Lunar Gravity Research Articles

Skipping vs. running as the bipedal gait of choice in hypogravity

Hypogravity challenges bipedal locomotion in its common forms. However, as previously theoretically and empirically suggested, humans can rely on "skipping," a less common gait available as a functional analog (perhaps a vestigium) of quadrupedal gallop, to confidently move when gravity is much lower than on Earth. We set up a 17-m-tall cavaedium (skylight shaft) with a bungee rubber body-suspension system and a treadmill to investigate the metabolic cost and the biomechanics of low-gravity (Mars, Moon) locomotion. Although skipping is never more metabolically economical than running, the difference becomes marginal at lunar gravities, with both bouncing gaits approaching values of walking on Earth (cost ≈ 2 J · kg(-1)· m(-1)). Nonmetabolic factors may thus be allowed to dominate the choice of skipping on the Moon. On the basis of center of pressure measurements and body segments kinetics, we can speculate that these factors may include a further reduction of mechanical work to move the limbs when wearing space suits and a more effective motor control during the ground (regoliths)-boot interaction.

Improvement in the Recovery Accuracy of the Lunar Gravity Field Based on the Future Moon-ILRS Spacecraft Gravity Mission

This study mostly concentrates on the sensitivity analysis regarding the future dedicated Moon-ILRS spacecraft gravity mission. Firstly, the new single and combined analytical error models for the cumulative lunar geoid height impacted by the major error sources comprising the inter-spacecraft range-rate of the interferometric laser ranging system (ILRS), the spacecraft orbital position tracked by the deep space network (DSN) and the non-conservative force of the drag-free control system (DFCS) are developed on the basis of the spacecraft-to-spacecraft tracking in the low–low mode (SST-LL) from the future twin Moon-ILRS spacecraft. Secondly, the correctness of the new single and combined analytical error models is proved according to the compliance of the cumulative lunar geoid height errors among the inter-spacecraft range-rate, orbital position and non-conservative force. Finally, in comparison with the past gravity recovery and interior laboratory (GRAIL) program, the preferred design for the future Moon-ILRS mission is achieved in this paper. We recommend that the future twin Moon-ILRS formation-flying spacecraft had better adopt the new-type space-borne instruments involving the ILRS and DFCS. We demonstrate the compatible accuracy indexes of the key sensors (e.g., 10−9 m/s in the inter-spacecraft range-rate, 1 m in the orbital position and 3 × 10−13 m/s2 in the non-conservative force) and the optimal orbital parameters (e.g., 25-km orbital altitude, 100-km inter-spacecraft range and 1-s sampling interval) in the future Moon-ILRS twin-spacecraft mission.

Tides on the Moon: Theory and determination of dissipation

AbstractSolid body tides on the Moon vary by about ±0.1 m each month. In addition to changes in shape, the Moon's gravity field and orientation in space are affected by tides. The tidal expressions for an elastic sphere are compact, but dissipation introduces modifications that depend on the forcing period. Consequently, a Fourier representation of the tide‐raising potential is needed. A mathematical model for the distortion‐caused tidal potential may be used for the analysis of precise spacecraft tracking data. Since tides affect gravitational torques on the Moon from the Earth's attraction, the lunar orientation is also affected. Expressions for five periodic perturbations of orientation are presented. The rheological properties of lunar materials determine how the Moon responds to different tidal periods. New lunar laser ranging solutions for the tidal orientation terms are presented. The quality factor Q is 38 ± 4 at 1 month, 41 ± 9 at 1 year, ≥74 at 3 years, and ≥58 at 6 years. The ranging results can be matched with absorption band models that peak at ~120 days and single relaxation time models that peak at ~100 days. Combined models are possibilities. Dissipation can modify laser ranging solutions; previously reported core flattening is too uncertain to be useful. Strong lunar tidal dissipation, modeled to arise in the deep hot mantle, appears to be from a region with radius ≥535 km. Classical Maxwell‐type dissipation is too weak to detect at 3 and 6 year periods.

Approach to imitate maneuvering of lunar roving vehicle under lunar gravity using a terrestrial vehicle

A lunar roving vehicle (LRV) is an important and indispensable detection tool that can not only transport astronauts a long distance from the lunar module but also ensures their safety when moving around the lunar surface. Thus, it is very important to train astronauts to drive the LRV on Earth. However, astronauts will experience different properties and driving sensations for the same vehicle owing to the difference in the gravities of Earth and the Moon. Thus, it is hard to train them on Earth using a normal LRV. Therefore, an approach is used to produce a vehicle that has the same steering properties and driving sensations as the LRV on the lunar surface. This approach involves a control algorithm that is developed in this paper using the H∞ control theory. The math calculation and visual simulation results show that a four-wheel steering imitating LRV, which uses an imitating control algorithm, with either a higher stiffness torsion bar spring or lower payload than the LRV has a high imitation accuracy for the yaw speed, slip angle, and lateral acceleration at the driver’s position. Finally, a highly accurate approach for imitating the steering of an LRV on the lunar surface has been realized, which lays the foundation for training astronauts to drive an LRV.

Lunar gravity affects leaf movement of Arabidopsis thaliana in the International Space Station.

Cyclic leaf ascent and descent occur in synchrony and phase congruence with the lunisolar tidal force under a broad range of conditions. Digitized records of the vertical leaf movements of Arabidopsis thaliana were collected under space flight conditions in the International Space Station (ISS). Oscillations of leaf movements with periods of 45 and 90min were found under light-adapted conditions, whereas in darkness, the periods were 45, 90, and 135min. To demonstrate the close relationship between these oscillations and cyclical variations of the lunisolar gravitational force, we estimated the oscillations of the in-orbit lunisolar tide as they apply to the ISS, with the aid of the Etide software application. In general, in-orbit lunisolar gravitational profiles exhibited a periodicity of 45min. Alignment of these in-orbit oscillations with the oscillations of Arabidopsis leaf movement revealed high degrees of synchrony and a congruence of phase. These data corroborate previous results which suggested a correlative relationship and a possible causal link between leaf movement rhythms obtained on ground and the rhythmic variation of the lunisolar tidal force.

Transfer orbits to the Earth–Moon triangular libration points

The particular positions and dynamics of the triangular libration points in the Earth–Moon system make them potential candidates for future space applications. Taking the leading L4 point as an example, this paper studies the transfer orbits to the vicinity of this equilibrium point. Two basic models are used: the circular restricted three-body problem (CRTBP) and the bi-circular problem (BCP). The order-three analytical solution of the motion around the triangular libration points in the CRTBP model is taken as the nominal orbit. Three different approaches are studied: direct transfer, transfer utilizing powered lunar gravity assist, and transfer utilizing the Sun’s gravity. Lastly, low energy transfer orbits are extensively studied in the BCP model via a numerical approach. Our studies show that the total delta-v cost is considerably reduced if the Moon’s gravity or the Sun’s gravity can be used, at the cost of a longer transfer time. The delta-v cost and the time of flight (TOF) in our work are approximately: 3.90–4.40km/s and 4–8days for the direct transfer; 3.41–3.48km/s and 18–52days for the transfer utilizing powered lunar gravity assist; 3.33–3.40km/s and 70–95days for the transfer utilizing the Sun’s gravity. For the low energy transfer orbits, the lower limit of the delta-v cost is around 3.10km/s.

Origin of native silicon and iron silicides in the Dhofar 280 lunar meteorite

Native silicon and iron silicides were studied in the Dhofar 280 lunar anorthositic meteorite representing an impact-melt breccia. Such rocks are widespread in the highland crust of the Moon. It was established that cryptocrystalline objects containing native silicon are close in composition to the silicon monoxide SiO. Experimental data demonstrate that this compound is the main component of the vapor forming during vaporization of an anorthitic melt. It is suggested that the formation of native silicon was related to the condensation of SiO from an impact-derived vapor cloud. Reducing conditions are determined by the mass-fractionation of silica monoxide and oxygen in the expanding vapor cloud in the gravity field of the Moon. Gaseous SiO may be condensed directly into a solid phase or a mixture of silicon with silica. The condensed SiO phase incorporated into an impact melt should be decomposed into silicon and silica. Interaction of Si, SiO, and SiO2 solid condensates with an impact melt could lead to the observed enrichment of the surrounding liquid in silica. The formation of iron silicides is provided by the reaction of native silicon with FeO presenting in an impact melt. The other iron source could be a meteoritic component, which is identified in silicides by elevated Ni contents. Obtained mineralogical and experimental data show that metallic silicon can be obtained under lunar conditions by distillation of anorthositic melts and can be used for production of solar batteries to provide lunar settlements with energy.

Cardiovascular autonomic adaptation in lunar and martian gravity during parabolic flight

Weightlessness has a well-known effect on the autonomic control of the cardiovascular system. With future missions to Mars in mind, it is important to know what the effect of partial gravity is on the human body. We aim to study the autonomic response of the cardiovascular system to partial gravity levels, as present on the Moon and on Mars, during parabolic flight. ECG and blood pressure were continuously recorded during parabolic flight. A temporal analysis of blood pressure and heart rate to changing gravity was conducted to study the dynamic response. In addition, cardiovascular autonomic control was quantified by means of heart rate (HR) and blood pressure (BP) variability measures. Zero and lunar gravity presented a biphasic cardiovascular response, while a triphasic response was noted during martian gravity. Heart rate and blood pressure are positively correlated with gravity, while the general variability of HR and BP, as well as vagal indices showed negative correlations with increasing gravity. However, the increase in vagal modulation during weightlessness is not in proportion when compared to the increase during partial gravity. Correlations were found between the gravity level and modulations in the autonomic nervous system during parabolic flight. Nevertheless, with future Mars missions in mind, more studies are needed to use these findings to develop appropriate countermeasures.

Translation Dynamical Nonlinear Models in Perturbed Keplerian Conditions For a Geostationary Satellite

The dynamics of a GEO satellite will be studied in this work to obtain a dynamical model as accurate as possible. This model will be obtained in terms of Gauss' variation of osculating parameter (VOP) equations containing the environmental perturbing accelerations, which are traditionally used to plan the station keeping maneuvers. The idea is to implement a controller for geostationary station keeping purposes based on a model written in terms of osculating orbital elements instead of averaged elements. Such a controller plans in an automatic way the station keeping (SK) maneuvers and it could be integrated on board in view of autonomous station keeping control loop. The Geostationary Earth Orbit (GEO) satellites maintain an essentially fixed position with respect to the surface of the Earth. This is made possible by inserting the spacecraft into a circular, equatorial orbit at an altitude of roughly 36000 km. At this altitude, if the main environmental disturbing forces (the Earth's non-spherical gravity attraction, the Moon's and Sun's gravity attraction and the solar radiation pressure) are neglected except the Kepler attraction of the Earth, the geostationary motion is ideal. The satellite remains fixed with respect to the surface of the Earth. The mean motion n matches the Earth's rotation rate  of one revolution per 23 hours and 56 minutes. In presence of perturbations, it is a common practice to control a GEO satellite actively via station keeping maneuvers such that it stays confined in a box of 100-150 km width around a nominal geostationary longitude and latitude (1). Traditionally this is done with an open loop control technique based on a dynamical model of the satellite state vector subject to the only environmental perturbing forces and on a separate dynamical model taking into account the only thrust effects. Moreover, this latter model is derived supposing to use a chemical propulsion system characterized by high thrusts and very short thrust durations relative to the orbital period. These impulsive thrust hypotheses lead to assume that maneuvers induce jumps in the velocity part of the state vector but not in the position part. The GEO station keeping problem is thus dealt with in a discrete way, without considering spacecraft acceleration but only velocity and position vectors. With a view to substitute chemical propulsion systems with electrical ones, the solution approaches of the GEO station keeping problem should become continuous, in order to gain benefit from the technology change. A GEO satellite dynamics model has to be obtained taking into account all the perturbing forces (environmental or not) acting on the spacecraft. In this paper, we explain in detail the nonlinear dynamical model used to design the station keeping controller and the analytical approximations done to implement this

Linear and nonlinear control strategies for formation and station keeping of spacecrafts within the context of the three body problem

The problem of spacecraft formation control and reconfiguration for halo orbit around the second libration point (L2) of the Sun–Earth Three Body (TB) system is investigated. Station keeping, reconfiguration and precision formation control of spacecrafts on halo orbits are performed via the use of the nonlinear Integral Sliding Mode (ISM) method as well as the optimal closed loop Linear Quadratic Regulator (LQR) approach. In this regard the nonlinear relative dynamics of deputy–chief spacecrafts are derived within the concept of the three body problem. The behavior of the two controllers are compared for different tasks of the formation mission in order to determine the more preferred strategy that fulfills the desired response behavior. In addition the controllers are evaluated for robustness in terms of their compensation against the major source of environmental disturbance, namely the Moon's gravity perturbation.

Gravitation of the Moon Gives Rise to Oceanic Currents

At present there is no theory of sea and oceanic currents due to the lack of understanding of the driving forces. The currents have a vortex character, so only moments of force can set them in motion. In the article, it is shown that the gravitation field of the Moon affecting the rotating Earth produces two moments of force: associated and tidal. Although the gravitation field is potential, the rotating Earth is a nonenertial system, in which the moment can occur due to the external potential force. Estimates show that the associated force can be sufficient to produce the observed flow rates. The associated force field tends to increase the natural rotation of the Earth and slow down the speed of the revolution of the Moon around the Earth, i.e. bring the Moon nearer the Earth, its action is opposite to the action of the tidal force. The action of the associated force is examined by the example of the circumpolar and local currents. The associated force produces vortices counterclockwise in the Northern hemisphere and clockwise in the Southern one. The associated force affects the atmosphere resulting in the observed predominance of western winds. It is necessary to take into account the above force when considering such atmospheric phenomena as cyclones and anticyclones, tradewinds, monsoons, etc. In the lithosphere, the associated force makes tectonic plates turn.

Geophysical parameters inversion for Apollo crater based on recent high-resolution lunar gravity field and topography data

Geophysical parameters inversion for Apollo crater based on recent high-resolution lunar gravity field and topography data

Earthy, solaris and atmospheric energy sources

Earth, sun and atmosphere are the ultimate energy resources. In addition to fossil fuels, earth radiates over 45 TW geothermal energy. Sun radiates about 89 PW energy to earth’s surface. Lunar gravity supplies over 100 GW tidal ocean energy. Accessible energy from geothermal, solar, tides, waves and winds is far more than our current 17 TW energy demand, yet there are new avenues like tornadoes and lightning energies. We have to harness storms to serve humanity rather than destroying it. Fossil fuels and uranium reserves will continue to exist beyond 21st century, yet energy transition from fossil fuels to renewable energy sources is necessary to fight against looming climate changes.

Psychological strain: Examining the effect of hypoxic bedrest and confinement

The aim was to assess the effect of a 10-day exposure to the environmental stressors anticipated in future lunar habitats on indices of psychological strain. In addition to the reduced gravity of the Moon, future habitats on the Moon will likely maintain a hypobaric hypoxic environment. The hypobaric environment will eliminate the need for long decompression profiles prior to each extra-vehicular activity. We investigated the indices of psychological strain during three 10-day conditions, designed to assess the separate and combined effects of inactivity/unloading and normobaric hypoxia on several physiological systems. Eleven male participants underwent three 10-day campaigns in a randomised manner: 1) normobaric normoxic bed rest (NBR), 2) normobaric hypoxic bed rest (HBR) and 3) normobaric hypoxic ambulatory confinement (HAMB). The most negative psychological profile appeared on day 10 of the HBR and HAMB (hypoxic) conditions. Concomitantly, a decrease in positive emotions was observed from baseline to day 10 of the HBR and NBR conditions. Thus, confinement in a hypoxic environment seems to exert a negative effect on an individual's psychological mood.

Designing solar sail formations in sun-synchronous orbits for geomagnetic tail exploration

Exploration of the Earth׳s magnetosphere using solar sails has advantages over the use of traditional spacecraft in inertially fixed orbits because of the solar sails׳ capability to stay in the geomagnetic tail for longer periods. In this paper, solar sail formation flying in Earth-centered slightly inclined orbits is investigated, with each solar sail employing a simple sun-pointing steering law that precesses the orbit apse-line sun-synchronously. An analytic condition for determining target states that lead to in-plane quasi-periodic relative motion under solar radiation pressure is derived, assuming all sails use the same steering law. Even though active control is required to achieve these target states, only the simple steering law is required for flying the formation upon achieving the target states. The condition is verified in the design of two-craft and three-craft formations. The effects of Earth׳s nonsphericity, lunar gravity, and solar gravity are included to determine the stability of the designed formations under these perturbations.

The formation of lunar mascon basins from impact to contemporary form

AbstractPositive free‐air gravity anomalies associated with large lunar impact basins represent a superisostatic mass concentration or “mascon.” High‐resolution lunar gravity data from the Gravity Recovery and Interior Laboratory spacecraft reveal that these mascons are part of a bulls‐eye pattern in which the central positive anomaly is surrounded by an annulus of negative anomalies, which in turn is surrounded by an outer annulus of positive anomalies. To understand the origin of this gravity pattern, we modeled numerically the entire evolution of basin formation from impact to contemporary form. With a hydrocode, we simulated impact excavation and collapse and show that during the major basin‐forming era, the preimpact crust and mantle were sufficiently weak to enable a crustal cap to flow back over and cover the mantle exposed by the impact within hours. With hydrocode results as initial conditions, we simulated subsequent cooling and viscoelastic relaxation of topography using a finite element model, focusing on the mare‐free Freundlich‐Sharonov and mare‐infilled Humorum basins. By constraining these models with measured free‐air and Bouguer gravity anomalies as well as surface topography, we show that lunar basins evolve by isostatic adjustment from an initially subisostatic state following the collapse stage. The key to the development of a superisostatic inner basin center is its mechanical coupling to the outer basin that rises in response to subisostatic stresses, enabling the inner basin to rise above isostatic equilibrium. Our calculations relate basin size to impactor diameter and velocity, and they constrain the preimpact lunar thermal structure, crustal thickness, viscoelastic rheology, and, for the Humorum basin, the thickness of its postimpact mare fill.

Local model better describes lunar gravity

Two satellites orbiting the Moon as a part of NASA's Gravity Recovery and Interior Laboratory (GRAIL) mission have been mapping its inner structure by measuring subtle shifts in the pull of gravity on the satellites from points on the ground below. The stronger the shift is, the greater the mass of structures below the surface is.

Lunar explorers will walk at higher speeds than thought

Anyone who has seen the movies of Neil Armstrong's first bounding steps on the moon couldn't fail to be intrigued by his unusual walking style. But, contrary to popular belief, the astronaut's peculiar walk was not the result of low gravity. Wyle Science, Engineering and Technology scientist John De Witt explains that the early space suits were not designed for walking, so the astronauts adapted their movements to the restrictions of the suit. Michael Gernhardt, the head of NASA's Extravehicular Activity Physiology, Systems and Performance Project, wants to learn more about how humans move in low gravity, including the speed at which we break from a walk into a run, to design a modern space suit that permits freer movement. However, the only way to test the effects of true lunar gravity on our movements while based on earth is to hop aboard NASA's adapted DC-9 aircraft – which reduces the gravity on board by performing swooping parabolic flights – and get running (p. 3200).De Witt and colleagues Brent Edwards, Melissa Scott-Pandorf and Jason Norcross recruited three astronauts and five other registered test subjects that could tolerate the discomfort of the aircraft's bucking flight to test their running. ‘There is some unpleasantness,’ recalls De Witt, adding, ‘if you get sick you're done…. We wanted to be sure we had people that were used to flying.’ Once the subjects were airborne, the team only had 20 s during each roller-coaster cycle – when the gravity on-board fell to one-sixth of that on Earth – when they could test the runner's walking and running styles on a treadmill as the volunteers shifted over a range of speeds from 0.67 to 2 m s−1. However, the experiments ran smoothly after the first few parabolas once the team had settled into a routine.Back on the ground, De Witt and colleagues analysed the speed at which the walkers gently transitioned into a run. ‘Running is defined as a period of time with both feet off the ground’, explains De Witt, adding that the walk to run transition was expected to occur at 0.8 m s−1 in lunar gravity, based on theoretical calculations. However, when the team calculated the transition speed from their experiments, they were in for a surprise: ‘The average was 1.4 m s−1’, recalls De Witt.‘This difference is, to me, the most interesting part of the experiment; to try to figure out why we got these numbers’, says De Witt, who suggests that the acceleration forces generated by the counter-swinging arms and legs could account for the shift in transition speed. ‘What I think ends up happening is that even though the atmosphere is lunar gravity, the effective gravity on our system is lunar gravity plus the forces generated by our swinging arms and legs’, says De Witt. He explains that this arm-and-leg swinging effect probably happens here on Earth too, but the forces generated by the swinging limbs are negligible relative to our gravity. However, he suspects that they are more significant in weaker lunar gravity, saying, ‘They contribute more to the gravity keeping you attached to the ground.’De Witt also adds that the higher transition value is not without precedent. He explains that scientists on Earth have simulated lunar gravity by supporting five-sixths of a runner's weight in a sling, and the athletes also transitioned from a walk to a run at speeds of around 1.4 m s−1. ‘This tells researchers [that] what they have in the lab, which is a fraction of the cost of the airplane, is probably adequate at giving you the information you need’, he says.

The preferred walk to run transition speed in actual lunar gravity.

Quantifying the preferred transition speed (PTS) from walking to running has provided insight into the underlying mechanics of locomotion. The dynamic similarity hypothesis suggests that the PTS should occur at the same Froude number across gravitational environments. In normal Earth gravity, the PTS occurs at a Froude number of 0.5 in adult humans, but previous reports found the PTS occurred at Froude numbers greater than 0.5 in simulated lunar gravity. Our purpose was to (1) determine the Froude number at the PTS in actual lunar gravity during parabolic flight and (2) compare it with the Froude number at the PTS in simulated lunar gravity during overhead suspension. We observed that Froude numbers at the PTS in actual lunar gravity (1.39±0.45) and simulated lunar gravity (1.11±0.26) were much greater than 0.5. Froude numbers at the PTS above 1.0 suggest that the use of the inverted pendulum model may not necessarily be valid in actual lunar gravity and that earlier findings in simulated reduced gravity are more accurate than previously thought.

How much gravity is needed to establish the perceptual upright?

Might the gravity levels found on other planets and on the moon be sufficient to provide an adequate perception of upright for astronauts? Can the amount of gravity required be predicted from the physiological threshold for linear acceleration? The perception of upright is determined not only by gravity but also visual information when available and assumptions about the orientation of the body. Here, we used a human centrifuge to simulate gravity levels from zero to earth gravity along the long-axis of the body and measured observers' perception of upright using the Oriented Character Recognition Test (OCHART) with and without visual cues arranged to indicate a direction of gravity that differed from the body's long axis. This procedure allowed us to assess the relative contribution of the added gravity in determining the perceptual upright. Control experiments off the centrifuge allowed us to measure the relative contributions of normal gravity, vision, and body orientation for each participant. We found that the influence of 1 g in determining the perceptual upright did not depend on whether the acceleration was created by lying on the centrifuge or by normal gravity. The 50% threshold for centrifuge-simulated gravity's ability to influence the perceptual upright was at around 0.15 g, close to the level of moon gravity but much higher than the threshold for detecting linear acceleration along the long axis of the body. This observation may partially explain the instability of moonwalkers but is good news for future missions to Mars.