what is the radius of the earth in meters

= Examples collapse all Earth Radius in Meters View the mean radius of the Earth using the default units, meters. The first published reference to the Earth's size appeared around 350BC, when Aristotle reported in his book On the Heavens[19] that mathematicians had guessed the circumference of the Earth to be 400,000 stadia. He observed lunar eclipses and noticed that only a round sphere could imply a circular shadow. , Answer: Starter The radius of the moon is 1,737,000 meters. Chapter P, Problem 13E is solved. Regardless of the model, any radius falls between the polar minimum of about 6,357km and the equatorial maximum of about 6,378km (3,950 to 3,963mi). is the unit normal to the surface at 0 The dashed line designates the radius to one point on the surface. 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. Thus the curvature found this way is smaller than the curvature of a circle of constant latitude, except at the equator. So, for him the following relationship between objects will apply: 7.2 / 360 = 787 / x. Surface Gravity Metric: 9.80665 m/s 2 English: 32.041 ft/s 2 Escape Velocity Metric: 40,284 km/h English: 25,031 mph Scientific Notation: 1.119 x 10 4 m/s Sidereal Rotation Period 0.99726968 Earth Days 23.934 Hours Surface Temperature Metric: -88/58 (min/max) C English: -126/136 (min/max) F Scientific Notation: 185/331 (min/max) K Compute the radius of the Earth using the formula C (circumference) = 2 x pi x r (radius). The geoid height can change abruptly due to earthquakes (such as the Sumatra-Andaman earthquake) or reduction in ice masses (such as Greenland).[5]. nasa.gov. It is known that the equatorial radius of the earth is R=6371km R = 6371 k m so, convert the unit of radius using the conversion factor. Do NOT follow this link or you will be banned from the site! Oceanic crust is denser and thinner and mainly composed of basalt. What is the radius of the sun in meters? - Answers Another global radius is the Earth's rectifying radius, giving a sphere with circumference equal to the perimeter of the ellipse described by any polar cross section of the ellipsoid. example R = earthRadius (lengthUnit) returns the mean radius of the Earth using the length unit specified by lengthUnit. The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. Necessary cookies are absolutely essential for the website to function properly. Mean radius of planet Earth - MATLAB earthRadius - MathWorks 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. h is the transmitting antenna height above the ground,. Tack one end of a piece of string to the top of the stick. How to convert latitude or longitude to meters? - Stack Overflow The majority of the data posted was remarkably good, stated Jennifer Fischer, the APS project leader. How do you use the Pythagorean Theorem to find the radius of the earth? 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. 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 . , and because Eastwest directions can be misleading. 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. Because of the Earths rapid rotation, it stretches out the planet; this results in the South pole and North pole actually being slight closer than locations opposite on the equator because the shape of the Earth is not a spheroid (not a perfect sphere). Example 2. The cookie is used to store the user consent for the cookies in the category "Analytics". T The winners are: Princetons Nima Arkani-Hamed, Juan Maldacena, Nathan Seiberg and Edward Witten. Step 2 of 5. [d] It is also common to refer to any mean radius of a spherical model as "the radius of the earth". Online calculator: Earth Radius by Latitude (WGS 84) - PLANETCALC [7] Additional discrepancies caused by topographical variation at specific locations can be significant. This value is between 6,378 km, particularly around the equator and about 6,357 km at the poles. The cookie is used to store the user consent for the cookies in the category "Performance". [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. Note that this arc is along a great circle. So if you measure at 11:00am in New York, they should measure at 9:00am in Colorado because of the time difference. 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. At room temperature, it will go from a solid to a gas directly. 6,371,000 metersThe value, symbolized rearth, is equal to approximately 6,371,000 meters (6.371 x 106 m). {\displaystyle w^{2}=\lambda ,}. The mathematical expressions above apply over the surface of the ellipsoid. And we end up with 12.6 meters per second , Firearm muzzle velocities range from approximately 120 m/s (390 ft/s) to 370 m/s (1,200 ft/s) in black powder muskets, to more than 1,200 m/s (3,900 ft/s) in modern rifles with high-velocity cartridges such as the , Summary. Earth, the third planet from the sun, is one of the most unique celestial bodies in our solar system. 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). 752 km (3949. The planet's rotation causes it to bulge at the equator. R = earthRadius returns the scalar value 6,371,000, the mean radius of the Earth in meters. [9] 1 Hence, the Earth deviates from a perfect sphere by only a third of a percent, which supports the spherical model in most contexts and justifies the term "radius of the Earth". So, radius of nth orbit is rn=rn2, as Z=1 for H atom. A) 4.5 x 10-7 B) 4.5 x 107 C) 45 x 10-6 D) 45 x 106 T he circumference of the Earth (around the equator) is approximately 24,887 miles. A globally-average value is usually considered to be 6,371 kilometres (3,959mi) with a 0.3% variability (10 km) for the following reasons. As such, they are topographical geocentric distances, Rt, which depends not only on latitude. 4.23 x 10 7 m - 6.37 x 10 6 m . 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):. It has an average density of 5.5 g/cm3. But opting out of some of these cookies may affect your browsing experience. Karren Doll Tolliver holds a Bachelor of English from Mississippi University for Women and a CELTA teaching certificate from Akcent Language School in Prague. The one exception: The flattening in the original definition of WGS84 was a calculated value, based on the Earths second dynamic form factor as determined from satellite orbits ($\bar C_{2,0}$ in WGS84, $J_2$ in GRS80). Make sure both sticks are perpendicular to the Earth and that the same length of stick protrudes from the ground. Using the parameters from WGS84 ellipsoid of revolution, a = 6,378.137 km and b = 6,356.7523142km, V = 1.083211012km3 (2.59881011cumi). The circumference of the Earth is the length or distance measured around it. The equatorial radius is most commonly used to calculate the volume of Earth, so as not to leave out any territory. These cookies will be stored in your browser only with your consent. This video explains how humans managed to measure the circumference of the earth long long ago using simple math, reasoning and assumptions. Drive one of the meter sticks into the ground in your location in a sunny spot. By knowing the Equatorial diameter or the polar diameter of the Earth, the circumference can be found. When we rearrange the equation and plug all the numbers in, we find that the mass of the Earth is 5.96 1024 kg. This cookie is set by GDPR Cookie Consent plugin. [13], Earth's authalic radius (meaning "equal area") is the radius of a hypothetical perfect sphere that has the same surface area as the reference ellipsoid. N The distance between Syene and Alexandria is 787 kilometers. Example 2. 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. The geoid height variation is under 110m (360ft) on Earth. Here x is the circumference of the earth. 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). How do you find the radius of the Earth using trigonometry? As satellite remote sensing and especially the Global Positioning System gained importance, true global models were developed which, while not as accurate for regional work, best approximate the Earth as a whole. The radius of the earth's orbit is 45,000,000 meters. What is the How do you find the radius in circular motion? Its mean density is 1410 kg/m 3 or 0.255 times the mean density of Earth. Escape velocity = = 22.4 km/sec. The planet's rotation causes it to bulge at the equator. Your partner should measure at the same time, regardless of time difference. The radius of a parallel of latitude is given by At what distance above the surface of earth, the gravitational force will be reduced by 10%, if the radius of earth is 6370 Km. Earth radius - Wikipedia As an example, we will use Eratosthenes situation. Solved: The Size of the Earth The radius of the Earth is appro - Chegg Have Bugged an area Rock to pay attention In on Earthlings? The Earth's mean radius of curvature at latitude is:[12]:97. This is the outside layer of the earth and is made of solid rock, mostly basalt and granite. x = 3 Using the Gauss-Bonnet theorem, this gives, Another spherical model is defined by the Earth's volumetric radius, which is the radius of a sphere of volume equal to the ellipsoid. E The Earth's azimuthal radius of curvature, along an Earth normal section at an azimuth (measured clockwise from north) and at latitude , is derived from Euler's curvature formula as follows:[12]:97. 149597870700 meters nearly This is 10-sd (significant digits) approximation. for an oblate spheroid, the curvatures are. 371 106 m), the bottom unit of length within the Worldwide System of Units (SI). r = m v 2 F c . How do you compute the earth's radius at a given geodetic latitude? Solve the following problems. If mass of a planet is eight times the 903 mi) at the poles and 6371. Radius of the earth in meters - AssignmentGeek , over the surface of the ellipsoid. These cookies track visitors across websites and collect information to provide customized ads. This topographical average is 6,371.230km (3,958.899mi) with uncertainty of 10m (33ft).[16]. det [4], The variation in density and crustal thickness causes gravity to vary across the surface and in time, so that the mean sea level differs from the ellipsoid. Solution for the radious of earth is 6378.1 km, which is 2981.1 km greater than the radius of mars. It does not store any personal data. This length is also used as a unit of distance, especially in astronomy and geology, where it is usually denoted by R. {\displaystyle w^{1}=\varphi } det Mathematically, Earth is a spheroid. (b) Repeat part (a) with the sun in place of the earth. . Eratosthenes was born around 276 B.C., which is now Shahhat, Libya. Answered: A space traveler weighs 640 N on Earth. | bartleby 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. Compute the radius of the Earth using the formula C (circumference) = 2 x pi x r (radius). What is the radius of Earth in meters? find the radius of mars. Part 4: Computation . 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. r Have your partner do the same in her location at the exact same time. What is the radius of the parallel of latitude? Analytical cookies are used to understand how visitors interact with the website. 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. In general, this points to an important conclusion about nature itself. The meridional mean is well approximated by the semicubic mean of the two axes,[citation needed]. In Eratosthenes case, the distance was 787 kilometers, so for him, the following relation applied: where x = the circumference of the Earth in kilometers. Where K is the Gaussian curvature, Andrew Blum gives some tips that could students in the high-school class in Clinton, Mississippi because they focus on the Eratosthenes project. Let us calculate area of earth using this formula area=4x22/76370= 5.110 4. J For Earth, the arithmetic mean radius is 6,371.0088km (3,958.7613mi). By knowing the Equatorial diameter or the polar diameter of the Earth, the circumference can be found. also corresponds to the radius of (global) mean curvature, obtained by averaging the Gaussian curvature, Acceleration due to gravity - Simple English Wikipedia, the free A cylinder has a radius of 8 meters. 2 You can do this, too, by using his method. [ A body on the surface of a planet with the same radius as Earth's weighs 10 times more than it does on Earth. 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). Of course, no one is claiming the size of Earth has actually changed. When it's closest, the Moon is 225,623 miles away. nasa.gov. Geometrically, the second fundamental form gives the distance from Solar System Homework #1 Answers - austincc.edu Additionally, the bulge at the equator shows slow variations. 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. Also, explore tools to convert Earths equatorial radius or meter to other length units or learn more about length conversions. => When indoor location is available, the accuracy range can be as small as 5 meters. 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. We use cookies on our website to give you the most relevant experience by remembering your preferences and repeat visits. Hence, we create models to approximate characteristics of Earths surface, generally relying on the simplest model that suits the need. where. Geodetic ellipsoids are better suited to regional idiosyncrasies of the geoid. close. For the WGS84 ellipsoid, that's respectively: Earth's circumference equals the perimeter length. ), In geophysics, the International Union of Geodesy and Geophysics (IUGG) defines the Earth's arithmetic mean radius (denoted R1) to be[2], The factor of two accounts for the biaxial symmetry in Earth's spheroid, a specialization of triaxial ellipsoid. E How far (in meter) does it travel in the first 3 seconds? [13], The authalic radius The mass of the sun is $329,320$ times that of the earth and | Quizlet Q4. Most experts think planet Earth can support about 10 billion people, and that when our population reaches that number, it will start to decline. [Mass of the earth is 6 x 1024 kg and radius of the earth is 6.4 x 106 m]. r Thus, the surface of the earth at the equator moves at a speed of 460 meters per secondor roughly 1,000 miles per hour. = What is the Radius and Diameter of a Circle? Also a photographer, she records adventures by camera, combining photos with journals in her blogs. R 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. f Earth's volume is estimated at 1 trillion cubic kilometers. 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? [2], For Earth, the volumetric radius equals 6,371.0008km (3,958.7564mi).[13]. The various radii derived here use the notation and dimensions noted above for the Earth as derived from the WGS-84 ellipsoid;[6] namely. 1o = 180 radian. Earth: By the Numbers - NASA What is the permiter of the Earth? That's between 28 and 29 Earths. [21] The first known scientific measurement and calculation of the circumference of the Earth was performed by Eratosthenes in about 240BC. \text{Circumference} = 39,350 \text{\ kilometers}. Earth Radius by Latitude Calculator - Rechneronline - Ntzliche Rechner The Earth's polar radius of curvature (either meridional or prime-vertical) is: The principal curvatures are the roots of Equation (125) in:[11]. Our goal is to make science relevant and fun for everyone. Because these measurements are not done with more sensitive equipment, the radius calculation will be only approximate. Acceleration due to gravity is a vector, which means it has both a magnitudeand a direction. About Earth radiusThe Earth radius, or even the radius of the world, may be the distance from the middle of our planet towards the surface. He was the first one to use the word geography and he also had a small-scale notion of the planet that helped him to determine the circumference of the earth. This calculated value became a defining value in 1993. Exponential or Scientific Notation: It is easier to write very large numbers such as 100,000,000 as 10 8 (1 followed by 8 0s). The radius of a circle is the straight-line distance from the very center of the circle to any point on the circle. 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. Mass of the Earth - The Physics Factbook - hypertext-book We also use third-party cookies that help us analyze and understand how you use this website. e What is the real radius of the earth? Likewise for surface area, either based on a map projection or a geodesic polygon. Derived quantities: diameter, circumference, arc-length, area, volume, There is no single center to the geoid; it varies according to local. | The value of standard gravity corresponds to the gravity on Earth at a radius of 6,375.4 kilometres (3,961.5 mi). N Explanation: The Earth's radius (r) is 6371 km or 3959 miles, based on numbers from Wikipedia, which gives a circumference (c) of c = 2 * * r = 40 030 km We wish to find the height (h) which is the drop in curvature over the distance (d) Using the circumference we find that 1 kilometer has the angle 360 / 40 030 km = 0.009.