization problem is reduced to solving the boundary value problem, which is solved by the continuation method by parameter. The paper presents the results of the optimization problem of multi-revolutionary transfer and analysis of the energy characteristics of combined flight profile for insertion of spacecraft into geostationary orbit.

Periodic Approximation of the Rotational Motion of the Photon-12 Satellite

The results of repeated processing of magnetic measurements carried out on the Photon-12 satellite (which was in orbit from September 9 to 24, 1999) are described. The processing was performed in order to reconstruct the uncontrolled rotational motion of this satellite. In re-processing, the simplified mathematical model of rotational motion was used. The actual orbit of a satellite (the apogee height is 380 km, the perigee height is 220 km) is replaced by a circular orbit; the expression for the aerodynamic moment acting on a satellite is simplified. The system of differential equations underlying the new model is autonomous and proved to be sufficiently accurate to reconstruct the satellite motion based on magnetic measurements in the case in which the satellite angular velocity was not very low and grew gradually. In the last third of the flight, when the satellite motion became virtually stable and had a sufficiently high angular velocity, this system could be reduced to a generalized-conservative system. Such a reduction makes more definite the set of its solutions suitable for approximate description of the actual motion of a satellite. In some segments of motion, the combining of which covers about 3 days, it was possible to use, for this purpose, the periodic solutions continued from the Lyapunov periodic solutions.

РЕСУРСОЭФФЕКТИВНОЕ УПРАВЛЕНИЕ РАДИОЛОКАЦИОННОЙ СТАНЦИЕЙ ДАЛЬНЕГО ОБНАРУЖЕНИЯ ДЛЯ НАБЛЮДЕНИЯ ВЫСОКООРБИТАЛЬНЫХ КОСМИЧЕСКИХ ОБЪЕКТОВ С ОДНОВРЕМЕННЫМ КОНТРОЛЕМ БАРЬЕРНОЙ ЗОНЫ

Radar surveillance (RS) of space objects has a number of advantages over the optical one. An urgent task is the RS of remote spacecraft, including high Earth orbit (HEO) spacecraft with the apogee height of more than 2500 km above the Earth's surface. In modern radars, well-known models, methods and technical solutions for observing remote spacecraft are implemented by increasing the duration (energy) of transmitted signals and observation time. This restriction does not allow to simultaneously detect and track objects of the "barrier zone" (BZ) while solving routine tasks using a long-range detection (LRD) radar. As a result, the radar throughput may decrease. It is proposed to use resource-efficient methods of multi-scanning monitoring (MSM). The methods make it possible to efficiently accumulate the energy of echo signals received during several radar observations. Purpose. In this paper, we research how to ensure the required throughput of the LRD radar when monitoring the BZ and observing the HEO objects using the MSM methods in conditions of a limited time resource. The study sets and solves the task of resource-efficient management of the LRD radar. This method consists in planning and organizing RS of the LRD radar for observation of the HEO objects with simultaneous control (detection and tracking) of BZ objects. In general, we formulate the task of RS of remote spacecraft and substantiate the algorithm for planning and organizing a RS for monitoring the HEO objects in conditions of a limited energy (time) resource. Methods. Analytical methods are used to substantiate the algorithm of resource-efficient control of the LRD radar using the MSM methods. Resource-efficient management is based on the use of a priori information about the parameters of the HEO objects trajectories, planning, organization and joint processing of RS results. The model of the LRD radar with the MSM channel is also substantiated in the form of a queuing system for assessing the radar throughput. Results. The simulation results indicate maintenance of the required throughput of the radar during the observations of the radar. It confirms the operability and effectiveness of the radar control method for solving the problem of simultaneous observation of the radar and monitoring of the objects of the BZ. Conclusion. The structure of the radar with the MSM channel and the method of resource-efficient management allow to implement the monitoring of the HEO objects with simultaneous detection and tracking of BZ objects. In contrast to the existing ones, the proposed algorithm for planning and control of the surveillance provides the required radar throughout during monitoring of the HEO objects.

Highly elliptical orbits for polar regions with reduced total ionizing dose

The study reports results of analysis related to minimization of the total ionizing dose (TID) for the Multiple Apogee Highly Elliptical Orbit with periods 14 h, 15 h and 16 h introduced earlier for continuous observation of the Earth’s polar regions. The modeling of space environment has been conducted with use of the European Space Agency’s SPENVIS tool based on the AE8/AP8 radiation models. Originally, the set of orbital parameters has been derived through the optimization process that included among other factors criteria for the apogee height limit and minimization of the radiation dose caused by trapped protons. By relaxing the apogee altitude limit, this study found the total ionizing dose TID can be significantly reduced for 15-h and 16-h orbits, while the originally proposed 14-h orbit is already at the minimum of radiation dose. For 15-h and 16-h orbits this converts into reduction of the thickness of aluminum shielding by factor 1.24–1.28 or an equivalent increase in the mission lifetime by up to 8.1 years. For example, an increase in apogee altitude to 49,620 km for 16-h orbit (eccentricity e = 0.74) in comparison to the originally proposed 16-h orbit (altitude equal to 43,500 km, e = 0.55) reduces the TID so that the shielding thickness decreases to 3.53 mm, instead of 4.35 mm of aluminum slab for the same 15-year duration of mission. Decrease of the TID is achieved due to significant reduction of ionizing radiation from the trapped electrons through the better placing of the orbit trajectory in the slot area, but at the expense of slight increase of ionizing radiation from the trapped protons and increase in apogee altitude to 46,640 km and 49,620 km for 15-h and 16-h orbit, correspondingly.

Obtaining a Horizontal Panoramic Image in a High-Power Rocket after Landing

During the 2017-2018 Collegiate Rocket Launch (CRL) competition, teams were required to design and construct a high-power rocket meeting certain design criteria. The goals for the 2018 competition were that it would complete a safe flight, reaching as close as possible to the target apogee height of 3,000 feet, as well as take a 360° horizontal image of the surrounding landscape after landing. The UW-Fox Valley team, the Rocketeers, designed a three-inch diameter, thin-walled fiberglass airframe at a final length of 67 inches that completed three safe flights on competition day. In order to get the 360° image, a Raspberry Pi micro-computer was used with a Pi Camera, which took multiple pictures that would be post-processed and stitched together. To orient the camera correctly, three legs were attached to the bottom of the booster section of rocket which were released at the first ejection after apogee. These legs were designed to orient the booster section to land upright. The camera module, located at the top of the booster, would then take multiple pictures of the surrounding landscape.

Utilizing NACA Ducts and an Inner Turbine System in a High-Power Rocket to Generate an Electric Current

During the 2016-2017 Collegiate Rocket Launch (CRL) competition, teams were required to design and construct a high-power rocket that would complete a safe flight that would reach as close as possible to a target apogee height of 3,000 feet, as well as generate an electric current during the pre-apogee portion of the rocket’s flight. The UW-Fox Valley team, the Rocketeers, designed a three-inch diameter, thin-walled fiberglass airframe at a final length of 188cm that was able to achieve safe flights. In order to generate electricity during the flight, the team used a ducting system that allowed air through an inner turbine system. On competition day, three safe flights were completed, with altitude, velocity, and acceleration data recorded. Electric generation data was recorded during the first flight, but due to environmental factors data was not recorded for voltage generation on the second and third flight. Â

The Chinese space Millimeter-wavelength VLBI array—A step toward imaging the most compact astronomical objects

The Shanghai Astronomical Observatory (SHAO) of the Chinese Academy of Sciences (CAS) is studying a space VLBI (Very Long Baseline Interferometer) program. The ultimate objective of the program is to image the immediate vicinity of the supermassive black holes (SMBHs) in the hearts of galaxies with a space-based VLBI array working at sub-millimeter wavelengths and to gain ultrahigh angular resolution. To achieve this ambitious goal, the mission plan is divided into three stages. The first phase of the program is called the Space Millimeter-wavelength VLBI Array (SMVA) consisting of two satellites, each carrying a 10-m diameter radio telescope into elliptical orbits with an apogee height of 60,000km and a perigee height of 1200km. The VLBI telescopes in space will work at three frequency bands, 43, 22 and 8GHz. The 43- and 22-GHz bands will be equipped with cryogenic receivers. The space telescopes, observing together with ground-based radio telescopes, enable the highest angular resolution of 20μarcsec at 43GHz. The SMVA is expected to conduct a broad range of high-resolution research, e.g. imaging the shadow of (dark region surrounding) the supermassive black hole in the heart of the galaxy M87 for the first time, studying the kinematics of water megamasers surrounding the SMBHs, and exploring the power source of active galactic nuclei. Pre-research funding has been granted by the CAS in October 2012, to support scientific and technical feasibility studies. These studies also include the manufacturing of a prototype of the deployable 10-m space-based telescope and a 22-GHz receiver. Here we report on the latest progress of the SMVA project.

Three-Apogee 16-h Highly Elliptical Orbit as Optimal Choice for Continuous Meteorological Imaging of Polar Regions

Abstract A highly elliptical orbit (HEO) with a 16-h period is proposed for continuous meteorological imaging of polar regions from a two-satellite constellation. This orbit is characterized by three apogees (TAP) separated by 120°. The two satellites are 8 h apart, with repeatable ground track in the course of 2 days. Advantages are highlighted in comparison to the Molniya 12-h orbit described in detail in a previous study (Trishchenko and Garand). Orbital parameters (period, eccentricity, and inclination) are obtained as a result of an optimization process. The principles of orbit optimization are based on the following four key requirements: spatial resolution (apogee height), the altitude of crossing the trapped proton region at the equator (minimization of radiation doze caused by trapped protons), imaging time over the polar regions, and the stability of the orbit, which is mostly defined by the rotation of perigee. The interplay between these requirements points to a 16-h period with an eccentricity of 0.55 as the optimum solution. The practical range of orbit inclinations that could be maintained during the spacecraft lifetime can vary from a critical value of 63.435° to 70° (subject to the amount of propellant available for orbital maneuvers). In comparison to Molniya, this type of orbit reduces the radiation exposure to high-energy protons by factor of 103–104. On the other hand, the main advantage of 16 h versus longer orbital periods up to 24 h is better spatial resolution as a result of a lower apogee height. A two-satellite TAP constellation with an orbital inclination of 66° provides 100% temporal coverage above 60°N, >95% above 55°N, >85% above 50°N, and >75% above 45°N.

Fourth order expansions of the luni-solar gravity perturbations along rotating axes for trajectory optimization

A fourth order extension of the analytic form of the accelerations due to the luni-solar gravity perturbations along rotating axes is presented. These derivations are carried out in order to increase the accuracy of the dynamic modeling of perturbed optimal low-thrust transfers between general elliptic orbits, and enhance the fidelity of trajectory optimization software used in simulations and mission analyses. A set of rotating axes attached to the thrusting spacecraft is used such that both the thrust and perturbation accelerations due to Earth's geopotential and the luni-solar gravity are mathematically resolved along these axes prior to numerical integration of the actual trajectory. This Gaussian form of the state as well as the adjoint differential equations form a set of equations that are readily integrated and an iterative process is used to achieve convergence to a desired transfer. This analysis further reveals that further extensions to higher orders, say to the fifth order and beyond, are not needed to extract even more accuracy in the solutions because the minimum-time transfer solutions become fully stabilized in the sense that they do not exhibit any differences beyond a fraction of a second, or at most a few seconds even in the more extreme cases of very large orbits with apogee heights around 100,000 km with strong lunar influence.

Launch windows for libration point missions

The four upcoming ESA missions to the collinear Lagrange points in the sun–Earth system, Herschel and Planck, GAIA, and LISA Pathfinder, will be launched from French Guiana by different Rockets, namely Ariane 5, Soyuz, and VEGA. Herschel and Planck will be launched together in 2008 on an Ariane 5. The launcher injects Herschel directly into the stable manifold of a large amplitude quasi-Halo orbit at L 2 . Departing from this launch orbit, Planck performs a three manoeuvre transfer to a Lissajous orbit, on which the sun–spacecraft–Earth angle remains below 15 ∘ . The daily and seasonal launch window for Herschel/Planck will be constrained by sun aspect angle conditions, by eclipse conditions, and by the propellant allocation on the Planck satellite. GAIA will be launched by Soyuz/Fregat end 2011. The target orbit at L 2 is similar to that of Planck, with a constrained sun–spacecraft–Earth angle. Initially, to reach a full year launch window, a launch scenario was preferred using a nearly circular parking orbit at 19 ∘ inclination, before igniting the Fregat upper stage to enter into the transfer. Recently alternative launch scenarios have been introduced, to guarantee a controlled re-entry of the Soyuz third stage, but leading to a reduction of the launch window. LISA Pathfinder will be delivered 2010 by the VEGA launcher to a low inclination elliptical orbit, with 1624 km apogee height. From there an apogee raising manoeuvre sequence, using a propulsion module connected to the spacecraft, reaches L 1 transfer conditions. Launch window calculations for these projects combine the choice of lift-off time and launch orbit conditions, with the selection of the target orbit at the Lagrange points and the minimisation of propellant to reach that orbit. For Herschel and LISA Pathfinder the target orbits have been chosen such that a transfer without deterministic manoeuvres is possible. Planck and GAIA both use a multiple manoeuvre fast transfer strategy reaching the Lissajous orbit at L 2 within 50 days.

Introduction to special section on Double Star‐Cluster Coordinated Studies on Magnetospheric Dynamic Processes

[1] The Double Star Program (DSP) is not only the first Chinese scientific satellite program but also the first collaborative mission between the China National Space Administration (CNSA) and the European Space Agency (ESA) [Liu et al., 2005]. This mission consists of two spacecraft, designed to investigate magnetospheric, global dynamic processes, and their response to solar wind-forcing and interplanetary magnetic field (IMF) disturbances, in conjunction with the previously launched four-satellite ESA Cluster Mission (Figure 1). The first spacecraft of DSP, called in Chinese ‘‘Tan Ce –1’’ (TC-1–Explorer-1), was launched successfully by a Chinese Long March 2C rocket at 2006 CET on 29 December 2003, into an elliptical orbit with perigee height of 550 km and apogee of 66,970 km, and inclined at 28.5 degrees to the equator (orbital period 27.4 h). TC-2 was launched also by a Chinese Long March 2C rocket at 1515 CET on 25 July 2004 into a polar orbit, having a perigee height of 700 km and apogee height of 39,000 km, with a period of 11.7 h. [2] The orbits of the two Double Star spacecraft have been specially designed to complement the ESA Cluster mission by maximizing the time periods when both Cluster and Double Star are in the same magnetospheric regions or connected magnetically with each other. The two missions together allow simultaneous observations of the Earth magnetosphere from six points in space in a three-dimensional manner. Together with the four Cluster spacecraft, on the dayside, the TC-1 orbit enables prolonged observations of the Earth’s bow shock and simultaneous observations of magnetic reconnection near the subsolar point and near the cusp, as well as on the flanks of the magnetosphere at both high and low latitudes. On the nightside, the combined spacecraft allow Earth’s dynamic magnetotail to be investigated, simultaneously in key regions where magnetospheric substorm onset and particle acceleration are thought to occur. The TC-2 orbit design focused on physical processes taking place over the high-latitude magnetospheric region, the development of auroral substorms, and the intensification of the ring current. [3] Both Double Star satellites are cylindrical in shape with a diameter of 2.1 m, a height of 1.2 m, and a mass of 340 kg (Figure 2). The two Double Star spacecraft structures are identical and only differ in the communication booms. TC-1 carries one communication boom and TC-2 has two booms. In addition, two deployable 3.5 m booms are attached at the bottom of the spacecraft and carry the fluxgate and search coil magnetometers. The spin axis is set to lie perpendicular to the ecliptic and the spacecraft makes 15 rotations per minute (the same as Cluster) enabling the full, three-dimensional particle distribution functions to be measured every 4 s. [4] Each Double Star spacecraft carries eight scientific instruments to measure the magnetic field, waves, electron, ions of low and high energy, and energetic neutral atoms. The highlight aspect of Europe’s participation in Double Star program was to provide seven identical instruments (spares or duplicates) to those flying on the Cluster spacecraft.

A constant gain Kalman filter approach for the prediction of re-entry of risk objects

The accurate estimation of the predicted re-entry time of decaying space debris objects is very important for proper planning of mitigation strategies and hazard assessment. This paper highlights the implementation strategies adopted for the online reentry prediction using Kalman filter approach with constant gains with the states being the semi-major axis, eccentricity and ballistic coefficient and using the measurements of the apogee height and perigee height derived from the Two Line Elements provided by agencies like USSPACECOM. Only a very simple model is utilised for the orbit propagation and a basic feature of the present approach is that any unmodellable state and measurement errors can be accounted for by adjusting the Kalman gains which are chosen based on a suitable cost function. In this paper we provide the details of validating this approach by utilising three re-entries of debris objects, namely, US Sat. No. 25947, SROSS-C2 Satellite and COSMOS 1043 rocket body. These three objects re-entered the Earth's atmosphere on 4th March 2000, 12th July 2001 and 19th January 2002, respectively.

Rocket observation of energetic electrons in the low-altitude auroral ionosphere during the DELTA campaign

Abstract This paper reports on properties of energetic electrons observed by the Auroral Particle Detector (APD) on board the sounding rocket S-310-35, which was launched from And/0ya Rocket Range, Norway, at 0033:00 UT on 13 December 2004 during the DELTA campaign. The APD was designed to measure energy spectra of energetic electrons in the range of 3.5 to 65 keV every 10 ms using avalanche photodiodes. The measurement was done at altitudes of 90–140 km (apogee height of the rocket flight), which corresponded to the collisional interaction region of precipitating electrons with the atmospheric constituents. The overall profile of energetic electron precipitations was consistent with auroral images taken from the ground. The downward fluxes almost always exceeded those of upward electrons, and the ratio of downward to upward fluxes increased with energy and also with altitude. This is reasonably understood in terms of the effect of collisions between the energetic electrons and the atmospheric constituents. An interesting feature in energy spectra of precipitating electrons is the existence of non-thermal electrons at higher energies, regardless of inside or outside of auroral arcs. In order to predict the incident downward spectra at the top of the atmosphere, we have applied an analytic method of Luhmann (1976) to evaluate the collisional effect on the electron spectra. As a result, most of the observed energy spectra of precipitating electrons are well expressed by kappa distributions with the thermal energy of a few hundreds of eV and kappa of 5–8, while the spectrum inside a strong arc is better fitted by the sum of a Maxwellian distribution on the lower energy side and a power law at higher energies. To the authors’ knowledge, this is the first direct and reliable measurement of energy spectra of electrons in the 10-keV energy range in the auroral ionosphere.

A solution to the problem of phaseless mapping for a high-orbit space—Ground radio interferometer

We consider the problem of mapping with ultra-high angular resolution using a space—ground radio interferometer with a space antenna in a high orbit, whose apogee height exceeds the radius of the Earth by a factor of ten. In this case, a multielement interferometer essentially degenerates into a two-element interferometer. The degeneracy of the close-phase relations prevents the use of standard methods for hybrid mapping and self-calibration for the correct reconstruction of images. We propose a new phaseless mapping method based on methods for the reconstruction of images in the complete absence of phase information, using only the amplitudes of the spatial-coherence function of the source. In connection with this problem, we propose a new method for the reliable solution of the phase problem, based on optimizing information-carrying nonlinear functionals, in particular, the Shannon entropy. Results of simulations of mapping radio sources with various structures with ultra-high angular resolution in the framework of the RADIOASTRON mission are presented.

ALOFT: A Potential Low Frequency Space VLBI Mission

We present a preliminary study of A LOw Frequency Orbiting Telescope (ALOFT) which co-observes with ground radio telescopes, in a similar fashion to the current VSOP mission. Our current straw-man ALOFT mission has a spacecraft operating at three frequency bands (0.33, 0.6, and 1.4—1.6 GHz) in an orbit with a 10,000 km apogee height. It should be relatively low cost as the lower frequencies less stringently constrain the design, for example uncooled receivers, narrower bandwidth, and simple antennae. The major science goal to be addressed by this mission is to examine scattering phenomena through the technique of space VLBI, although other problems, such as AGN physics, can of course also be addressed.

Contraction of satellite orbits using KS elements in an oblate diurnally varying atmosphere

A non‐singular analytical theory for the motion of near‐Earth satellite orbits with air drag is developed in terms of KS elements, utilizing a model of the atmosphere that allows for oblateness and in which the density behaviour approximates to the observed diurnal variation. The series expansions include up to cubic terms in e (eccentricity) and c (a small parameter dependent on the flattening of the atmosphere). Only two of the nine equations are solved analytically to compute the state vector at the end of each revolution due to symmetry in the KS element equations. Numerical comparisons between the analytical and numerically integrated values of the drag perturbed orbital parameters (semi‐major axis, eccentricity and argument of perigee) are made up to 100 revolutions for the test cases with different inclinations, over a range of perigee and apogee heights, which experience significant diurnal bulge effects. The comparisons are found to be good. The accuracies of the numerical computations are checked with the bilinear relation in KS elements, and are found to be very satisfactory.

Strategies for Maximizing a Satellite Lifetime by Tether-Mediated Orbital Injection

The tether slingshot technique, which is based on the exchange of angular momentum between a satellite and a platform, is analyzed here with the goal of maximizing the satellite lifetime after release. Once the tether is deployed and the system librates about the local vertical, the tether is cut twice: the first time at the platform end in order to increase the apogee height of the satellite-tether system and later on at the satellite end in order to increase the perigee height of the satellite. The goal is to define the conditions at the end of deployment and the timing and parameters of the two cuts in order to maximize the satellite lifetime. Two separate strategies are followed: (a) the first tether cut occurs when the libration angle reaches a critical value for which the tether crosses the local vertical (with prograde libration) at the second apogee passage, i.e., when the second cut provides the maximum increase of perigee altitude; and (b) the first cut takes place when the tether crosses the local vertical and the true anomaly at the second tether cut is taken as an additional free parameter of the optimization process. In both strategies we assume, at first, that the maximum lifetime corresponds to the minimum semi-major axis decay rate or, conversely, to the maximum increase of the satellite perigee. Since increasing perigee height means sacrificing apogee height, the assumption above is tested by directly computing the satellite lifetime as a function of the free parameters in order to refine the estimate of the optimal cut parameters. The orbital-parameters-oriented approaches (a) and (b), together with the direct computation of the lifetime, allow us to select the end-of-deployment and cut parameters which maximize the satellite lifetime.

On the low latitude topside models: I. Electron density

Ion density measured within the scope of the ACTIVE Project was analyzed for range of ±30 invariant latitude. Apogee (2500 km) and perigee (500 km) data of December 1989 and March 1990, though in general agreement with the IRI, show a distinct equatorial anomaly yet at altitude of 500 km. A small longitude effect appears at local early morning at apogee height. Geomagnetic activity causes an increase of density, particularly in apogee.