what is the radius of the earth in meters
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). Mathematically, Earth is a spheroid. So if you measure at 11:00am in New York, they should measure at 9:00am in Colorado because of the time difference. Eratosthenes estimated Earth's circumference at about 46,250 kilometers (28,735 miles). 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. , Tack one end of a piece of string to the top of the stick. [clarification needed]. J Make sure both sticks are perpendicular to the Earth and that the same length of stick protrudes from the ground. 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. {\displaystyle K=\kappa _{1}\,\kappa _{2}={\frac {\det \,B}{\det \,A}}} Its the only planet with life. 4.23 x 10 7 m - 6.37 x 10 6 m . In his writing, Alexander covers a wide range of topics, from cutting-edge medical research and technology to environmental science and space exploration. {\displaystyle r+dr} Thus, the surface of the earth at the. Convert the Earth-Sun distance of 93,000,000 miles into. A 3.2.2.2Non-directional 4Global radii 4.1Nominal radius 4.2Arithmetic mean radius 4.3Authalic radius 4.4Volumetric radius 4.5Rectifying radius 5Topographical radii 5.1Topographical extremes 5.2Topographical global mean 6Derived quantities: diameter, circumference, arc-length, area, volume 7Published values 8History 9See also 10Notes 11References {\displaystyle r} Explore Asteroids In Depth Key Science Targets ( 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. 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. Solving for x reveals the circumference to be. nasa.gov. How do you find the radius of a gravitational field? ] {\displaystyle e} Required fields are marked *. 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. = . R = earthRadius returns the scalar value 6,371,000, the mean radius of the Earth in meters. find the radius of mars. [2] All three values are about 6,371 kilometres (3,959mi). 752 km (3949. Earth's rotation, internal density variations, and external tidal forces cause its shape to deviate systematically from a perfect sphere. Escape velocity = = 22.4 km/sec. r {\displaystyle w^{1}=\varphi } In late August of 2003, Mars was at its closest point to Earth in about 60,000 years! Thus, the radius of the earth in meters in scientific notation is 6.371106m. The mathematical expressions above apply over the top of ellipsoid. Karren Doll Tolliver holds a Bachelor of English from Mississippi University for Women and a CELTA teaching certificate from Akcent Language School in Prague. 1 Therefore, the distance you use in the equation is the distance between the two orbiting bodies. The planet's rotation causes it to bulge at the equator. This cookie is set by GDPR Cookie Consent plugin. The equatorial circumference is simply the circle perimeter: Ce=2a, in terms of the equatorial radius, a. Have your partner do the same in her location. {\displaystyle n={\frac {N}{|N|}}} The WGS84 ellipsoid can be used worldwide (such as the ridiculously over-precise flattening value). 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. In Eratosthenes case, the distance was 787 kilometers, so for him, the following relation applied: where x = the circumference of the Earth in kilometers. 001 km (3958. R=6370 3. 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. We also use third-party cookies that help us analyze and understand how you use this website. which differs from the exact result by less than 1m (4105in); the mean of the two axes. Science atlas, our goal is to spark the curiosity that exists in all of us. Skip to main content. Use scientific notation to show the above value of the radius. 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. E The mathematical expressions above apply over the surface of the ellipsoid. Place the loose end of the string at the end of the cast shadow and hold it taut. The Earths circumference is approximately 40,000,000 meters. p You can do this, too, by using his method. Earth's diameter is simply twice Earth's radius; for example, equatorial diameter (2a) and polar diameter (2b). The geoid height can change abruptly due to earthquakes (such as the Sumatra-Andaman earthquake) or reduction in ice masses (such as Greenland).[5]. Learn what is circumference of a sphere, how to calculate the circumference of the Earth with the help of solved examples. The bulge have been decreasing, consider 1998 the bulge has elevated, possibly because of redistribution of sea mass via currents. 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). , For Earth, the volumetric radius equals 6,371.0008km (3,958.7564mi). At the poles, = 90o and the length = 110.95 km, nearly. p Therefore, the Earth radius isn't constant, but it can be calculated for every location. 6,371,000 metersThe value, symbolized rearth, is equal to approximately 6,371,000 meters (6.371 x 106 m). So escape velocity = . 0008km (3,958. 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. Tack one end of a piece of string to the top of the stick. [7] Additional discrepancies caused by topographical variation at specific locations can be significant. What is the Radius of the Earth? His highly influential work, the Almagest,[26] left no doubt among medieval scholars that Earth is spherical, but they were wrong about its size. 191 mi) at the equator. The radius of the earth's orbit is 45,000,000 meters. Earth, the third planet from the sun, is one of the most unique celestial bodies in our solar system. In 200 B.C. At Baltimore, = 39.48o and the length is 111.16 km, nearly. (C = 2r) With this information, Eratosthenes inferred that the Earths radius was 6366 km. The height above sea level of the location is added. How cold is it on moon? {\displaystyle {\mathcal {R}}_{\mathrm {pE} }^{\mathrm {N} }} The formula for the volume of a sphere is V = 4/3 r. The expedition found that Newton's conjecture was correct:[30] the Earth is flattened at the poles due to rotation's centrifugal force. An arc of 1 radian = the radial distance of the the latitude circle, from. Though he did not have instant communications as we do now, he was able to determine the angle of the suns rays in Alexandria at the same time, which was about 7.2 degrees. 1 The winners are: Princetons Nima Arkani-Hamed, Juan Maldacena, Nathan Seiberg and Edward Witten. What is the formula to find radius of Earth? = 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. George Jackson is the founder and lead contributor of Physics Network, a popular blog dedicated to exploring the fascinating world of physics. = Most experts think planet Earth can support about 10 billion people, and that when our population reaches that number, it will start to decline. The value of standard gravity corresponds to the gravity on Earth at a radius of 6,375.4 kilometres (3,961.5 mi). At what distance above the surface of earth, the gravitational force will be reduced by 10%, if the radius of earth is 6370 Km. This equation for acceleration can , Dry ice is the name for carbon dioxide in its solid state. These cookies ensure basic functionalities and security features of the website, anonymously. What physical measurement / elevation is used to define Earths radius? K Subtract the angle measurements to determine the difference in the angle of shadows between the two locations. {\displaystyle {\frac {\partial r}{\partial \lambda }}} In a geocentric ellipsoid, the center of the ellipsoid coincides with some computed center of Earth, and best models the earth as a whole. This cookie is set by GDPR Cookie Consent plugin. , 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. Advertisement cookies are used to provide visitors with relevant ads and marketing campaigns. in the second fundamental form for a surface (Equation (123) in[11]): e, f, and g are elements of the shape tensor: n Added 2022-02-06 15:04:59 subject Physics by rsa072001. But opting out of some of these cookies may affect your browsing experience. Instant free online tool for Earths equatorial radius to meter conversion or vice versa. 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 radius of the Earth, re, is about 6.38 10 6 meters, and the mass of the Earth is 5.98 10 24 kilograms. Thus, the radius of the earth in meters in scientific notation is 6.371106m. Semi-minor axis b = 6356752.3142 meters. [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. The radius of orbit indicates the distance that the satellite is from the center of the earth. Its better to have a reference ellipsoid that is constant over time than it is to have an ever improving best fit ellipsoid. He received his Ph.D. in physics from the University of California, Berkeley, where he conducted research on particle physics and cosmology. Point B, which appears due east from A, will be closer to the equator than A. 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. {\displaystyle {\mathcal {R}}_{\mathrm {eE} }^{\mathrm {N} }} 2 The meridional mean is well approximated by the semicubic mean of the two axes,[citation needed]. Thus, the surface of the earth at the equator moves at a speed of 460 meters per secondor roughly 1,000 miles per hour. Using the curvature of the Earth relative to the parallel light from the sun, we can observe shadows at different locations on the surface of the Earth to find the Earths radius. Measuring the Circumference of the Earth. Obviously, nobody is claiming how big Earth has really altered. Today we know our planet's circumference is roughly 40,000 kilometers (24,850 miles). Likewise for surface area, either based on a map projection or a geodesic polygon. How do you find the radius of a planet in physics? This astronomical observation was confirmed by general observations made at sea. Hence 1km=10001000m=10m 6. 2a : the bone on the thumb side of the human forearm also : a corresponding part of vertebrates above fishes. [2] These cookies ensure basic functionalities and security features of the website, anonymously. Definition of radius 1 : a line segment extending from the center of a circle or sphere to the circumference or bounding surface. 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). Since the estimate by Eratosthenes, many models have been created. What is the radius of Earth in exponential form? r + 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. For Eratosthenes, at midday on the summer solstice where the suns angle was directly overhead, the angle was zero. You also have the option to opt-out of these cookies. det The Earth's Gaussian radius of curvature at latitude is:[12]. [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. What is the scientific name for Earth? 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. Compute the circumference of the Earth using the distance and angle measurements you have. The value for the polar radius in this section has been rounded to the nearest 0.1m, which is expected to be adequate for most uses. The Earth's polar radius of curvature (either meridional or prime-vertical) is: The principal curvatures are the roots of Equation (125) in:[11]. F As the parallels run east and west, places having the same latitude will be due east or due west of each other. r Our Planet radius is really a unit of distance utilized in astronomy and geology. Now we know 1km=1000m 5. 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? r What is the formula of radius of nucleus? Video advice: How We Calculated the Radius of Earth. The radius of a parallel of latitude is given by The value of the radius is completely dependent upon the latitude in the case of an ellipsoid model, and nearly so on the geoid. For example, if you stand at a point on the earth and move around the earth in a straight path, and reach the same point again, then the distance covered by you is the circumference of the earth. T [24] Claudius Ptolemy around 150AD gave empirical evidence supporting a spherical Earth,[25] but he accepted the lesser value attributed to Posidonius. If one point had appeared due east of the other, one finds the approximate curvature in the eastwest direction. This cookie is set by GDPR Cookie Consent plugin. The following radii are derived from the World Geodetic System 1984 (WGS-84) reference ellipsoid. You also have the option to opt-out of these cookies. Q4. Answer (1 of 3): First of all let us consider the shape of the earth to be a sphere. 2013-09-16 00:47:38. {\displaystyle R_{E}} Earths Equatorial Radius to Meter Conversion Table, How to Convert Earths Equatorial Radius to Meter, Convert Earths Equatorial Radius to Other Length Units. = Does Bohrs model explain radius of an orbit? 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. After completing his degree, George worked as a postdoctoral researcher at CERN, the world's largest particle physics laboratory. You need to solve physics problems. Measurement of Earths circumference has been important to navigation since ancient times. 1999. , Does Wittenberg have a strong Pre-Health professions program? Keplers Third law can be used to determine the orbital radius of the planet if the mass of the orbiting star is known (R3=T2Mstar/Msun, the radius is in AU and the period is in earth years). This video explains how humans managed to measure the circumference of the earth long long ago using simple math, reasoning and assumptions. m. [ Its "up" direction there is shown with a black segment: it is, by definition, perpendicular to the ellipse at that point. Mass (10 24 kg) 5.9722 Volume (10 10 km 3) 108.321 Equatorial radius (km) 6378.137 Polar radius (km) 6356.752 Volumetric mean radius (km) 6371.000 Core radius (km) 3485 Ellipticity (Flattening) 0.003353 Mean density (kg/m 3) 5513 Surface gravity (m/s 2) 9.798 Surface acceleration (m/s 2) 9.780 Escape velocity (km/s) 11.186 GM (x 10 6 km 3 /s 2) One reason that our program is so strong is that our . d How do you use the Pythagorean Theorem to find the radius of the earth? [1]:3 The nominal polar Earth radius is defined as 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. R View a sample solution. As such, they are topographical geocentric distances, Rt, which depends not only on latitude. What is the radius of the parallel of latitude? A nominal Earth radius is sometimes used as a unit of measurement in astronomy and geophysics, which is recommended by the International Astronomical Union to be the equatorial value.[1]. This topographical average is 6,371.230km (3,958.899mi) with uncertainty of 10m (33ft).[16]. 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. What are the formula in calculating the earth? Gravitational attraction from the Moon or Sun can cause the Earth's surface at a given point to vary by tenths of a meter over a nearly 12-hour period (see Earth tide). cos x What is the Radius and Diameter of a Circle? These cookies will be stored in your browser only with your consent. Note that the dimensions of h, R and d must be . For information on the Earth, see the Earth Fact Sheet. det 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. Eratosthenes, the ancient Greek scholar is called the father of geography. This value is between 6,378 km, particularly around the equator and about 6,357 km at the poles. This table summarizes the accepted values of the Earth's radius. How do you find the radius with mass and gravity? 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. Earth radius conversions Convert Earth radius to other length and distance measurement units using a free online calculator for length/distance unit conversions. What is the radius of the parallel of latitude? 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. {\displaystyle r} However, Earth is not quite a sphere. Part 4: Computation . [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. T By clicking Accept, you consent to the use of ALL the cookies. 2 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):. How do you solve for radius and diameter? Surveyors today use a variety of instruments and calculations to determine the size of the Earth and collect other relevant data. {\displaystyle R_{2}} The magnitude of the gravitational force between earth and an object is given by the formula. The cookie is used to store the user consent for the cookies in the category "Analytics". where in the first fundamental form for a surface (Equation (112) in[11]): E, F, and G are elements of the metric tensor: r So, radius of nth orbit is rn=rn2, as Z=1 for H atom. , = \text {Circumference} = 39,350 \text {\ kilometers} Circumference = 39,350 kilometers. A) 4.5 x 10-7 B) 4.5 x 107 C) 45 x 10-6 D) 45 x 106 This requires an elliptic integral to find, given the polar and equatorial radii: The rectifying radius is equivalent to the meridional mean, which is defined as the average value of M:[14]. Like a torus, the curvature at a point will be greatest (tightest) in one direction (northsouth on Earth) and smallest (flattest) perpendicularly (eastwest). These cookies will be stored in your browser only with your consent. West can be exchanged for east in this discussion. Hence, we create models to approximate characteristics of Earth's surface, generally relying on the simplest model that suits the need. However, Earth is not quite a sphere. Also, explore tools to convert Earths equatorial radius or meter to other length units or learn more about length conversions. about 6,367.445km (3,956.547mi), can also be used. The radius of the sun at 696,000 km is 109 times the Earth's radius. [Mass of the earth is 6 x 1024 kg and radius of the earth is 6.4 x 106 m]. 257. Compute the radius of the Earth using the formula C (circumference) = 2 x pi x r (radius). N Sun: radius = 696,000 kilometers, > 100 occasions bigger. Use a scientific calculator. Solving for x reveals the circumference to be. 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 . A closed-form solution exists for a spheroid:[14]. w Earth radius at sea level is 6378. r This website uses cookies to improve your experience while you navigate through the website. Chapter P, Problem 13E is solved. Its mean density is 1410 kg/m 3 or 0.255 times the mean density of Earth. As an example, we will use Eratosthenes measurements. 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. Earth's polar radius is 3,950 miles (6,356 km) a difference of 13 miles (22 km). Responsibility disclaimer and privacy policy | About Us | Terms & Conditions | Site Map, Scientific discoveries from around the world. It does not store any personal data. The various radii derived here use the notation and dimensions noted above for the Earth as derived from the WGS-84 ellipsoid;[6] namely. [ These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. Andrew Blum gives some tips that could students in the high-school class in Clinton, Mississippi because they focus on the Eratosthenes project. For the WGS84 ellipsoid, that's respectively: Earth's circumference equals the perimeter length. Hence, we create models to approximate characteristics of Earths surface, generally relying on the simplest model that suits the need. A cylinder has a radius of 8 meters. The cookies is used to store the user consent for the cookies in the category "Necessary". The information were posted by senior high school classes all over the US, plus some in Canada and Mexico, employed in pairs. arrow_forward. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". 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. The diameter is the distance from side to side, if you. Analytical cookies are used to understand how visitors interact with the website. In the third century B.C., Eratosthenes, a Greek mathematician, became the first person to mathematically calculate the diameter of the earth by comparing differences in the angle of the suns rays at two separate geographic points. This cookie is set by GDPR Cookie Consent plugin. This cookie is set by GDPR Cookie Consent plugin. . At room temperature, it will go from a solid to a gas directly. Multiplyin. 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.