Value Of Gravitational Acceleration Research Articles

Penentuan Percepatan Gravitasi Bumi Menggunakan Bandul Sederhana Di Daerah Kampus UPI

Many people assume that the value of gravitational acceleration always has a fixed value. However, if we look closely, the value of gravitational acceleration always changes in each place. This research aims to compare differences in Earth's gravitational acceleration in various locations. Through this research, researchers can identify the causes of differences in gravity, one of which is differences in height. The method used in this research is a simple pendulum experimental method, with a quantitative approach to collecting data from various places. The results obtained for g in the JICA building on the 5th floor were 9,47 m/s², g in the FIP building on the 10th floor was 9,72 m/s², g in the FPTK 9,59 m/s², and g at the National Museum of Education is 9,72 m/s². Apart from that, it can be found the average magnitude of the gravitational acceleration from these four places is 9,62 m/s². From these results it can be concluded that the magnitude of the Earth’s gravitational acceleration is different in each place. Apart from height, this difference can also occur due to uncertainty in measuring gravity.

YOLOv3 Algorithm to Measure Free Fall Time and Gravity Acceleration

Computer vision methods as an alternative to sensors in modern measurements are feasible in physics experiments due to their speed, accuracy, and low cost. The You Only Look Once (YOLO) algorithm is widely used in computer vision because it detects object positions quickly and accurately. This research uses YOLO version 3 (YOLOv3) to compute an object’s falling time and gravitational acceleration. Two steps are performed in this study: first, the detection of predefined objects using YOLOv3, and second, the use of trained YOLOv3 to track the object's coordinate. According to the object tracking results, the object's falling time can be measured based on the object tracking results. The gravitational acceleration is calculated using the time data after the fall time of the object is measured. The measurement result of the fall time of the object will be compared with the data from the sensor. The result of the gravitational acceleration calculation is measured for its relative error against the value of 9.78150 m/s2, which is the value of gravitational acceleration in Jakarta city. The results show that YOLOv3 can accurately detect objects and measure free-fall motion, with a time measurement error of only 1.1 milliseconds compared to sensor measurements. The error obtained from the measurement of the Earth's gravity is 0.634%.

Analisis Percepatan Gravitasi Pada Gerak Jatuh Bebas Menggunakan Aplikasi Video Tracker

This study aims to analyze the acceleration of gravity (g) in free fall with a height of 2 meters using a video tracking application. This research is located in the Department of Geological Engineering, Pattimura University, Ambon. The method used in this research is the experimental method. The tools and materials used in this study were tennis balls (2 grams), baseball (80 grams), roll meter, camera and laptop. Based on the results of data analysis, it was found that the value of gravitational acceleration at a height of 2 meters for samples of tennis balls (2 grams) and baseballs (80 grams) was 9.67 ± 0.27 m/s2 and 9.60 ± 0.27 m/s2.

Rancang Bangun Alat Gerak Jatuh Bebas Berbasis Arduino Uno Pada Praktikum Fisika

Free fall motion is a falls down movement of an object due to the influence of the earth's gravitational force without any other significant forces affecting the movement. In free fall, the acceleration of an object is always constant and heading downward, and its value is about 9.8 meters per second squared (m/s²) on the Earth's surface. The implementation of free fall motion technology is expected to help students in doing their basic physics practicum so that observations is no longer done manually using a stopwatch. In addition, with this teaching media, the measurement data will be more constant in value because it has been arranged in the system, so that the results will be more accurate. The implementation of this free fall motion media is used to measure the travel time of an object, its speed and gravity value during free fall from a height of 60 cm and 30 cm. The travel time can be determined using a timer of an Arduino Uno and an Infrared Sensor that will be detected and read when there is an object passing by. Based on experiments that have been carried out at a height of 60 cm using ping pong ball, large marble, and small marble, the obtained value of gravitational acceleration is almost the same as the average value of gravitational acceleration measured namely 9.99, 10.00, and 10.24 m⁄s2 respectively. At a height of 30 cm, using the same objects, the obtained value of gravitational acceleration is 10.62 m⁄s2 .

Optimal zero-crossing group selection method of the absolute gravimeter based on improved auto-regressive moving average model

An absolute gravimeter is a precision instrument for measuring gravitational acceleration, which plays an important role in earthquake monitoring, crustal deformation, national defense construction, etc. The frequency of laser interference fringes of an absolute gravimeter gradually increases with the fall time. Data are sparse in the early stage and dense in the late stage. The fitting accuracy of gravitational acceleration will be affected by least-squares fitting according to the fixed number of zero-crossing groups. In response to this problem, a method based on Fourier series fitting is proposed in this paper to calculate the zero-crossing point. The whole falling process is divided into five frequency bands using the Hilbert transformation. The multiplicative auto-regressive moving average model is then trained according to the number of optimal zero-crossing groups obtained by the honey badger algorithm. Through this model, the number of optimal zero-crossing groups determined in each segment is predicted by the least-squares fitting. The mean value of gravitational acceleration in each segment is then obtained. The method can improve the accuracy of gravitational measurement by more than 25% compared to the fixed zero-crossing groups method. It provides a new way to improve the measuring accuracy of an absolute gravimeter.

The Development and Perception of Trainee Teachers towards Smartphone Based Free Fall Measurement Kit Using Arduino

Free fall motion is one of the topics that is always considered challenging for Physics Students. The lack of teaching aids concerning this topic is also why students are less exposed to the free fall concept. Thus, this study aims to develop a Free Fall Kit as a teaching aid for the Physics Form Four under the subtopic Free Fall Movement. This kit is developed using an Arduino microcontroller where the result of gravitational acceleration will be displayed on the smartphone through the Bluetooth module. This study also aims to test the trainee teacher’s perceptions of majoring in physics at Universiti Pendidikan Sultan Idris towards the Free Fall Kit. The validity study was conducted with three experts among the physics lecturers at the Sultan Idris University of Education. These validity data were analyzed using the Percentage of Consent. The validity value obtained showed a high value where the total percentage of validity agreement from the three experts was 98.3% for face validity and 93.3% for content validity. This study uses a descriptive method to assess the instrument reliability and respondents perceptions of the developed kits. The data obtained showed that Cronbach’s Alpha value is 0.97, while an average mean score is 3.82 and an average standard deviation value is 0.28, indicating that the level of reliability and perception is at a high level of agreement among the respondents. In conclusion, the Free Fall Kit has a good perception among trainee teachers at Universiti Pendidikan Sultan Idris and has achieved the objectives of this research. The implication is that the Free Fall Kit can be an alternative teaching aid for teachers to teach the subtopic of free fall motion to determine the value of gravitational acceleration.

Determining Gravitational Acceleration Accurately and Simply

There are several ways in the literature to determine the value of gravitational acceleration. we will present a way that allows us to determine the we used an audio plug (3.5-mm jack) that can be reused from types of plugs can also be purchased and are very cheap. In this article, a computer speaker or microphone that are damaged. These value of gravitational acceleration very accurately using every-day materials. For this, we will use an electromagnet, a coil, a steel sphere, a speaker, an audio cable (3.5-mm jack), a direct current power supply, connecting wires, a computer, and the Audacity software.

Analysis of vibration correction performance of vibration sensor for absolute gravity measurement

Absolute gravity measurement refers to the measurement of the absolute value of gravitational acceleration (<i>g</i>, approximately 9.8 m/s<sup>2</sup>). The precision of absolute gravity measurement is limited mainly by vibration noises. Vibration correction is a simple and feasible way to deal with vibration noises, which corrects the measurement results by detecting vibration noises with a sensor. At present, the vibration correction performance of different sensors lacks systematic analysis and evaluation. In this paper, the theoretical analysis of how the sensor characteristics affect the correction performance is carried out. The vibration correction performances of three sensors, two different seismometers and one accelerometer, are evaluated experimentally in the three cases with different vibration noises. The experimental results show that the correction precision obtained by using low-noise seismometer is limited mainly by its bandwidth and range. In case I i.e. the quiet environment, the standard deviation of corrected results obtained by using both seismometers can reach tens of μGal (1 μGal = 10<sup>–8</sup> m/s<sup>2</sup>), which is close to that obtained by using an ultra-low-frequency vibration isolator. However, in case II i.e. the noisy environment, the standard deviation of corrected results obtained by both seismometers increase to hundreds of μGal due to the enhancement of high-frequency vibration components. This means that the correction performances of both seismometers deteriorate, and the performance of seismometer with narrower bandwidth turns even worse. Moreover, two seismometers cannot even work in case III with stronger vibration noises due to the range limitation. On the other hand, the correction precision obtained by using accelerometer is affected mainly by its resolution which is on the order of mGal (1mGal = 10<sup>–5</sup> m/s<sup>2</sup>). Its bandwidth can reach hundreds of or even thousands of hertz and its range is generally over ±2 g, which is large enough to meet the needs for noisy and dynamic applications. In case I, the standard deviation after correction with accelerometer is larger than that before correction. This is because the intensity of vibration noises in this case is close to or even smaller than the self-noise of accelerometer so that it could not be detected effectively by accelerometer. In case II, the resolution of accelerometer is sufficient to detect the vibration noises effectively. The standard deviation of the results is reduced from 2822 μGal to 1374 μGal after correction with accelerometer, and equal to a precision of 0.1 mGal after 100 drops. In case III where the amplitude of vibration noise rises to 0.1 m/s<sup>2</sup> and seismometer cannot work, the accelerometer could still achieve a precision of 0.3 mGal after 100 drops. The systematic deviation is corrected from –1158 mGal to –285 μGal and the standard deviation is reduced from 34 mGal to 3.3 mGal. Therefore, the low-noise seismometer is more suitable for vibration correction in a quiet environment with stable foundation, which could realize a standard deviation superior to hundreds of μGal, while the accelerometer is more appropriate for vibration correction in a complex or dynamic environment, which could achieve a standard deviation of mGal-level. Finally, the present results and analysis provide a theoretical guidance for selecting and designing the sensors in vibration correction applications.

The Atwood machine experiment assisted by smartphone acceleration sensor for enhancing classical mechanics experiments

Newton’s second law can be demonstrated by classical mechanical experiments, one of which is using the Atwood machine. Atwood machines consist of two weights suspended by a rope and connected by a pulley. In this study, an Atwood machine experiment was carried out, where the smartphone was placed on one of the loads, so that the vertical acceleration of the motion system could be measured easily using an acceleration sensor. We also consider the effect of pulley rotation which is usually missed from previous studies. By deriving the second law equation of Newton on rotational and translational motion, we can get the relationship between the system acceleration and the gravitational acceleration of the earth. The results of the earth’s gravitational acceleration obtained, compared with the results of the experiment using a stopwatch (conventional method), and with the value of the standard earth gravitational acceleration at that place. Earth’s gravitational acceleration from the experiment using a smartphone is closer to the standard earth gravitational acceleration value than using a stopwatch. So, in this experiment, the use of a smartphone acceleration sensor contributes to enhance a conventional demonstration of classical mechanics experiments.

Development of gravitational acceleration measurement set up based on laser beams

In this paper, using three parallel laser beams system we have calculated the value of gravitational acceleration (g) by deriving a simple equation, where there is no velocity term, is reported. The numerator of the equation is always positive irrespective of distances. The setup consists of commonly available three red laser light-emitting diodes and three sensors using very common fast transistors. A free-fall object intercepts the laser beams to produce three voltage pulses across the collector-emitters of three transistors. These voltage pulses are fed to a storage oscilloscope for measuring the two time-intervals between two subsequent gaps of three laser beams with millisecond resolutions. Time intervals are also measured by two-microsecond timers in microsecond resolution. The object may fall from any height above first laser beam, but the 'g' calculated remains the same. Measurements were done by letting an object fall from two different heights, six times from each height, and the average value of 'g' of 9.8036916315 meters per second squared is calculated using the data of two-microsecond timers, which has a 0.03% deviation from the standard value of 9.80665 meters per second squared. Results obtained using microsecond timers are more accurate than that obtained using oscilloscope millisecond data.

Development of gravitational acceleration measurement set up based on laser beams

In this paper, using three parallel laser beams system we have calculated the value of gravitational acceleration (g) by deriving a simple equation, where there is no velocity term, is reported. The numerator of the equation is always positive irrespective of distances. The setup consists of commonly available three red laser light-emitting diodes and three sensors using very common fast transistors. A free-fall object intercepts the laser beams to produce three voltage pulses across the collector-emitters of three transistors. These voltage pulses are fed to a storage oscilloscope for measuring the two time-intervals between two subsequent gaps of three laser beams with millisecond resolutions. Time intervals are also measured by two-microsecond timers in microsecond resolution. The object may fall from any height above first laser beam, but the 'g' calculated remains the same. Measurements were done by letting an object fall from two different heights, six times from each height, and the average value of 'g' of 9.8036916315 meters per second squared is calculated using the data of two-microsecond timers, which has a 0.03% deviation from the standard value of 9.80665 meters per second squared. Results obtained using microsecond timers are more accurate than that obtained using oscilloscope millisecond data.

Development of gravitational acceleration measurement set up based on laser beams

In this paper, using three parallel laser beams system we have calculated the value of gravitational acceleration (g) by deriving a simple equation, where there is no velocity term, is reported. The numerator of the equation is always positive irrespective of distances. The setup consists of commonly available three red laser light-emitting diodes and three sensors using very common fast transistors. A free-fall object intercepts the laser beams to produce three voltage pulses across the collector-emitters of three transistors. These voltage pulses are fed to a storage oscilloscope for measuring the two time-intervals between two subsequent gaps of three laser beams with millisecond resolutions. Time intervals are also measured by two-microsecond timers in microsecond resolution. The object may fall from any height above first laser beam, but the 'g' calculated remains the same. Measurements were done by letting an object fall from two different heights, six times from each height, and the average value of 'g' of 9.8036916315 meters per second squared is calculated using the data of two-microsecond timers, which has a 0.03% deviation from the standard value of 9.80665 meters per second squared. Results obtained using microsecond timers are more accurate than that obtained using oscilloscope millisecond data.

Analysis and Comparison of the Vibration Correction Accuracy of Different Optimization Objectives for the Classical Absolute Gravimeter

Accurate absolute gravimeters are important instruments in applications, such as metrology, geophysics, and geological exploration. Vibration is one of the limiting factors that cause deterioration in measurement accuracy, which includes trueness and precision. The vibration correction method, in which a seismometer is used to record the vibration, provides an effective method to deal with the disturbances. The theoretical analysis shows that the ultimate correction accuracy is limited by the inherent frequency performance of the seismometer. The correction algorithm is an optimization problem to achieve this ultimate accuracy. The selection of the optimization objectives affects the correction accuracy dramatically. Although the real gravitational acceleration is unknown before the measurement is taken, minimization of the standard deviation of the fitting residual for a single drop (SDFRSD) is proven to realize better trueness. Enhanced precision is achieved through minimization of the Type A uncertainty of gravitational accelerations for all drops (UGAAD). Simulations and experimental measurements with the T-1 absolute gravimeter verify the theoretical analysis results. In addition, the results also show that the SDFRSD correction contains the real gravitational acceleration value, while the UGAAD correction exceeds the valid range. Therefore, the SDFRSD correction approach provides better comprehensive accuracy than the UGAAD correction method.

Numerical investigations of phase change material (PCM) based thermal control module (TCM) under the influence of low gravity environment

The present work aims to address the effect of gravity on the melting and solidification of phase change materials (PCM) in an optimized thermal control module (TCM) having pin fins as heat transfer enhancers. The enthalpy-porosity technique is used to model the solid-liquid phase change process and flow evaluation inside TCM. The melting and solidification processes are simulated for three-phase change materials (hexadecane, acetic acid, and glycerol) at different values of gravitational accelerations (i.e., melting at g, g/2, g/10, g/20, g/40, g/80 and solidification at g, g/80). The governing equations are non-dimensionalized, and results are reported in the form of dimensionless numbers. It is evident from the study that the gravity environment significantly influences the melting and solidification of PCM. The research shows that the value of PCM average liquid fraction gradually decreases by 18% as the value of gravitational acceleration reduces from g to g/80. The effect of the natural convection is noticeable on the melting of hexadecane and acetic acid. However, the minimal effect of natural convection was observed on the melting of glycerol due to highly viscous nature and faster heat propagation through the material. The effect of gravity on the solidification is small compared to the melting because the conduction heat transfer primarily dominates the solidification process. The present study provides information on the effect of gravity on performance parameters of the PCMs, which helps determine the size of the heat sinks operating under terrestrial and space environments.

Venous reflux in the great saphenous vein is driven by a suction force provided by the calf muscle pump in the compression–decompression maneuver

ObjectiveThe gravitational pressure gradient is considered the driving force of venous reflux. The results from our previous study demonstrated that gravitational force is not a necessary condition for the occurrence of venous reflux. We hypothesized that a force exists in addition to gravity that drives venous reflux. The present study was designed to test this hypothesis by measuring the acceleration of blood flow during venous reflux in a clinical study and by simulating reflux ex vivo in physical models. MethodsA total of 80 lower extremities of 80 patients with primary incompetence of the great saphenous vein were included in the present study. The cross-sectional area of the great saphenous vein, peak velocity of venous reflux (PV), and time required to achieve the PV (Δt, seconds) were measured on duplex ultrasound scans taken with the patient in the standing rest position. Noncycling operator-dependent distal cuff inflation–deflation was used as the reflux provoking maneuver. The acceleration of venous reflux (areflux) was calculated as areflux = PV/Δt in m/s2. Physical models were used to demonstrate the difference in acceleration between the free-fall stream and the flow forced by suction. ResultsThe magnitude of areflux was greater than gravity in 24 of 80 extremities (30%), with a range of 9.83 to 24.13 m/s2. The maximum observed value of areflux was approximately 2.5g (24.13 m/s2). The areflux weakly, but statistically significant inversely, correlated with the subject height (r = −0.26; P = .001). The difference in water flow acceleration was 2.5 times between the free-fall model and suction model (9.07 ± 0.2 m/s2 vs 23.32 ± 2.6 m/s2, respectively). ConclusionsThe acceleration of blood flow during reflux exceeded the value of gravitational acceleration, suggesting the action of an additional nongravitational force. The calf muscle pump might create such force by negative pressure during muscle diastole.

Clinorotation as a promising and environmentally friendly biotechnology in agriculture and some industries

Aim. To investigate the direct and indirect impact of clinorotation on vital activity of gilled mushrooms (Agaricales) using the mycelium of the model organism Agaricus bisporus, clinorotated by the ground-based facility Ekoloh, as the example. Methods. The mycelium of Agaricus bisporus was cultivated on the medium with agar and compost extract. The microgravitational environment was simulated using the method of uniaxial clinorotation at the ground-based facility Ekoloh. The mycelia of Agaricus bisporus from the experimental group were clinorotated for 4 h a day for 12 days. The samples from the control group were cultivated in normal (1 g) conditions. The simulated gravitational acceleration value was 3.5 × 10–4 g at the rotational velocity of 2.5 rpm and the rotation radius of 0.05 m. The centrifugal acceleration, affecting the mycelium of Agaricus bisporus under clinorotation, was 0.00343 m/s2. The two-way ANOVA analysis demonstrated that the effects of g-level, the duration of the impact and their interaction were all statistically signifi cant. At the same time, 73.1 % of the variance in mycelium growth coeffi cient was triggered by the simulated value of the g, i.e. the duration of the impact was a minor factor. Results. Clinorotation stimulated growth and development of gilled mushroom (Agaricales) mycelium. In particular, in this study the clinorotated mycelium of Agaricus bisporus had approximately 3.4, 2.5, 1.6 times higher coeffi cients of mycelium growth compared against the mycelium, cultivated in stationary conditions (1 g) on day 5, 10, and 15 of the cultivation respectively. Contrary to the control mycelial colonies, the growth of clinorotated mycelial colonies of Agaricus bisporus was asymmetric. The direction of the gravitational acceleration vector regarding mycelium colonies was constantly changing in the microgravitational environment, simulated by the ground-based facility Ekoloh. At the same time, different organs of Agaricus bisporus are characterized by gravitropism of different orientation. Therefore, constant changes in the direction of gravitational acceleration vector regarding mycelium could have caused constant re-orientation of mycelium cells in terms of the gravitational acceleration vector, and thus, multidirectional asymmetric growth. In addition, the centrifugal acceleration, generated during clinorotation, is a mechanostimulator, capable of triggering stress responses in different living systems. The accelerated growth is one of the stress responses. At the same time, mycelium could expand in the environment mechanically due to the impact of centrifugal acceleration. However, the centrifugal acceleration was insignifi cant, thus, we believe that the main effect was caused by microgravity. Conclusions. Since clinorotation stimulates the growth and development of gilled mushrooms and is an effi cient way of forming virus-free planting material of different plants, this technology may have a wide scope of application. It may be used in agriculture, forestry and different industries, using raw plants or mushrooms, for instance, in food, pharmaceutical and textile industries, etc.

THE MAGNETIC PROPERTIES MEASUREMENT OF COIL FOR GRAVITATIONAL ACCELERATION DETERMINATION

The value of the gravitational acceleration of the earth above the earth’s surface depends on the position of the latitude and longitude of the earth’s surface, in other words, because the shape of the earth’s surface is not round like a ball. The magnitude of gravity is not the same everywhere on the surface of the earth. The purpose of this study is to analyze the value of the earth’s gravitational acceleration in a laboratory using a current balance with a graphical method. Fluctuations in the value of the magnetic field strength (B) and the value of the electric current strength (i) on the current balance cause the value of laboratory gravitational acceleration (glab) to vary in the transfer of electric charge (q) according to coil type. The magnitude of the earth’s gravitational acceleration value obtained in a laboratory with a current balance for each type of coil is as follows: SF-37 glab-nr=9.89 m/s2, SF-38 glab-nr=9.90 m/s2, SF-39 glab-nr=9.76 m/s2, SF-40 glab-nr=9.95 m/s2, SF-41 glab-nr=9.75 m/s2 dan SF-42 glab-nr=9.93 m/s2. The results obtained indicate that the value of the earth’s gravitational acceleration in a laboratory close to the literature value is the value of the glab-nr in the SF-37 coil type of 9.89 m/s2.

Influence of Gravity on the Sliding Angle of Water Drops on Nanopillared Superhydrophobic Surfaces.

Molecular dynamics (MD) simulations were used to study the effects of gravity, solid surface energy, and the fraction of water-solid interface area on the water droplet sliding angles on nanopillared surfaces. To effectively simulate the influence of gravity on drop sliding, we developed a protocol in which we scale the value of gravitational acceleration used in our simulations according to the Bond number (Bo). In this way, we approximate the behavior of drops larger than we can effectively simulate using MD. The sliding angle decreased with an increase in Bo, while it increased with an increase in the liquid-solid surface interaction. The sliding angles exhibit a minimum with an increase in the fraction of water-solid interface area, due to meniscus formation at high fractions. Trends predicted by our model are in agreement with experiment. Using our model, we investigated the mechanisms of droplet movement along nanopillared surfaces. Depending on the pinning state of the droplets at equilibrium, either the advancing or the receding contact angle initiates motion. Moreover, the minimum dynamic advancing and receding contact angles of drops with gravity are close to the static contact angle and the intrinsic contact angle, respectively, while the maxima of both angles are as large as 180°. We find that the drops move through a combination of sliding and rolling, in agreement with experiment. Our studies offer clarity to conflicting experimental reports and present new results awaiting experimental confirmation.

Measurement of gravitational acceleration with the leak tank method

<p class="Abstract">An experimental device of the mechanics of tank draining under gravity has been constructed. It mainly consists of a cylindrical tank with a circular orifice at the center bottom of the tank. The inner radius of the tank is 134 mm, while there are seven variations of orifice radius, those are 2.25 mm, 2.50 mm, 3.00 mm, 3.50 mm, 4.00 mm, 5.00 mm, and 6.00 mm. The tank is filled by water which is then allowed to flow out throuh the orifice. This experiment can be used to measure the value of gravitational acceleration () on the experiment location. We call this method as the leak tank method. The measurement of g is carried out by measuring the total time to drain the tank from 300 mm initial height of water surface inside the tank for various orifice radius. It is found in this experiment that = (9.89± 0.03) m/s<sup>2</sup>. This result is good enough because it is almost the same as the conventional standar value of 9.80665 m/s<sup>2</sup> with discrepancy of around 0.85%. It indicates that the leak tank method which is described in this paper can be used to estimate the gravitational acceleration value with a good result.</p>

A novel real-time data acquisition using an Excel spreadsheet in pendulum experiment tool with light-based timer

In this study, a pendulum experimental tool with a light-based timer has been developed to measure the period of a simple pendulum. The obtained data was automatically recorded in an Excel spreadsheet. The intensity of monochromatic light, sensed by a 3DU5C phototransistor, dynamically changes as the pendulum swings. The changed intensity varies the resistance value and was processed by the microcontroller, ATMega328, to obtain a signal period as a function of time and brightness when the pendulum crosses the light. Through the experiment, using calculated average periods, the gravitational acceleration value has been accurately and precisely determined.