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90-573: Earth is massive enough that the pull of gravity maintains its roughly spherical shape. Most of its deviation from spherical stems from the centrifugal force caused by rotation around its north-south axis. This force deforms the sphere into an oblate ellipsoid . The Solar System formed from a dust cloud that was at least partially the remnant of one or more supernovas that produced heavy elements by nucleosynthesis . Grains of matter accreted through electrostatic interaction. As they grew in mass, gravity took over in gathering yet more mass, releasing

180-454: A force causing any two bodies to be attracted toward each other, with magnitude proportional to the product of their masses and inversely proportional to the square of the distance between them. Current models of particle physics imply that the earliest instance of gravity in the universe, possibly in the form of quantum gravity , supergravity or a gravitational singularity , along with ordinary space and time , developed during

270-588: A belfry in Dunkerque and Montjuïc castle in Barcelona to estimate the length of the meridian arc through Dunkerque. The length of the first prototype metre bar was based on these measurements, but it was later determined that its length was short by about 0.2 millimetres because of miscalculation of the flattening of the Earth, making the prototype about 0.02% shorter than the original proposed definition of

360-578: A falling object is proportional to the square of the time elapsed. This was later confirmed by Italian scientists Jesuits Grimaldi and Riccioli between 1640 and 1650. They also calculated the magnitude of the Earth's gravity by measuring the oscillations of a pendulum. In 1657, Robert Hooke published his Micrographia , in which he hypothesised that the Moon must have its own gravity. In 1666, he added two further principles: that all bodies move in straight lines until deflected by some force and that

450-596: A figure that was checked yearly), i.e. 250,000 stadia . Depending on whether he used the "Olympic stade" (176.4 m) or the Italian stade (184.8 m), this would imply a circumference of 44,100 km (an error of 10%) or 46,100 km, an error of 15%. A value for the stadion of 157.7 metres has even been posited by L.V. Firsov, which would give an even better precision, but is plagued by calculation errors and false assumptions. In 2012, Anthony Abreu Mora repeated Eratosthenes's calculation with more accurate data;

540-429: A force applied to an object would cause it to deviate from a geodesic. For instance, people standing on the surface of the Earth are prevented from following a geodesic path because the mechanical resistance of the Earth exerts an upward force on them. This explains why moving along the geodesics in spacetime is considered inertial. Einstein's description of gravity was quickly accepted by the majority of physicists, as it

630-438: A force, but as the curvature of spacetime , caused by the uneven distribution of mass, and causing masses to move along geodesic lines. The most extreme example of this curvature of spacetime is a black hole , from which nothing—not even light—can escape once past the black hole's event horizon . However, for most applications, gravity is well approximated by Newton's law of universal gravitation , which describes gravity as

720-928: A gravitational attraction as well. In contrast, Al-Khazini held the same position as Aristotle that all matter in the Universe is attracted to the center of the Earth. In the mid-16th century, various European scientists experimentally disproved the Aristotelian notion that heavier objects fall at a faster rate. In particular, the Spanish Dominican priest Domingo de Soto wrote in 1551 that bodies in free fall uniformly accelerate. De Soto may have been influenced by earlier experiments conducted by other Dominican priests in Italy, including those by Benedetto Varchi , Francesco Beato, Luca Ghini , and Giovan Bellaso which contradicted Aristotle's teachings on

810-404: A great degree of precision in his computation. Treating the Earth as a sphere , its circumference would be its single most important measurement. Earth deviates from spherical by about 0.3%, as characterized by flattening . In modern times, Earth's circumference has been used to define fundamental units of measurement of length: the nautical mile in the seventeenth century and the metre in

900-399: A groundbreaking book called Philosophiæ Naturalis Principia Mathematica ( Mathematical Principles of Natural Philosophy ). In this book, Newton described gravitation as a universal force, and claimed that "the forces which keep the planets in their orbs must [be] reciprocally as the squares of their distances from the centers about which they revolve." This statement was later condensed into

990-415: A group of Muslim astronomers led by Al-Khwarizmi to measure the distance from Tadmur ( Palmyra ) to Raqqa , in modern Syria . They calculated the Earth's circumference to be within 15% of the modern value, and possibly much closer. How accurate it actually was is not known because of uncertainty in the conversion between the medieval Arabic units and modern units, but in any case, technical limitations of

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1080-399: A kilometre is one ten thousandth) of the arc from pole to equator ( quarter meridian ). The accuracy of measuring the circumference has improved since then, but the physical length of each unit of measure had remained close to what it was determined to be at the time, so the Earth's circumference is no longer a round number in metres or nautical miles. The measure of Earth's circumference is

1170-480: A nautical mile as 6,080 feet, the length of one minute of arc at 48 degrees latitude. In 1793, France defined the metre so as to make the polar circumference of the Earth 40,000 kilometres. In order to measure this distance accurately, the French Academy of Sciences commissioned Jean Baptiste Joseph Delambre and Pierre Méchain to lead an expedition to attempt to accurately measure the distance between

1260-456: A new approach to quantum mechanics) is required. Testing the predictions of general relativity has historically been difficult, because they are almost identical to the predictions of Newtonian gravity for small energies and masses. Still, since its development, an ongoing series of experimental results have provided support for the theory: In 1919, the British astrophysicist Arthur Eddington

1350-409: A non-rotating, gravitationally self-attracting liquid. The outward acceleration caused by Earth's rotation is greater at the equator than at the poles (where is it zero), so the sphere gets deformed into an ellipsoid , which represents the shape having the lowest potential energy for a rotating, fluid body. This ellipsoid is slightly fatter around the equator than a perfect sphere would be. Earth's shape

1440-444: A number of effects and phenomena that when combined disprove flat Earth beliefs . Gravity In physics, gravity (from Latin gravitas  'weight' ) is a fundamental interaction primarily observed as mutual attraction between all things that have mass . Gravity is, by far, the weakest of the four fundamental interactions, approximately 10 times weaker than the strong interaction , 10 times weaker than

1530-429: A simple motion, will continue to move in a straight line, unless continually deflected from it by some extraneous force, causing them to describe a circle, an ellipse, or some other curve. 3. That this attraction is so much the greater as the bodies are nearer. As to the proportion in which those forces diminish by an increase of distance, I own I have not discovered it.... Hooke's 1674 Gresham lecture, An Attempt to prove

1620-450: A single person from a single location. From the top of the mountain, he sighted the dip angle which, along with the mountain's height (which he determined beforehand), he applied to the law of sines formula. This was the earliest known use of dip angle and the earliest practical use of the law of sines. However, the method could not provide more accurate results than previous methods, due to technical limitations, and so al-Biruni accepted

1710-578: A spherical Earth as the center of the universe. The knowledge of the Greeks was inherited by Ancient Rome, and Christian and Islamic realms in the Middle Ages. Circumnavigation of the world in the Age of Discovery provided direct evidence. Improvements in transportation and other technologies refined estimations of the size of the Earth, and helped spread knowledge of it. The earliest documented mention of

1800-493: A sufficiently large and compact object. General relativity states that gravity acts on light and matter equally, meaning that a sufficiently massive object could warp light around it and create a gravitational lens . This phenomenon was first confirmed by observation in 1979 using the 2.1 meter telescope at Kitt Peak National Observatory in Arizona, which saw two mirror images of the same quasar whose light had been bent around

1890-526: A theory of general relativity which was able to accurately model Mercury's orbit. In general relativity, the effects of gravitation are ascribed to spacetime curvature instead of a force. Einstein began to toy with this idea in the form of the equivalence principle , a discovery which he later described as "the happiest thought of my life." In this theory, free fall is considered to be equivalent to inertial motion, meaning that free-falling inertial objects are accelerated relative to non-inertial observers on

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1980-412: A tower. In the late 16th century, Galileo Galilei 's careful measurements of balls rolling down inclines allowed him to firmly establish that gravitational acceleration is the same for all objects. Galileo postulated that air resistance is the reason that objects with a low density and high surface area fall more slowly in an atmosphere. In 1604, Galileo correctly hypothesized that the distance of

2070-652: A vertical rod known as a gnomon and under the previous assumptions, he knew that at local noon on the summer solstice in Syene (modern Aswan , Egypt), the Sun was directly overhead, as the gnomon cast no shadow. Additionally, the shadow of someone looking down a deep well at that time in Syene blocked the reflection of the Sun on the water. Eratosthenes then measured the Sun's angle of elevation at noon in Alexandria by measuring

2160-486: A wide range of ancient scholars. In Greece , Aristotle believed that objects fell towards the Earth because the Earth was the center of the Universe and attracted all of the mass in the Universe towards it. He also thought that the speed of a falling object should increase with its weight, a conclusion that was later shown to be false. While Aristotle's view was widely accepted throughout Ancient Greece, there were other thinkers such as Plutarch who correctly predicted that

2250-427: Is 40,075.017 km (24,901.461 mi). Measured passing through the poles , the circumference is 40,007.863 km (24,859.734 mi). Measurement of Earth's circumference has been important to navigation since ancient times. The first known scientific measurement and calculation was done by Eratosthenes , by comparing altitudes of the mid-day sun at two places a known north–south distance apart. He achieved

2340-407: Is also slightly lumpy because it is composed of different materials of different densities that exert slightly different amounts of gravitational force per volume. The liquidity of a hot, newly formed planet allows heavier elements to sink down to the middle and forces lighter elements closer to the surface, a process known as planetary differentiation . This event is known as the iron catastrophe ;

2430-623: Is concerned with measuring parts of the surface. Earth's shape can be thought of in at least two ways: As the science of geodesy measured Earth more accurately, the shape of the geoid was first found not to be a perfect sphere but to approximate an oblate spheroid , a specific type of ellipsoid . More recent measurements have measured the geoid to unprecedented accuracy, revealing mass concentrations beneath Earth's surface. The roughly spherical shape of Earth can be empirically evidenced by many different types of observation , ranging from ground level, flight, or orbit. The spherical shape causes

2520-458: Is especially vexing to physicists because the other three fundamental forces (strong force, weak force and electromagnetism) were reconciled with a quantum framework decades ago. As a result, modern researchers have begun to search for a theory that could unite both gravity and quantum mechanics under a more general framework. One path is to describe gravity in the framework of quantum field theory , which has been successful to accurately describe

2610-456: Is often expressed in the form G μ ν + Λ g μ ν = κ T μ ν , {\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu },} where G μν is the Einstein tensor , g μν is the metric tensor , T μν is the stress–energy tensor , Λ

2700-460: Is primarily concerned with positioning and the gravity field and geometrical aspects of their temporal variations, although it can also include the study of Earth's magnetic field . Especially in the German speaking world, geodesy is divided into geomensuration ("Erdmessung" or "höhere Geodäsie"), which is concerned with measuring Earth on a global scale, and surveying ("Ingenieurgeodäsie"), which

2790-545: Is the cosmological constant , G {\displaystyle G} is the Newtonian constant of gravitation and c {\displaystyle c} is the speed of light . The constant κ = 8 π G c 4 {\displaystyle \kappa ={\frac {8\pi G}{c^{4}}}} is referred to as the Einstein gravitational constant. A major area of research

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2880-445: Is the discovery of exact solutions to the Einstein field equations. Solving these equations amounts to calculating a precise value for the metric tensor (which defines the curvature and geometry of spacetime) under certain physical conditions. There is no formal definition for what constitutes such solutions, but most scientists agree that they should be expressable using elementary functions or linear differential equations . Some of

2970-507: Is what causes tides in the oceans ' water, which can flow freely along the changing potential. The spherical shape of the Earth was known and measured by astronomers, mathematicians, and navigators from a variety of literate ancient cultures, including the Hellenic World, and Ancient India. Greek ethnographer Megasthenes , c.  300 BC , has been interpreted as stating that the contemporary Brahmans of India believed in

3060-489: The Indian mathematician and astronomer Brahmagupta proposed the idea that gravity is an attractive force that draws objects to the Earth and used the term gurutvākarṣaṇ to describe it. In the ancient Middle East , gravity was a topic of fierce debate. The Persian intellectual Al-Biruni believed that the force of gravity was not unique to the Earth, and he correctly assumed that other heavenly bodies should exert

3150-481: The International System of Units (SI). The force of gravity on Earth is the resultant (vector sum) of two forces: (a) The gravitational attraction in accordance with Newton's universal law of gravitation, and (b) the centrifugal force, which results from the choice of an earthbound, rotating frame of reference. The force of gravity is weakest at the equator because of the centrifugal force caused by

3240-466: The Moon's gravity is responsible for sublunar tides in the oceans. The corresponding antipodal tide is caused by the inertia of the Earth and Moon orbiting one another. Gravity also has many important biological functions, helping to guide the growth of plants through the process of gravitropism and influencing the circulation of fluids in multicellular organisms . The gravitational attraction between

3330-489: The Planck epoch (up to 10 seconds after the birth of the universe), possibly from a primeval state, such as a false vacuum , quantum vacuum or virtual particle , in a currently unknown manner. Scientists are currently working to develop a theory of gravity consistent with quantum mechanics , a quantum gravity theory, which would allow gravity to be united in a common mathematical framework (a theory of everything ) with

3420-405: The electromagnetic force and 10 times weaker than the weak interaction . As a result, it has no significant influence at the level of subatomic particles . However, gravity is the most significant interaction between objects at the macroscopic scale , and it determines the motion of planets , stars , galaxies , and even light . On Earth , gravity gives weight to physical objects , and

3510-402: The potential energy of their collisions and in-falling as heat . The protoplanetary disk also had a greater proportion of radioactive elements than Earth today because, over time, those elements decayed . Their decay heated the early Earth even further, and continue to contribute to Earth's internal heat budget . The early Earth was thus mostly liquid. A sphere is the only stable shape for

3600-485: The Annual Motion of the Earth , explained that gravitation applied to "all celestial bodies" In 1684, Newton sent a manuscript to Edmond Halley titled De motu corporum in gyrum ('On the motion of bodies in an orbit') , which provided a physical justification for Kepler's laws of planetary motion . Halley was impressed by the manuscript and urged Newton to expand on it, and a few years later Newton published

3690-649: The Big Bang. Neutron star and black hole formation also create detectable amounts of gravitational radiation. This research was awarded the Nobel Prize in Physics in 2017. In December 2012, a research team in China announced that it had produced measurements of the phase lag of Earth tides during full and new moons which seem to prove that the speed of gravity is equal to the speed of light. This means that if

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3780-629: The Earth , which has not been preserved; what has been preserved is the simplified version described by Cleomedes to popularise the discovery. Cleomedes invites his reader to consider two Egyptian cities, Alexandria and Syene (modern Aswan ): According to Cleomedes ' On the Circular Motions of the Celestial Bodies , around 240 BC, Eratosthenes calculated the circumference of the Earth in Ptolemaic Egypt . Using

3870-457: The Earth's rotation and because points on the equator are furthest from the center of the Earth. The force of gravity varies with latitude and increases from about 9.780 m/s at the Equator to about 9.832 m/s at the poles. General relativity predicts that energy can be transported out of a system through gravitational radiation. The first indirect evidence for gravitational radiation

3960-463: The Earth) is surrounded by its own gravitational field, which can be conceptualized with Newtonian physics as exerting an attractive force on all objects. Assuming a spherically symmetrical planet, the strength of this field at any given point above the surface is proportional to the planetary body's mass and inversely proportional to the square of the distance from the center of the body. The strength of

4050-513: The Elder mentions Posidonius among his sources and—without naming him—reported his method for estimating the Earth's circumference. He noted, however, that Hipparchus had added some 26,000 stadia to Eratosthenes's estimate. The smaller value offered by Strabo and the different lengths of Greek and Roman stadia have created a persistent confusion around Posidonius's result. Ptolemy used Posidonius's lower value of 180,000 stades (about 33% too low) for

4140-569: The Roman engineer and architect Vitruvius contended in his De architectura that gravity is not dependent on a substance's weight but rather on its "nature". In the 6th century CE, the Byzantine Alexandrian scholar John Philoponus proposed the theory of impetus, which modifies Aristotle's theory that "continuation of motion depends on continued action of a force" by incorporating a causative force that diminishes over time. In 628 CE,

4230-573: The Sun suddenly disappeared, the Earth would keep orbiting the vacant point normally for 8 minutes, which is the time light takes to travel that distance. The team's findings were released in Science Bulletin in February 2013. In October 2017, the LIGO and Virgo detectors received gravitational wave signals within 2 seconds of gamma ray satellites and optical telescopes seeing signals from

4320-427: The attraction of gravity was not unique to the Earth. Although he did not understand gravity as a force, the ancient Greek philosopher Archimedes discovered the center of gravity of a triangle. He postulated that if two equal weights did not have the same center of gravity, the center of gravity of the two weights together would be in the middle of the line that joins their centers of gravity. Two centuries later,

4410-503: The attractive force is stronger for closer bodies. In a communication to the Royal Society in 1666, Hooke wrote I will explain a system of the world very different from any yet received. It is founded on the following positions. 1. That all the heavenly bodies have not only a gravitation of their parts to their own proper centre, but that they also mutually attract each other within their spheres of action. 2. That all bodies having

4500-425: The basis for a unit of measurement for distance and proposed the nautical mile as one minute or one-sixtieth ( ⁠ 1 / 60 ⁠ ) of one degree of latitude. As one degree is ⁠ 1 / 360 ⁠ of a circle, one minute of arc is ⁠ 1 / 21600 ⁠ of a circle – such that the polar circumference of the Earth would be exactly 21,600 miles. Gunter used Snellius's circumference to define

4590-598: The concept dates from around the 5th century BC, when it appears in the writings of Greek philosophers . In the 3rd century BC, Hellenistic astronomy established the roughly spherical shape of Earth as a physical fact and calculated the Earth's circumference . This knowledge was gradually adopted throughout the Old World during Late Antiquity and the Middle Ages . A practical demonstration of Earth's sphericity

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4680-728: The earth's circumference in his Geography . This was the number used by Christopher Columbus in order to underestimate the distance to India as 70,000 stades. Around AD 525, the Indian mathematician and astronomer Aryabhata wrote Aryabhatiya , in which he calculated the diameter of earth to be of 1,050 yojanas . The length of the yojana intended by Aryabhata is in dispute. One careful reading gives an equivalent of 14,200 kilometres (8,800 mi), too large by 11%. Another gives 15,360 km (9,540 mi), too large by 20%. Yet another gives 13,440 km (8,350 mi), too large by 5%. Around AD 830, Caliph Al-Ma'mun commissioned

4770-402: The eighteenth. Earth's polar circumference is very near to 21,600 nautical miles because the nautical mile was intended to express one minute of latitude (see meridian arc ), which is 21,600 partitions of the polar circumference (that is 60 minutes × 360 degrees). The polar circumference is also close to 40,000 kilometres because the metre was originally defined to be one ten millionth (i.e.,

4860-429: The energy release from these processes halts, then they tend to erode away over time and return toward the lowest potential-energy curve of the ellipsoid. Weather powered by solar energy can also move water, rock, and soil to make Earth slightly out of round. Earth undulates as the shape of its lowest potential energy changes daily due to the gravity of the Sun and Moon as they move around with respect to Earth. This

4950-471: The fall of bodies. The mid-16th century Italian physicist Giambattista Benedetti published papers claiming that, due to specific gravity , objects made of the same material but with different masses would fall at the same speed. With the 1586 Delft tower experiment , the Flemish physicist Simon Stevin observed that two cannonballs of differing sizes and weights fell at the same rate when dropped from

5040-433: The following inverse-square law: F = G m 1 m 2 r 2 , {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},} where F is the force, m 1 and m 2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant 6.674 × 10  m ⋅kg ⋅s . Newton's Principia

5130-409: The framework for the understanding of gravity. Physicists continue to work to find solutions to the Einstein field equations that form the basis of general relativity and continue to test the theory, finding excellent agreement in all cases. The Einstein field equations are a system of 10 partial differential equations which describe how matter affects the curvature of spacetime. The system

5220-458: The galaxy YGKOW G1 . Frame dragging , the idea that a rotating massive object should twist spacetime around it, was confirmed by Gravity Probe B results in 2011. In 2015, the LIGO observatory detected faint gravitational waves , the existence of which had been predicted by general relativity. Scientists believe that the waves emanated from a black hole merger that occurred 1.5 billion light-years away. Every planetary body (including

5310-523: The gravitational field is numerically equal to the acceleration of objects under its influence. The rate of acceleration of falling objects near the Earth's surface varies very slightly depending on latitude, surface features such as mountains and ridges, and perhaps unusually high or low sub-surface densities. For purposes of weights and measures, a standard gravity value is defined by the International Bureau of Weights and Measures , under

5400-472: The ground. In contrast to Newtonian physics , Einstein believed that it was possible for this acceleration to occur without any force being applied to the object. Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight paths are called geodesics . As in Newton's first law of motion, Einstein believed that

5490-421: The horizon (the meridian arc between the latitude of the two locales is actually 5 degrees 14 minutes). Since he thought Rhodes was 5,000 stadia due north of Alexandria, and the difference in the star's elevation indicated the distance between the two locales was 1/48 of the circle, he multiplied 5,000 by 48 to arrive at a figure of 240,000 stadia for the circumference of the earth. It is generally thought that

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5580-596: The idea that time runs more slowly in the presence of a gravitational field. The time delay of light passing close to a massive object was first identified by Irwin I. Shapiro in 1964 in interplanetary spacecraft signals. In 1971, scientists discovered the first-ever black hole in the galaxy Cygnus . The black hole was detected because it was emitting bursts of x-rays as it consumed a smaller star, and it came to be known as Cygnus X-1 . This discovery confirmed yet another prediction of general relativity, because Einstein's equations implied that light could not escape from

5670-457: The interactions of three or more massive bodies (the " n -body problem"), and some scientists suspect that the Einstein field equations will never be solved in this context. However, it is still possible to construct an approximate solution to the field equations in the n -body problem by using the technique of post-Newtonian expansion . In general, the extreme nonlinearity of the Einstein field equations makes it difficult to solve them in all but

5760-405: The length of another gnomon's shadow on the ground. Using the length of the rod, and the length of the shadow, as the legs of a triangle, he calculated the angle of the sun's rays. This angle was about 7°, or 1/50th the circumference of a circle ; assuming the Earth to be perfectly spherical, he concluded that its circumference was 50 times the known distance from Alexandria to Syene (5,000 stadia,

5850-527: The methods and tools would not permit an accuracy better than about 5%. A more convenient way to estimate was provided in Al-Biruni 's Codex Masudicus (1037). In contrast to his predecessors, who measured the Earth's circumference by sighting the Sun simultaneously from two locations, al-Biruni developed a new method of using trigonometric calculations, based on the angle between a plain and mountain top, which made it possible for it to be measured by

5940-449: The most abundant heavier elements were iron and nickel , which now form the Earth's core . Though the surface rocks of Earth have cooled enough to solidify, the outer core of the planet is still hot enough to remain liquid. Energy is still being released; volcanic and tectonic activity has pushed rocks into hills and mountains and blown them out of calderas . Meteors also cause impact craters and surrounding ridges. However, if

6030-412: The most famous among the results obtained by Eratosthenes , who estimated that the meridian has a length of 252,000 stadia , with an error on the real value between −2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres; the exact value of the stadion remains a subject of debate to this day; see stadion ). Eratosthenes described his technique in a book entitled On the measure of

6120-429: The most notable solutions of the equations include: Today, there remain many important situations in which the Einstein field equations have not been solved. Chief among these is the two-body problem , which concerns the geometry of spacetime around two mutually interacting massive objects, such as the Sun and the Earth, or the two stars in a binary star system . The situation gets even more complicated when considering

6210-405: The most specific cases. Despite its success in predicting the effects of gravity at large scales, general relativity is ultimately incompatible with quantum mechanics . This is because general relativity describes gravity as a smooth, continuous distortion of spacetime, while quantum mechanics holds that all forces arise from the exchange of discrete particles known as quanta . This contradiction

6300-422: The orbit of the planet Mercury which could not be explained by Newton's theory: the perihelion of the orbit was increasing by about 42.98 arcseconds per century. The most obvious explanation for this discrepancy was an as-yet-undiscovered celestial body, such as a planet orbiting the Sun even closer than Mercury, but all efforts to find such a body turned out to be fruitless. In 1915, Albert Einstein developed

6390-514: The order of 1/300 ( Delambre , Everest ). The modern value as determined by the US DoD World Geodetic System since the 1960s is close to 1/298.25. Geodesy , also called geodetics, is the scientific discipline that deals with the measurement and representation of Earth, its gravitational field and geodynamic phenomena ( polar motion , Earth tides , and crustal motion) in three-dimensional time-varying space. Geodesy

6480-453: The original gaseous matter in the universe caused it to coalesce and form stars which eventually condensed into galaxies, so gravity is responsible for many of the large-scale structures in the universe. Gravity has an infinite range, although its effects become weaker as objects get farther away. Gravity is most accurately described by the general theory of relativity , proposed by Albert Einstein in 1915, which describes gravity not as

6570-465: The other fundamental interactions . The electromagnetic force arises from an exchange of virtual photons , where the QFT description of gravity is that there is an exchange of virtual gravitons . This description reproduces general relativity in the classical limit . However, this approach fails at short distances of the order of the Planck length , where a more complete theory of quantum gravity (or

6660-483: The other side, believe that Eratosthenes introduced a new length unit based on the length of the meridian, as stated by Pliny, who writes about the stadion "according to Eratosthenes' ratio". Posidonius calculated the Earth's circumference by reference to the position of the star Canopus . As explained by Cleomedes , Posidonius observed Canopus on but never above the horizon at Rhodes , while at Alexandria he saw it ascend as far as 7 + 1 ⁄ 2 degrees above

6750-473: The other three fundamental interactions of physics. Gravitation , also known as gravitational attraction, is the mutual attraction between all masses in the universe. Gravity is the gravitational attraction at the surface of a planet or other celestial body; gravity may also include, in addition to gravitation, the centrifugal force resulting from the planet's rotation (see § Earth's gravity ) . The nature and mechanism of gravity were explored by

6840-461: The place where he made landfall was not Asia , but rather a New World . In 1617 the Dutch scientist Willebrord Snellius assessed the circumference of the Earth at 24,630 Roman miles (24,024 statute miles). Around that time British mathematician Edmund Gunter improved navigational tools including a new quadrant to determine latitude at sea. He reasoned that the lines of latitude could be used as

6930-502: The planet's actual trajectory. In order to explain this discrepancy, many astronomers speculated that there might be a large object beyond the orbit of Uranus which was disrupting its orbit. In 1846, the astronomers John Couch Adams and Urbain Le Verrier independently used Newton's law to predict Neptune's location in the night sky, and the planet was discovered there within a day. Eventually, astronomers noticed an eccentricity in

7020-520: The result was 40,074 km, which is 66 km different (0.16%) from the currently accepted polar circumference. Eratosthenes' method was actually more complicated, as stated by the same Cleomedes, whose purpose was to present a simplified version of the one described in Eratosthenes' book. Pliny, for example, has quoted a value of 252,000 stadia. The method was based on several surveying trips conducted by professional bematists , whose job

7110-410: The same direction. This confirmed that the speed of gravitational waves was the same as the speed of light. There are some observations that are not adequately accounted for, which may point to the need for better theories of gravity or perhaps be explained in other ways. Earth%27s circumference Earth's circumference is the distance around Earth . Measured around the equator , it

7200-423: The scientific community. In 1959, American physicists Robert Pound and Glen Rebka performed an experiment in which they used gamma rays to confirm the prediction of gravitational time dilation . By sending the rays down a 74-foot tower and measuring their frequency at the bottom, the scientists confirmed that light is redshifted as it moves towards a source of gravity. The observed redshift also supported

7290-523: The shape of Earth include a seven-layered ziggurat or cosmic mountain , alluded to in the Avesta and ancient Persian writings (see seven climes ). The realization that the figure of the Earth is more accurately described as an ellipsoid dates to the 17th century, as described by Isaac Newton in Principia . In the early 19th century, the flattening of the earth ellipsoid was determined to be of

7380-461: The stadion used by Posidonius was almost exactly 1/10 of a modern statute mile. Thus Posidonius's measure of 240,000 stadia translates to 24,000 mi (39,000 km), not much short of the actual circumference of 24,901 mi (40,074 km). Strabo noted that the distance between Rhodes and Alexandria is 3,750 stadia, and reported Posidonius's estimate of the Earth's circumference to be 180,000 stadia or 18,000 mi (29,000 km). Pliny

7470-408: The value calculated the previous century by the al-Ma'mun expedition. 1,700 years after Eratosthenes's death, Christopher Columbus studied what Eratosthenes had written about the size of the Earth. Nevertheless, based on a map by Toscanelli , he chose to believe that the Earth's circumference was 25% smaller. If, instead, Columbus had accepted Eratosthenes's larger value, he would have known that

7560-421: Was able to confirm the predicted gravitational lensing of light during that year's solar eclipse . Eddington measured starlight deflections twice those predicted by Newtonian corpuscular theory, in accordance with the predictions of general relativity. Although Eddington's analysis was later disputed, this experiment made Einstein famous almost overnight and caused general relativity to become widely accepted in

7650-468: Was able to explain a wide variety of previously baffling experimental results. In the coming years, a wide range of experiments provided additional support for the idea of general relativity. Today, Einstein's theory of relativity is used for all gravitational calculations where absolute precision is desired, although Newton's inverse-square law is accurate enough for virtually all ordinary calculations. In modern physics , general relativity remains

7740-434: Was achieved by Ferdinand Magellan and Juan Sebastián Elcano 's circumnavigation (1519–1522). The concept of a spherical Earth displaced earlier beliefs in a flat Earth : In early Mesopotamian mythology , the world was portrayed as a disk floating in the ocean with a hemispherical sky-dome above, and this forms the premise for early world maps like those of Anaximander and Hecataeus of Miletus . Other speculations on

7830-410: Was measured on 14 September 2015 by the LIGO detectors. The gravitational waves emitted during the collision of two black holes 1.3 billion light years from Earth were measured. This observation confirms the theoretical predictions of Einstein and others that such waves exist. It also opens the way for practical observation and understanding of the nature of gravity and events in the Universe including

7920-543: Was through measurements of the Hulse–Taylor binary in 1973. This system consists of a pulsar and neutron star in orbit around one another. Its orbital period has decreased since its initial discovery due to a loss of energy, which is consistent for the amount of energy loss due to gravitational radiation. This research was awarded the Nobel Prize in Physics in 1993. The first direct evidence for gravitational radiation

8010-491: Was to precisely measure the extent of the territory of Egypt for agricultural and taxation-related purposes. Furthermore, the fact that Eratosthenes' measure corresponds precisely to 252,000 stadia (according to Pliny) might be intentional, since it is a number that can be divided by all natural numbers from 1 to 10: some historians believe that Eratosthenes changed from the 250,000 value written by Cleomedes to this new value to simplify calculations; other historians of science, on

8100-540: Was well received by the scientific community, and his law of gravitation quickly spread across the European world. More than a century later, in 1821, his theory of gravitation rose to even greater prominence when it was used to predict the existence of Neptune . In that year, the French astronomer Alexis Bouvard used this theory to create a table modeling the orbit of Uranus , which was shown to differ significantly from

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