which differs from the exact result by less than 1m (4105in); the mean of the two axes. det George Jackson is the founder and lead contributor of Physics Network, a popular blog dedicated to exploring the fascinating world of physics. Measured around the Equator, it is 40,075.017 km (24,901.461 mi). It is a physical constant which represents the most probable distance between the electron and the nucleus in a hydrogen atom in its ground state. Multiplyin. After many, many years, you will have some intuition for the physics you studied. These cookies ensure basic functionalities and security features of the website, anonymously. e [1]:3 The nominal polar Earth radius is defined as Solving for x reveals the circumference to be. In a geocentric ellipsoid, the center of the ellipsoid coincides with some computed center of Earth, and best models the earth as a whole. Convert the Earth-Sun distance of 93,000,000 miles into. b) Calculate the surface free-fall acceleration. Eratosthenes methods result in a formula that would look like this: 39,350 = 2 x 3.14 x r, or 6,267 kilometers. {\displaystyle p=N\cos(\varphi )} 3 The distance between Syene and Alexandria is 787 kilometers, Eratosthenes used the ancient Greek measurement of stadia, but his calculations use the proportionality of angles between two locations, so any system of measurement will work. One can only adopt an idealized model. Each pair measured the position from the sun, in the same manner the Greek philosopher Eratosthenes exceeded 2000 years back in Alexandria, Egyptby evaluating the size of an item to the size of its shadow, measured at local noon. But opting out of some of these cookies may affect your browsing experience. What is the biggest problem with wind turbines? . Therefore, if the earth is taken to be a two dimensional object, its perimeter would be equal to the. N When the Moon is the farthest away, it's 252,088 miles away. Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. As an example, we will use Eratosthenes situation. However, Earth is not quite a sphere. The Earths equatorial radius to meter (m) conversion table and conversion steps are also listed. Born and raised in the city of London, Alexander Johnson studied biology and chemistry in college and went on to earn a PhD in biochemistry. A closed-form solution exists for a spheroid:[14]. Earths Equatorial Radius to Meter Conversion Table, How to Convert Earths Equatorial Radius to Meter, Convert Earths Equatorial Radius to Other Length Units. The Earth can be modeled as a sphere in many ways. N ] Because these measurements are not done with more sensitive equipment, the radius calculation will be only approximate. Compute the radius of the Earth using the formula C (circumference) = 2 x pi x r (radius). Calculating Earths Volume Averaging these two numbers yields a mean radius of 6,371.0 kilometers (3,958.7 miles), which in turn yields an approximate value for the volume of the Earth of 1.08 quadrillion cubic kilometers (259 trillion cubic miles). MITs Alan , In 2020, as a response to the disruption caused by COVID-19, the College Board modified the AP exams so they were shorter, administered online, covered less material, and had a different format than previous tests. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. We also use third-party cookies that help us analyze and understand how you use this website. What physical measurement / elevation is used to define Earths radius? Tack one end of a piece of string to the top of the stick. Like a torus, the curvature at a point will be greatest (tightest) in one direction (northsouth on Earth) and smallest (flattest) perpendicularly (eastwest). The red dot at the lower left corner is its center. The recent Juno mission launched with the goal of examining Jupiters composition and underlying structure, the wikipedia article on the Juno spacecraft provides an a great overview of this type of process. det Record the distance between your location and your partners location. [24] Claudius Ptolemy around 150AD gave empirical evidence supporting a spherical Earth,[25] but he accepted the lesser value attributed to Posidonius. As such, they are topographical geocentric distances, Rt, which depends not only on latitude. [ In 1993 the WGS84 governing committee voted, with one exception, to retain the 1984 defining values, despite improvements to those defining values. z {\displaystyle r} The Earth's Gaussian radius of curvature at latitude is:[12]. They are vertices of the ellipse and also coincide with minimum and maximum radius of curvature. The structure of the Earths upper mantle can be derived from seismic waves. 1 Earths equatorial radius637816 m1 Earths equatorial radius6378160 m2 Earths equatorial radius12756320 m3 Earths equatorial radius19134480 m5 Earths equatorial radius31890800 m10 Earths equatorial radius63781600 m20 Earths equatorial radius127563200 m50 Earths equatorial radius318908000 m100 Earths equatorial radius637816000 m1000 Earths equatorial radius6378160000 mHow to Convert Earths Equatorial Radius to Meter1 Earths equatorial radius = 6378160 m1 m = 1. less than 6400 km. The tropical radius of the world (or semi-major axis) is all about 6,378 km (3,963 miles or 3,444 maritime miles), as the polar radius of the world (or semi-minor axis) is all about 6,357 km (3,950 miles or 3,432 maritime miles). Given you're looking for a simple formula, this is probably the simplest way to do it, assuming that the Earth is a sphere with a circumference of 40075 km. Since the earth's surface is 6.37 x 10 6 m from its center (that's the radius of the earth), the satellite must be a height of. Eratosthenes, the ancient Greek scholar is called the father of geography. Asked By: Lena Frontelo | Last Updated: 18th May, 2020, Earth is the third planet from the sun. The IUGG denotes the volumetric radius as R3. In late August of 2003, Mars was at its closest point to Earth in about 60,000 years! 371 106 meters (Earth radius 6. Around 1690, Isaac Newton and Christiaan Huygens argued that Earth was closer to an oblate spheroid than to a sphere. Here x is the circumference of the earth. He also shares personal stories and insights from his own journey as a scientist and researcher. There are two principal radii of curvature: along the meridional and prime-vertical normal sections. After completing his degree, George worked as a postdoctoral researcher at CERN, the world's largest particle physics laboratory. Performance cookies are used to understand and analyze the key performance indexes of the website which helps in delivering a better user experience for the visitors. The following is a partial list of models of Earth's surface, ordered from exact to more approximate: In the case of the geoid and ellipsoids, the fixed distance from any point on the model to the specified center is called "a radius of the Earth" or "the radius of the Earth at that point". The geocentric radius is the distance from the Earth's center to a point on the spheroid surface at geodetic latitude : where a and b are, respectively, the equatorial radius and the polar radius. What is the radius of Earth in meters? Since the estimate by Eratosthenes, many models have been created. The following equation estimates the ellipsoid radius ( r s ) using flattening ( f ) , geocentric latitude ( s ) , and equatorial radius ( R ) : r s = R 2 1 + [ 1 / ( 1 f ) 2 1 ] sin 2 s . Although the precise strength of Earth's gravity varies depending on location, the nominal "average" value at the Earth's surface, known as standard gravity is, by definition, 9.80665 m/s 2 (32.1737 ft/s 2 ). Using the parameters from WGS84 ellipsoid of revolution, a = 6,378.137 km and b = 6,356.7523142km, V = 1.083211012km3 (2.59881011cumi). How cold is it on moon? E Escape velocity = = 22.4 km/sec. {\displaystyle {\mathcal {R}}_{\mathrm {eE} }^{\mathrm {N} }} Enchanted Learning. If you wish to convert a small difference of latitude or longitude into the linear distance on the surface of the earth, then the spherical earth equation would be, = = dE R cos d dN R d , How did early mathematicians determine the radius of the earth? Do NOT follow this link or you will be banned from the site! The cookies is used to store the user consent for the cookies in the category "Necessary". This topographical average is 6,371.230km (3,958.899mi) with uncertainty of 10m (33ft).[16]. The radius of the Earth is 6371 km. When he's not busy exploring the mysteries of the universe, George enjoys hiking and spending time with his family. The Earth. More than 2,000 years ago Eratosthenes compared the position of the Suns rays in two locations to calculate the spherical size of the Earth with reasonable accuracy. The current best estimate for the mass of the Earth is M = 5.97221024 kg, with a standard uncertainty of 61020 kg (relative uncertainty 104). 6,371 kmEarth / RadiusAccording to data taken by 183 high-school classes participating in a World Year of Physics project, "Measure the Earth with Shadows", the radius of Earth is 6563 km, compared to the accepted value for the mean radius of 6371 km. Hence, we create models to approximate characteristics of Earth's surface, generally relying on the simplest model that suits the need. Because the Earth isnt perfectly spherical but instead an oblate spheroid, our planet radius is larger in the equator than in the rods. arrow_forward. When we rearrange the equation and plug all the numbers in, we find that the mass of the Earth is 5.96 1024 kg. When considering the Earth's real surface, on the other hand, it is uncommon to refer to a "radius", since there is generally no practical need. However, around 1730, Jacques Cassini argued for a prolate spheroid instead, due to different interpretations of the Newtonian mechanics involved. With [Mass of the earth is 6 x 1024 kg and radius of the earth is 6.4 x 106 m]. Eastwest directions can be misleading. In simple words, radius refers to that line, which originates from any point of the circle and touches the centre point the circle. e It is with the values I gave you. What happens to the dry ice at room pressure and temperature? You must measure the angle of shadows in the two locations at the exact same time on the exact same day or the calculations will be erroneous. F It is the smallest planet in the Solar System, with an equatorial radius of 2,439.7 km. is the unit normal to the surface at Therefore, the distance you use in the equation is the distance between the two orbiting bodies. 137 km (3963. The core is found about 2,900 kilometers (1,802 miles) below Earth's surface, and has a radius of about 3,485 kilometers (2,165 miles). The radius of orbit indicates the distance that the satellite is from the center of the earth. It is possible to combine the principal radii of curvature above in a non-directional manner. When it's closest, the Moon is 225,623 miles away. 06. m. 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. In particular, the Earth's meridional radius of curvature (in the northsouth direction) at is: where The radius of the Earth, re, is about 6.38 10 6 meters, and the mass of the Earth is 5.98 10 24 kilograms. cos nasa.gov. The average light travel time to the earth is 8.3 minutes. In 200 B.C. . b : the third and usually largest vein of an insect's wing. The planet's rotation causes it to bulge at the equator. Sun: radius = 696,000 kilometers, > 100 occasions bigger. Its nice to determine that measurements taken by a lot of groups, sometimes in under ideal conditions, came so near to the right answer. , Its the only planet with life. Scholars have interpreted Aristotle's figure to be anywhere from highly accurate[20] to almost double the true value. {\displaystyle w^{1}=\varphi } If no sub- or superscripts appear on this page - for example, if the "Mass" is given in units of "(1024 kg)" - you may want to check the notes on the sub- and superscripts. the center.of the Earth. All Right Reserved. is normal to the surface at So, for him the following relationship between objects will apply: 7.2 / 360 = 787 / x. . Earth, on the other hand, isn't quite a sphere. {\displaystyle r+dr} The cookies is used to store the user consent for the cookies in the category "Necessary". It has a diameter of 12,756.3 km (Scientific notation: 1.2756 x 10e4) and a radius of 56,378.15 km (Scientific notation: 5.6378 x 10e4 km.) An Enormous, Unknown Cambrian Bug Fossil Has Been Discovered within the Eerie Burgess Shale, Ancient Tracks May Be The Oldest Hominin Footprints Ever Found, Scientists Say, By 2500, Earth Will Be Alien To Humans If We Dont Act Now, Scientists Warn, Responsibility disclaimer and privacy policy, Topics Related to Circumference of the Earth. You need to solve physics problems. Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. The height above sea level of the location is added. At Baltimore, = 39.48o and the length is 111.16 km, nearly. Since the locations are points on a circle that goes around the Earth, the distance between them can be expressed as an arc measurement on a 360-degree circle. You can do this, too, by using his method. What is the earths radius in meters?Earth radiusSI base unit6.3781106 mMetric system6,357 to 6,378 kmEnglish units3,950 to 3,963 miEarth radiusSI base unit6.3781106 mMetric system6,357 to 6,378 kmEnglish units3,950 to 3,963 miWhat is the radius of the earth?According to data taken by 183 high-school classes participating in a World Year of Physics project, "Measure the Earth West can be exchanged for east in this discussion. The extrema geocentric radii on the ellipsoid coincide with the equatorial and polar radii. | Who first calculated the radius of the earth? The planet bulges at the equator as a result of its rotation. to the plane tangent at What is the number in scientific notation? The Earths circumference is approximately 40,000,000 meters. How do you use the Pythagorean Theorem to find the radius of the earth? Copyright 2022 - Science-Atlas.com. How do you find the radius of a planet in physics? [29] To settle the matter, the French Geodesic Mission (17351739) measured one degree of latitude at two locations, one near the Arctic Circle and the other near the equator. [1]:4 Since he knew the distance between the locations, he was able to determine the circumference of the earth, and therefore the diameter and radius as well. [2] All three values are about 6,371 kilometres (3,959mi). Added 2022-02-06 15:04:59 subject Physics by rsa072001. This section describes the common ways. Step 3 of 5. What are the formula in calculating the earth? Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. When it is measured around the equator, it is40,075 km (approximately, 24,901 miles), whereas, if it measured from the north pole to the south pole it is40,008 km (approximately, 24,860 miles). The first and second radii of curvature correspond, respectively, to the Earth's meridional and prime-vertical radii of curvature. [e] For the Earth .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num,.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0 0.1em}.mw-parser-output .sfrac .den{border-top:1px solid}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}1/q 289, which is close to the measured inverse flattening 1/f 298.257. In general, this points to an important conclusion about nature itself. Earth's diameter is simply twice Earth's radius; for example, equatorial diameter (2a) and polar diameter (2b). This calculated value became a defining value in 1993. Geodetic ellipsoids are better suited to regional idiosyncrasies of the geoid. Science atlas, our goal is to spark the curiosity that exists in all of us. How far (in meter) does it travel in the first 3 seconds? R The radius of a parallel of latitude is given by => When Wi-Fi is available location accuracy is usually between 20 - 50 meters. w 1 What you need is to convert a meter into degrees since long/lat is a polar coordinate system.With the circumference of Earth being 40,075 km, you get 0.00000898315 deg/m which you need to multiply with the size of the object (1 m) to get the degrees which you have to add to your coordinate to get a point which intersects with the radius of . The radius of the swimming pool water atom is roughly meters. Therefore, the Earth radius isn't constant, but it can be calculated for every location. Approximating the figure of Earth by an Earth spheroid, the radius ranges from a maximum of nearly 6,378km (3,963mi) (equatorial radius, denoted a) to a minimum of nearly 6,357km (3,950mi) (polar radius, denoted b). How far is the center of the Earth in KM? Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. mpanderla95. Obviously, nobody is claiming how big Earth has really altered. also corresponds to the radius of (global) mean curvature, obtained by averaging the Gaussian curvature, {\displaystyle {\frac {\partial r}{\partial \lambda }}} The equatorial radius of Earth is actually 6,378.1 kilometers. Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. r arrow_forward. A) 4.5 x 10-7 B) 4.5 x 107 C) 45 x 10-6 D) 45 x 106 Semi-minor axis b = 6356752.3142 meters. A How much is a trillion in scientific notation? University of Texas: Eratosthenese Finds Diameter of Earth, Partner in a distant location on about the same longitude or in the same time zone. A cylinder has a radius of 8 meters. We invite readers to visit us daily, explore topics of interest, and gain new perspectives along the way. The circumference of the Earth depends on how it is measured. What is the mass of this planet in terms of Earth's mass? The radius R of a nucleus of mass number A can be estimated by the formula R = (1.3 1015)A 1/3 m. The earth rotates once every 23 hours, 56 minutes and 4.09053 seconds, called the sidereal period, and its circumference is roughly 40,075 kilometers. NASA Telescope Takes 12-Year Time-Lapse Movie of Entire Sky. By clicking Accept, you consent to the use of ALL the cookies. (The notation is defined such that it can be easily generalized for other planets; e.g., Strictly speaking, spheres are the only solids to have radii, but broader uses of the term radius are common in many fields, including those dealing with models of Earth. Earth Radius by Latitude Calculator Calculates radius and diameter of the Earth for a given latitude. If we were to plot this it would show (setting, G = M = m = R = 1, and including force direction): A simple spring oscillator To understand what this means we'll look at a simple spring oscillator. r = 39350/ 6.28 = 6267 kilometer. What is the radius of Earth in gravitation? Let the mass of the earth be M and radius of the earth be R, The distance of the body from the center of the earth will also be equal to the radius R of the earth. The following radii are derived from the World Geodetic System 1984 (WGS-84) reference ellipsoid. and 1999. What does EARTH RADIUS mean? The total mass of all the asteroids combined is less than that of Earth's Moon. Earth's volume, or that of the reference ellipsoid, is V = 4/3a2b. {\displaystyle K} The bulge have been decreasing, consider 1998 the bulge has elevated, possibly because of redistribution of sea mass via currents. What is the radius of the parallel of latitude? 2019 11:40, yfnal3x. By knowing the Equatorial diameter or the polar diameter of the Earth, the circumference can be found. A model of a helicopter rotor has four blades, each of length 3.4 mm from the central shaft to the blade tip. Q4. are tangents to the surface. A consequence is that a distance to the true horizon at the equator is slightly shorter in the northsouth direction than in the eastwest direction. Most experts think planet Earth can support about 10 billion people, and that when our population reaches that number, it will start to decline. R = 6371 km is the mean Earth radius.. [6] It is an idealized surface, and the Earth measurements used to calculate it have an uncertainty of 2m in both the equatorial and polar dimensions. The size of a frictional force is given by F, start subscript, f, end subscript, is less than or equal to, mu, R,FfR where R is the magnitude of the normal reaction force between the two surfaces and is the coefficient of friction between the two surfaces. In this state, it would have approximately the same mass as it has now, but its radius would be equal to the radius of the Earth. ( Image credit: Ayhan Altun) There are nearly 8 billion people (opens in new tab) living on Earth today, but our planet wasnt always so crowded. , For Earth, the volumetric radius equals 6,371.0008km (3,958.7564mi). According to data taken by 183 high-school classes participating in a World Year of Physics project, Measure the Earth with Shadows, the radius of Earth is 6563 km, compared to the accepted value for the mean radius of 6371 km. Use a scientific calculator. Lunar night time is also about two weeks long, during which the moon's temperature plummets to -208 degrees F (-130 C, 140 K) according to NASA. \text{Circumference} = 39,350 \text{\ kilometers}. Acceleration due to gravity is a vector, which means it has both a magnitudeand a direction. 2 . R Our descriptions of Earths surface must be simpler than reality in order to be tractable. In the third century B.C., Eratosthenes was able to mathematically calculate the earths diameter by comparing differences in the angle of the suns rays at two separate geographic points. Likewise for surface area, either based on a map projection or a geodesic polygon. So if you measure at 11:00am in New York, they should measure at 9:00am in Colorado because of the time difference. While carbon dioxide gas is invisible, the very cold gas , Turbines produce noise and alter visual aesthetics. Length in km of 1 of latitude = always 111.32 km Length in km of 1 of longitude = 40075 km * cos ( latitude ) / 360 Share Follow edited Jul 21, 2022 at 14:03 answered Sep 16, 2016 at 21:29 Using the following data: the volume of a sphere = (4/3) (pi)R 3 Radius of the earth= 6.3106 m. Mass of earth= 5.9742 10 24 kilograms. 0008km (3,958. Where K is the Gaussian curvature, Chapter P, Problem 13E is solved. r Note that this arc is along a great circle. Does Bohrs model explain radius of an orbit? These values correspond to the zero Earth tide convention. Do NOT follow this link or you will be banned from the site! Similarly very small numbers are written using negative exponents, e. The very first printed mention of Earths size made an appearance around 350BC, when Aristotle reported in the book Around the Heavens(18) that mathematicians had suspected the circumference of the world to become 400,000 stadia. The radius of Earth at the equator is 3,963 miles (6,378 kilometers), according to NASA's Goddard Space Flight Center in Greenbelt, Maryland. Ans. It is the only planet in our solar system that sustains life and it is the planet that we can call our own. This is the radius that Eratosthenes measured in his arc measurement. It is a common misconception that Terra is the internationally-recognized scientific name of the planet, but in reality Earth does not have an official international name. a) The diameter of the earth is approximately 1.276 1 0 7 1.276 \times 10^7 1.276107 m in scientific notation. For a perfect sphere without any mountains, the distance d from a transmitting antenna to the horizon or the line of sight, or radio horizon, can be calculated from the Pythagorean theorem (see the picture above):. Eratosthenes was born around 276 B.C., which is now Shahhat, Libya. Earth radius is the distance from Earth's center to its surface, about 6,371 km (3,959 mi). You have to use the distance from the center of the Earth, not the distance above Earth's surface, as the radius. Analytical cookies are used to understand how visitors interact with the website. For Earth, the arithmetic mean radius is 6,371.0088km (3,958.7613mi). r As the parallels run east and west, places having the same latitude will be due east or due west of each other. Analytical cookies are used to understand how visitors interact with the website. The geoid height can change abruptly due to earthquakes (such as the Sumatra-Andaman earthquake) or reduction in ice masses (such as Greenland).[5]. How do you find the radius of the Earth using trigonometry? The IUGG denotes the authalic radius as R2. ( Drive one of the meter sticks into the ground in your location in a sunny spot. A partial surface of an ellipsoid gets fitted to the region, in which case the center and orientation of the ellipsoid generally do not coincide with the earth's center of mass or axis of rotation. Because these measurements are not done with more sensitive equipment, the radius calculation will be only approximate. r The circumference of the Earth can be calculated using the formula, Circumference = 2 R or D, where R is the radius of Earth and D is the diameter. 2 Using the parameters from WGS84 ellipsoid of revolution, a = 6,378.137 km and b = 6356.7523142km, V = 1.083211012km3 (2.59881011cumi).[17]. {\displaystyle r} Required fields are marked *. This video will show you how Eratosthenes calculated the circumference and radius of the Earth in 240 BC!! 149597870700 meters nearly This is 10-sd (significant digits) approximation. Make sure both sticks are perpendicular to the earth and that the same length of stick protrudes from the ground. = Learn what is circumference of a sphere, how to calculate the circumference of the Earth with the help of solved examples. An arc of 1 radian = the radial distance of the the latitude circle, from. Given local and transient influences on surface height, the values defined below are based on a "general purpose" model, refined as globally precisely as possible within 5m (16ft) of reference ellipsoid height, and to within 100m (330ft) of mean sea level (neglecting geoid height).