Low Perigee Research Articles

A HERO for General Relativity

HERO (Highly Eccentric Relativity Orbiter) is a space-based mission concept aimed to perform several tests of post-Newtonian gravity around the Earth with a preferably drag-free spacecraft moving along a highly elliptical path fixed in its plane undergoing a relatively fast secular precession. We considered two possible scenarios—a fast, 4-h orbit with high perigee height of 1047 km and a slow, 21-h path with a low perigee height of 642 km . HERO may detect, for the first time, the post-Newtonian orbital effects induced by the mass quadrupole moment J 2 of the Earth which, among other things, affects the semimajor axis a via a secular trend of ≃4–12 cm yr − 1 , depending on the orbital configuration. Recently, the secular decay of the semimajor axis of the passive satellite LARES was measured with an error as little as 0 . 7 cm yr − 1 . Also the post-Newtonian spin dipole (Lense-Thirring) and mass monopole (Schwarzschild) effects could be tested to a high accuracy depending on the level of compensation of the non-gravitational perturbations, not treated here. Moreover, the large eccentricity of the orbit would allow one to constrain several long-range modified models of gravity and accurately measure the gravitational red-shift as well. Each of the six Keplerian orbital elements could be individually monitored to extract the G J 2 / c 2 signature, or they could be suitably combined in order to disentangle the post-Newtonian effect(s) of interest from the competing mismodeled Newtonian secular precessions induced by the zonal harmonic multipoles J ℓ of the geopotential. In the latter case, the systematic uncertainty due to the current formal errors σ J ℓ of a recent global Earth’s gravity field model are better than 1 % for all the post-Newtonian effects considered, with a peak of ≃ 10 − 7 for the Schwarzschild-like shifts. Instead, the gravitomagnetic spin octupole precessions are too small to be detectable.

On the possibility of long-time existence of submicron particles injected in elongated elliptical orbits with low perigee in the near-Earth space

On the basis of numerical experiments the theoretical possibility of long-time (longer than 1 month) and superlong-time (longer than 1 year) existence in orbit of technogenic microparticles (MPs) with radii of a few hundredths of a micrometer is demonstrated. MPs are injected into the near-Earth space (NES) in elongated elliptical low-perigee orbits with parameters, corresponding to Molniya satellite’s orbital parameters. Calculations were carried out taking into account disturbing effects on the MP orbital motion in NES of the following factors: the gravitational disturbance caused by polar oblateness of the Earth, the solar pressure force (calculated with using the techniques of the Mie theory), the drag force of a neutral component of background gas, as well as the electrodynamic forces caused by interaction of electric charge, induced on MPs, with the magnetic and electric fields of the NES.

Orbit lifetime for microparticles in highly elliptical orbits with low perigee

On the basis of numerical experiments, we have shown the principal possibility of long (more than 1 month) and extremely long (more than 1 year) orbit lifetime of technogenic microparticles with radii from 1 to 100 μm injected into the near-Earth space in highly elliptical orbits with low perigee, including the case of an orbit with parameters corresponding to the orbital parameters of the Molniya satellite. Calculations are performed taking into account the perturbing effect on the orbital microparticle motion in the near-Earth space of gravitational perturbation caused by the Earth’s polar oblateness, the solar pressure force (calculated using methods of the Mie theory), and the drag force of neutral component of the background gas under conditions of low, medium, and high levels of solar and geomagnetic activities.

Operation of the dual magnetometer on Cassini: science performance

As part of the science preparation for the Cassini dual-technique magnetometer experiment, the operational behaviour of the instrument has been considered in terms of the investigation achieving its science aims. The experimental performance falls into two categories: passive, accurate determination of the in situ vector field at Saturn, using nominal mode time series measurements, and event capture, using the data snapshot memory capabilities of the instrument electronics. There are specific science planning aspects during the extended tour of the Saturnian System, for both the magnetospheric coverage in general and for the operational schedule of the instrument. The key science aim of mapping global magnetic structure, for instance, has specific implications for operating the dual mode experiment which differ in each magnetospheric region. The optimal, in situ determination of the intrinsic, planetary magnetic field, in particular, can be achieved through operation of the scalar mode of the Vector Helium magnetometer in addition to the vector measurements taken by the Fluxgate magnetometer. This instrument mode is used in combination with close perigee passes in order to provide high field measurements. During Saturn Orbit Insertion, the start of the Saturnian tour, an extremely low perigee pass is achieved, providing a critical opportunity for measurement. Because the scalar measurement has a restricted field of view, there are also orientation implications for the spacecraft if good science performance is to be realised. A vital opportunity to assess the use of data obtained during scalar operation is provided by the Earth flyby, which can provide high field measurements in a known environment. We relate here the study of these operational issues, based on the expected character of the measured field and in the context of the operating modes of the instrument.

Orbit determination and analysis for 1970-97B at 14th-order resonance

The orbit of the satellite 1970-97B, the rocket of Cosmos 378, at inclination 74°, has been determined at 18 epochs between April and August 1971, when the effects of 14th-order resonance with the Earth's gravitational field were appreciable. The orbits were determined with the PROP 6 program from Hewitt camera, kinetheodolite, U.S. Navy and visual observations, and an average accuracy of 90 m in perigee distance was achieved, despite the low perigee height (near 230 km) and the consequent high drag. The orbits, together with 13 previously evaluated, have been analysed to reveal the effects of the 14th-order resonance and to evaluate six lumped geopotential harmonics of order 14. Because the orbit passed through resonance rapidly, the values are not as accurate as those from slow resonances; but they are more accurate than any others available for an inclination near 74°, and have proved their worth in a recent determination of individual 14th-order coefficients.

Analysis of the orbit of Cosmos 316 (1969—108 A)

Cosmos 316 (1969-108A) was a most unusual satellite. It was launched on 23 December 1969 into an orbit having a very low perigee (height 154 km ) and inclined at 49.5° to the equator. But, because of its high mass/area ratio, Cosmos 316 remained in orbit for 8 months, thus offering a unique opportunity to study the atmosphere at heights near 150 km by analysis of orbital changes. Orbits have been determined at 36 epochs during the satellite’s life with the aid of the R .A .E . orbit determination program Prop ; about 1600 observations were used, mainly radar and visual, but also some accurate photographic observations. The orbits obtained, which utilize the full accuracy of the observations, are the most accurate and consistent yet pub­lished for a satellite with such a low perigee. The perigee and apogee distances are accurate to about 150 m , and the s.d. in inclination is generally between 0.0005° and 0.0025°. The final orbit, at an epoch 20 h before re-entry and with a perigee height of 118 km, is among the most accurate, and indicates how the drag coefficient decreases as the atmospheric mean free path decreases to less than the satellite’s dimensions. The changes in inclination are analysed to determine upper-atmosphere winds, which prove to be very variable: the most extreme is a west-to-east wind of order 300 m /s in the afternoon in near-equatorial regions of the southern hemisphere between 24 July and 7 August 1970. The perigee distances have been used previously in determining variations of upper-atmosphere density, and are now also used to evaluate scale height. It proved possible to detect the change in inclination at the time of 15th-order resonance with the Earth’s gravitational field, when successive ground track s are 24° apart, and an equation for the 15th-order coefficients in the geopotential was obtained which confirms recent results from Transit 1B .

Air density at heights near 180 km in 1968 and 1969, from the orbit of 1967-31a

The satellite 1967-31A (A.T.S. 2), launched in April 1967, was unusual in having a low perigee (180 km initially) a near-constant cross-sectional area and a lifetime of more than two years. We have analysed its orbit to obtain 212 values of air density, mainly at heights between 160 and 190 km, during 14 months of high solar activity between 4 July 1968 and 2 September 1969 (when the satellite decayed). In general the air density exhibits only a weak dependence on solar activity, but the link between density and geomagnetic disturbances is obvious throughout: the two strongest geomagnetic storms, on 1 November 1968 and 15 May 1969, are accompanied by increases in density of 30 per cent and 70 per cent respectively. When such short-term variations are ignored, the underlying trend is a semi-annual variation in density, with maxima in October–November 1968 and March 1969, and minima in July 1968, January 1969 and July–August 1969. The July minima are deeper than the January minimum, and the average density at the maxima exceeds that at the minima by 32 per cent. A profile of density vs. height between 150 and 180 km for mid-1969 is also obtained; and a detailed comparison is made with previous results from 1968-59A.

Air density at heights between 130 and 160 km, from analysis of the orbit of 1968-59b

The satellite 1968-59B was a heavy sphere, of mass 272 kg and dia. 0.61 m, launched by the United States Air Force on 11 July 1968 into a polar orbit with an initial perigee height of 150 km. Despite the low perigee, the satellite remained in orbit for 38 days because of its exceptionally large mass/area ratio, and offers the opportunity of finding values of air density at heights lower than has been possible in previous studies of satellite orbits. Analysis of the orbit gives 28 values of air density, which show that the density increased from 1.49 × 10 −9 kg/m 3 at a height of 155 km to 7.9 × 10 9 kgm 3 at 130 km height. These values are in surprisingly good agreement with the COSPAR International Reference Atmosphere 1965, being about 9 per cent lower than CIRA. When the values of density are converted to a fixed height near 150 km, the day-to-day variations are found to be remarkably smooth between 12 July and 13 August, the deviations from the mean being less than 4 per cent; but there was a significant increase in density at the time of the increased solar activity centred at 15 August.

Variations in air density at heights near 150 km, from the orbit of the satellite 1966-101G

The satellite 1966-101G was launched on 2 November 1966 into an orbit with an initial perigee height of 140 km. A satellite with such a low perigee usually decays within a few days, but 1966-101G was exceptionally dense and remained in orbit until 6 May 1967. Analysis of the changes in its orbital period provides an unique opportunity for studying continuously for six months the variations in air density at a height near 150 km. This paper records the results of such an analysis, applicable for the (medium) level of solar activity prevailing early in 1967. It is shown that at a height of 155 km the air density is greater by day than by night, with the maximum daytime density exceeding the minimum night-time density by a factor of 1.7: in contrast the COSPAR International Reference Atmosphere 1965 predicts that the density should be slightly greater by night than by day. It is also found that the night-time density increases as solar activity increases, and that the density scale height given by CIRA 1965 at heights near 150 km is too low, perhaps by about 20%.