This table summarizes the accepted values of the Earth's radius. Initially, the idea of a reference ellipsoid was an ellipsoid that best approximated mean ocean level. This measurement also introduces another fun source of error that actually comes from the motion of Earth and other similar planetary bodies in the solar system. A: . View a sample solution. (b) Repeat part (a) with the sun in place of the earth. Wittenberg is a nationally ranked liberal arts institution with a particular strength in the sciences. r = m v 2 F c . How do you find the radius in circular motion? a) The radius of the earth is 4000 miles. These values correspond to the zero Earth tide convention. K Venus is included with a thick, quickly spinning atmosphere, developing a scorched world with temperatures hot enough to melt lead along with a surface pressure 90 occasions those of Earth. Earth's polar radius is 3950 miles (Diameter = 7900 miles). [7] Additional discrepancies caused by topographical variation at specific locations can be significant. Mass of planet M = 8 x mass of earth = 8 x 6 x 10 24 kg. By clicking Accept, you consent to the use of ALL the cookies. The space station is 356 feet (109 meters) end-to-end, one yard shy of the full length of an American football field including the end . for an oblate spheroid, the curvatures are. R = earthRadius returns the scalar value 6,371,000, the mean radius of the Earth in meters. Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. One reason that our program is so strong is that our . [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. Write it in scientific notation. Definition of radius 1 : a line segment extending from the center of a circle or sphere to the circumference or bounding surface. {\displaystyle w^{2}=\lambda ,}. This is roughly 6,371 kilometers (km) or 3,960 statute miles. , All Right Reserved. But opting out of some of these cookies may affect your browsing experience. [1]:3 The nominal polar Earth radius is defined as The earth is made up of three different layers: the crust, the mantle and the core. For the Earth, the authalic radius is 6,371.0072km (3,958.7603mi). Circumference of Earth is the length or the distance around the Earth. [24] Claudius Ptolemy around 150AD gave empirical evidence supporting a spherical Earth,[25] but he accepted the lesser value attributed to Posidonius. Both of these values are very close to the accepted modern values for the Earths circumference and radius, 40,070 km and 6378 km respectively, which have since been measured by orbiting spacecraft. The planet's rotation causes it to bulge at the equator. Because these measurements are not done with more sensitive equipment, the radius calculation will be only approximate. Analytical cookies are used to understand how visitors interact with the website. However, for purposes of uniformity and use in geophysics and astronomy, the nominal earth radius is used, which is about 6, 371 km. This was due to the coincidence that Mars and Earth lined up with the Sun when the Earth was close to its farthest point from . It is 6356. What does EARTH RADIUS mean? 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. 752 km (3949. 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. Earth Radius by Latitude Calculator Calculates radius and diameter of the Earth for a given latitude. Surveyors today use a variety of instruments and calculations to determine the size of the Earth and collect other relevant data. Technology similar to the instruments that are used to survey Earth can also be found all across the solar system. R=6370 3. Eratosthenes methods result in a formula that would look like this: 39,350 = 2 x 3.14 x r, or 6,267 kilometers. also corresponds to the radius of (global) mean curvature, obtained by averaging the Gaussian curvature, 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. 2 A meter is a meter, no matter what your zoom level is. = The cases below considers Earth's topography, above or below a reference ellipsoid. How do you find the radius of a planet in physics? This answer is: The bulge had been decreasing, but since 1998 the bulge has increased, possibly due to redistribution of ocean mass via currents. Earth radius at sea level is 6378.137 km (3963.191 mi) at the equator. The planet bulges at the equator as a result of its rotation. Its surface gravity is 274 m/s 2 or 28.0 times that of the Earth. The geoid height can change abruptly due to earthquakes (such as the Sumatra-Andaman earthquake) or reduction in ice masses (such as Greenland).[5]. 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 example R = earthRadius (lengthUnit) returns the mean radius of the Earth using the length unit specified by lengthUnit. Nowadays there are better ellipsoids when it comes to supplying a much better fit to mean ocean level compared to WGS84 ellipsoid. z Compute the radius of the Earth using the formula C (circumference) = 2 x pi x r (radius). 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. | The radius of a circle is the straight-line distance from the very center of the circle to any point on the circle. R Physics, 22.06.2022 11:40, yfnal3x. Its the only planet with life. The radius of Earth is 6370000 m. Express this measurement in km in scientific notation with the correct number of significant digits. The dashed line designates the radius to one point on the surface. {\displaystyle r} Measured around the Equator, it is 40,075.017 km (24,901.461 mi). What is the radius of Earth in meters? e The first person to determine the size of Earth was Eratosthenes of Cyrene, who produced a surprisingly good measurement using a simple scheme that combined geometrical calculations with physical observations. Derived quantities: diameter, circumference, arc-length, area, volume, There is no single center to the geoid; it varies according to local. 1 Required fields are marked *. , Does Wittenberg have a strong Pre-Health professions program? There are two types of crust; oceanic and continental. The oblateness constant q is given by, where is the angular frequency, G is the gravitational constant, and M is the mass of the planet. What is the formula to find radius of Earth? This difference is the geoid height, positive above or outside the ellipsoid, negative below or inside. How cold is it on moon? (a) To what radius (in meters) would the earth have to be compressed in order for it to become a black holethe escape velocity from its surface equal to the velocity c = 3 \times 10 ^ { 8 } \mathrm { m } / \mathrm { s } c = 3108m/s of light? Refer to the WGS-84 ellipsoid if a more precise value for its polar radius is needed. The cookie is used to store the user consent for the cookies in the category "Performance". For the WGS84 ellipsoid, that's respectively: Earth's circumference equals the perimeter length. We also use third-party cookies that help us analyze and understand how you use this website. You can do this, too, by using his method. 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.) 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. where e2 = a2 b2/a2 and A is the surface area of the spheroid. which differs from the exact result by less than 1m (4105in); the mean of the two axes. {\displaystyle R_{E}} The winners are: Princetons Nima Arkani-Hamed, Juan Maldacena, Nathan Seiberg and Edward Witten. The cookie is used to store the user consent for the cookies in the category "Analytics". 2a : the bone on the thumb side of the human forearm also : a corresponding part of vertebrates above fishes. First week only $6.99! They are vertices of the ellipse and also coincide with minimum and maximum radius of curvature. 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. Asked By: Lena Frontelo | Last Updated: 18th May, 2020, Earth is the third planet from the sun. What is the radius of Earth in exponential form? After many, many years, you will have some intuition for the physics you studied. (8,849 meters), but it is not the highest point on Earth that is, the place most distant from the . 6.371 10 6 m . What is the Radius and Diameter of a Circle? Earth's diameter is simply twice Earth's radius; for example, equatorial diameter (2a) and polar diameter (2b). , For Earth, the volumetric radius equals 6,371. The acceleration due to gravity at the surface of Earthis represented by the letter g. New Arrivals Expand Space Stations Crew to 6. Earth radius is the distance from Earth's center to its surface, about 6,371 km (3,959 mi). Hence 1km=10001000m=10m 6. The cookies is used to store the user consent for the cookies in the category "Necessary". He also shares personal stories and insights from his own journey as a scientist and researcher. N Today we know our planet's circumference is roughly 40,000 kilometers (24,850 miles). The International Union of Geodesy and Geophysics (IUGG) provides three reference values: the mean radius (R1) of three radii measured at two equator points and a pole; the authalic radius, which is the radius of a sphere with the same surface area (R2); and the volumetric radius, which is the radius of a sphere having the same volume as the ellipsoid (R3). The first, titled Arturo Xuncax, is set in an Indian village in Guatemala. Do NOT follow this link or you will be banned from the site! [22] For both Aristotle and Eratosthenes, uncertainty in the accuracy of their estimates is due to modern uncertainty over which stadion length they meant. Around 100BC, Posidonius of Apamea recomputed Earth's radius, and found it to be close to that by Eratosthenes,[23] but later Strabo incorrectly attributed him a value about 3/4 of the actual size. {\displaystyle {\frac {\partial r}{\partial \varphi }}} You have to find the circumference. It was there that he first had the idea to create a resource for physics enthusiasts of all levels to learn about and discuss the latest developments in the field. However, other factors such as the rotation of the Earth also contribute to the net acceleration. Since pi is an infinite number, the calculations in Step 6 will be more accurate. He noticed that the difference in the angle of a shadow in his location at Syene, which is present-day Aswan in Egypt, and that of a shadow in Alexandria was about 7.2 degrees. When identifying the position of an observable location, the use of more precise values for WGS-84 radii may not yield a corresponding improvement in accuracy. A sphere being a gross approximation of the spheroid, which itself is an approximation of the geoid, units are given here in kilometers rather than the millimeter resolution appropriate for geodesy. In simple words, radius refers to that line, which originates from any point of the circle and touches the centre point the circle. Eratosthenes was born around 276 B.C., which is now Shahhat, Libya. All other parallels of latitude are small circles, each having a radius smaller than that of the earth, i.e. stands for the radius of the Earth. Step 3 of 5. Thus, the radius of the earth in meters in scientific notation is 6.371106m. The Earth. 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 , An international crew of seven people live and work while traveling at a speed of five miles per second, orbiting Earth about every 90 minutes. Estimates of the accuracy of Eratosthenes's measurement range from 0.5% to 17%. 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 Its SIunit is m/s2. Venus is covered by a thick, rapidly spinning atmosphere, creating a scorched world with temperatures hot enough to melt lead and a surface pressure 90 times that of Earth. {\displaystyle e} How do you find the radius of the Earth using trigonometry? Additionally, the bulge at the equator shows slow variations. The WGS84 reference ellipsoid is now just that, a reference ellipsoid (that is, its the ellipsoid used as a reference by GPS and related systems). 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. {\displaystyle {\frac {\partial r}{\partial \lambda }}} Have Bugged an area Rock to pay attention In on Earthlings? E There are two principal radii of curvature: along the meridional and prime-vertical normal sections. 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. Also see the Table of Physical Units and Constants. You also have the option to opt-out of these cookies. These cookies will be stored in your browser only with your consent. At the poles, = 90o and the length = 110.95 km, nearly. p r . w Q4. In 1993 the WGS84 governing committee voted, with one exception, to retain the 1984 defining values, despite improvements to those defining values. In physics, it is established that the acceleration due togravity, g (in meters/sec 2), at a height h meters abovesea level is given by g(h)= 3.99 *10 14 (6.374* 10 6 + h) 2 where 6.374 * 10 6 isthe radius of the Earth in meters. 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):. . The radius is more like 6,371 kilometers at the north and south poles. in the second fundamental form for a surface (Equation (123) in[11]): e, f, and g are elements of the shape tensor: n The circumference of the world may be the distance measured around it. r = 39350/ 6.28 = 6267 kilometer. For this calculation, the longitude isn't needed. The equation for Keplers Third Law is P = a, so the period of a planets orbit (P) squared is equal to the size semi-major axis of the orbit (a) cubed when it is expressed in astronomical units. Measurement of Earths circumference has been important to navigation since ancient times. The Earth's Gaussian radius of curvature at latitude is:[12]. nasa.gov. The cookie is used to store the user consent for the cookies in the category "Analytics". Have your partner do the same in her location. This video explains how humans managed to measure the circumference of the earth long long ago using simple math, reasoning and assumptions. Example 2. for an oblate spheroid, the curvatures are. Sometimes more are aboard the station during a crew handover. R = 6371 km is the mean Earth radius.. The radius of the earth's orbit is 45,000,000 meters. Start your trial now! r Rotation of a planet causes it to approximate an oblate ellipsoid/spheroid with a bulge at the equator and flattening at the North and South Poles, so that the equatorial radius a is larger than the polar radius b by approximately aq. Now we know 1km=1000m 5. You can do this, too, by using his method. Ocean Worlds Resources. Geometrically, the second fundamental form gives the distance from where. Hence, we create models to approximate characteristics of Earth's surface, generally relying on the simplest model that suits the need. {\displaystyle K} , over the surface of the ellipsoid. = Earths radius is usually given as 6378137 meters (equatorial radius), its flattening is defined as 1/298.257223 (WGS84), and thus its polar radius is calculated as 6356752 meters.However, the av. You have to use the distance from the center of the Earth, not the distance above Earth's surface, as the radius. 2013-09-16 00:47:38. Last edited on 10 February 2023, at 21:43, International Union of Geodesy and Geophysics, IAU 2006 General Assembly: Result of the IAU Resolution votes, Satellites Reveal A Mystery Of Large Change In Earth's Gravity Field, NASA's Grace Finds Greenland Melting Faster, 'Sees' Sumatra Quake, "Discover-TheWorld.com Guam POINTS OF INTEREST Don't Miss Mariana Trench", "Mean radius, mass, and inertia for reference Earth models", https://en.wikipedia.org/w/index.php?title=Earth_radius&oldid=1138658294, WGS-84 ellipsoid, polar radius of curvature (, WGS-84 ellipsoid, Mean radius of semi-axes (, WGS-84 ellipsoid, Radius of Sphere of Equal Area (, WGS-84 ellipsoid, Radius of Sphere of Equal Volume (, meridional radius of curvature at the equator, This page was last edited on 10 February 2023, at 21:43. 1999. In scientific notation, the radius of the earth in meters is equal to 6.37106 meters or approximately 6.4106 meters, and 6378100 or approximately 6370000 in standard form. The polar circumference equals Cp=4mp, four times the quarter meridian mp=aE(e), where the polar radius b enters via the eccentricity, e=(1b2/a2)0.5; see Ellipse#Circumference for details. r The magnitude of the gravitational force between earth and an object is given by the formula. {\displaystyle R_{2}} Video advice: How We Calculated the Radius of Earth. For information on the Earth, see the Earth Fact Sheet. Analytical cookies are used to understand how visitors interact with the website. Karren Doll Tolliver holds a Bachelor of English from Mississippi University for Women and a CELTA teaching certificate from Akcent Language School in Prague. How far is the center of the Earth in KM? Our goal is to make science relevant and fun for everyone. So, radius of nth orbit is rn=rn2, as Z=1 for H atom. [2], For Earth, the volumetric radius equals 6,371.0008km (3,958.7564mi).[13]. = Record the distance between your location and your partners location. r {\displaystyle p=N\cos(\varphi )} . Hence, we create models to approximate characteristics of Earths surface, generally relying on the simplest model that suits the need. Copyright 2022 - Science-Atlas.com. Earth's surface area is an estimated 510 km2, and about 29% of the area is land while the other 71% consists of water. Eratosthenes, the ancient Greek scholar is called the father of geography. Most experts think planet Earth can support about 10 billion people, and that when our population reaches that number, it will start to decline. This cookie is set by GDPR Cookie Consent plugin. An arc of 1 radian = the radial distance of the the latitude circle, from. [f], This Earth's prime-vertical radius of curvature, also called the Earth's transverse radius of curvature, is defined perpendicular (orthogonal) to M at geodetic latitude is:[g], N can also be interpreted geometrically as the normal distance from the ellipsoid surface to the polar axis. Well, the Moon is not always the same distance away from Earth. The typical Earth radius (RE) can also be comparable to about 6,371 kilometers (km) (an SI unit of length), or 3,440 maritime miles (nmi) (a maritime unit of length), or roughly 3,959 miles (mi) or 20,902,231 ft (foot), that are US customary / Imperial units of length. Do NOT follow this link or you will be banned from the site! 0 The mathematical expressions above apply over the surface of the ellipsoid. less than 6400 km. At what distance above the surface of earth, the gravitational force will be reduced by 10%, if the radius of earth is 6370 Km. After completing his doctoral studies, he decided to start "ScienceOxygen" as a way to share his passion for science with others and to provide an accessible and engaging resource for those interested in learning about the latest scientific discoveries. How to Calculate the Circumference of the Earth? So escape velocity of the planet will be 22.4 km/sec Since the estimate by Eratosthenes, many models have been created. The average radius of the earth is 6.38x106 meters. Measured around the poles, the circumference is 40,007.863 km (24,859.734 mi). This website uses cookies to improve your experience while you navigate through the website. c) Calculate the gravitational potential energy associated with a 4.93-kg object at the Around 1690, Isaac Newton and Christiaan Huygens argued that Earth was closer to an oblate spheroid than to a sphere. b : the third and usually largest vein of an insect's wing. The orbit is not a perfect circle. r Record the distance between your location and your partners location. By 1490, Christopher Colombus believed that traveling 3,000 miles west from the west coast of the Iberian peninsula would let him reach the eastern coasts of Asia. = Earth radius (denoted as R or What is the scientific name for Earth? Your email address will not be published. How do you use the Pythagorean Theorem to find the radius of the earth? In his writing, Alexander covers a wide range of topics, from cutting-edge medical research and technology to environmental science and space exploration. The diameter is the distance from side to side, if you. 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. Aristotle (384-322 BC) was among the first to recognize the fact of our planet being a round sphere. How did early mathematicians determine the radius of the earth? One can only adopt an idealized model. [Mass of the earth is 6 x 1024 kg and radius of the earth is 6.4 x 106 m]. The radius of earth, is the distance from the centre of the Earth to a point on or near its surface, and it ranges from nearly 6,378 km to nearly 6,357 km, dhanyaranjan Published On January 28th, 2022 Table of Contents Radius of Earth in Physics The symbol R? Earth, the third planet from the sun, is one of the most unique celestial bodies in our solar system. Earth, as we know now, is an oblate spheroid, as shown in the above figure. The red dot at the lower left corner is its center. 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". This value is between 6,378 km, particularly around the equator and about 6,357 km at the poles. = 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 magnitude of the gravitational force between earth and an object is given by the formula. It is with the values I gave you. We know that the acceleration due to gravity is equal to 9.8 m/s2, the Gravitational constant (G) is 6.673 1011 Nm2/kg2, the radius of the Earth is 6.37 106 m, and mass cancels out. Solution for the radious of earth is 6378.1 km, which is 2981.1 km greater than the radius of mars. [2] All three values are about 6,371 kilometres (3,959mi). (clarification needed). and The radius of the swimming pool water atom is roughly meters. So escape velocity = . r . For Eratosthenes, the arc was 7.2 degrees. Now we know 2 things- 1. 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. 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. The first and second radii of curvature correspond, respectively, to the Earth's meridional and prime-vertical radii of curvature. b : the third and usually largest vein of an insects wing. What is the radius of Earth in exponential form? Due to the exaggerated eccentricity, it is easy to see that "up" is not parallel to the radius. d Earths rotation, internal density variations, and external tidal forces cause its shape to deviate systematically from a perfect sphere. Reviving Erastosthenes, 2022-year-old experiment using the angle of the sun to measure the radius of the Earth. Out of these, the cookies that are categorized as necessary are stored on your browser as they are essential for the working of basic functionalities of the website. T Q. How did we determine the size of the Earth? What are the formula in calculating the earth? 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. . ) Also a photographer, she records adventures by camera, combining photos with journals in her blogs.