Record the measurements. What is the formula to find radius of Earth? The typical radius of the world is roughly 6. 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. The orbit is not a perfect circle. Arc length of more general surface curves, such as meridian arcs and geodesics, can also be derived from Earth's equatorial and polar radii. Record the distance between your location and your partners location. 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. Drive one of the meter sticks into the ground in your location in a sunny spot. {\displaystyle R_{2}} , For Earth, the volumetric radius equals 6,371. earthRadius Its mean density is 1410 kg/m 3 or 0.255 times the mean density of Earth. 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". 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. r . Not all deformations originate within the Earth. Earth, as we know now, is an oblate spheroid, as shown in the above figure. How do we measure the diameter of the Earth? The circumference of the world measured round the Equatoris approximtely 24,887. What is the Radius and Diameter of a Circle? Q4. What is the mass of this planet in terms of Earth's mass? det Earth's surface area is an estimated 510 km2, and about 29% of the area is land while the other 71% consists of water. What is the permiter of the Earth? 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.) [2] These cookies will be stored in your browser only with your consent. Necessary cookies are absolutely essential for the website to function properly. However, Earth is not quite a sphere. What is the radius of Earth in gravitation? | The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". It is 6356.752 km (3949.903 mi) at the poles and 6371.001 km (3958.756 mi) on average. The cookies is used to store the user consent for the cookies in the category "Necessary". [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. Make sure both sticks are perpendicular to the earth and that the same length of stick protrudes from the ground. The topographical mean geocentric distance averages elevations everywhere, resulting in a value 230m larger than the IUGG mean radius, the authalic radius, or the volumetric radius. 6.371 10 6 m . Semi-minor axis b = 6356752.3142 meters. z Part 4: Computation . Write it in scientific notation. Additionally, the radius can be estimated from the curvature of the Earth at a point. 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]. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. NASA Telescope Takes 12-Year Time-Lapse Movie of Entire Sky. m. The mathematical expressions above apply over the surface of the ellipsoid. which differs from the exact result by less than 1m (4105in); the mean of the two axes. 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). 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. The radius of a circle is the straight-line distance from the very center of the circle to any point on the circle. Other ways to define and measure the Earth radius involve the radius of curvature. 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 How do you express the earths diameter in scientific notation? Your email address will not be published. 2a : the bone on the thumb side of the human forearm also : a corresponding part of vertebrates above fishes. These cookies help provide information on metrics the number of visitors, bounce rate, traffic source, etc. 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. What are the formula in calculating the earth? By knowing the Equatorial diameter or the polar diameter of the Earth, the circumference can be found. Definition of radius 1 : a line segment extending from the center of a circle or sphere to the circumference or bounding surface. Its volume is 803.84 cubic meters. The Earth's Gaussian radius of curvature at latitude is:[12]. 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. T 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. = 371 106 meters (Earth radius 6. Our goal is to make science relevant and fun for everyone. nasa.gov. [2] All three values are about 6,371 kilometres (3,959mi). Step 2 of 5. The reason for keeping those older values was GPS. The radius of Earth is 6370000 m. Express this measurement in km in scientific notation with the correct number of significant digits. 2023 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. That's between 28 and 29 Earths. In a geocentric ellipsoid, the center of the ellipsoid coincides with some computed center of Earth, and best models the earth as a whole. Putting in the numbers, you have Dividing both sides by m1 gives you the acceleration due to gravity: Newton's law of gravitation gives you the acceleration due to gravity near the surface of the Earth: 9.8 meters/second 2. This topographical average is 6,371.230km (3,958.899mi) with uncertainty of 10m (33ft).[16]. 7564mi). are tangents to the surface. What is the scientific name for Earth? cos a) Calculate the average density of the white dwarf. Tack one end of a piece of string to the top of the stick. 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. {\displaystyle n={\frac {N}{|N|}}} 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). How do you find the radius of a gravitational field? 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. Acceleration due to gravity is a vector, which means it has both a magnitudeand a direction. By clicking Accept, you consent to the use of ALL the cookies. Point B, which appears due east from A, will be closer to the equator than A. where in the first fundamental form for a surface (Equation (112) in[11]): E, F, and G are elements of the metric tensor: r + How do you find the radius with mass and gravity? According to the law of gravitation, the gravitational force F of the earth acting on a body is given by: Mass of the Earth Formula =6 1024 kg Mass of earth in kg 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 , While specific values differ, the concepts in this article generalize to any major planet. Escape velocity = = 22.4 km/sec. to the plane tangent at 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. The bulge have been decreasing, consider 1998 the bulge has elevated, possibly because of redistribution of sea mass via currents. Use the protractor to measure the angle where the string meets the stick at the top. Has got the radius of Earth mysteriously grown by about 3%? Refer to the WGS-84 ellipsoid if a more precise value for its polar radius is needed. Because these measurements are not done with more sensitive equipment, the radius calculation will be only approximate. What is the formula of radius of nucleus? This section describes the common ways. Estimates of the accuracy of Eratosthenes's measurement range from 0.5% to 17%. In his writing, Alexander covers a wide range of topics, from cutting-edge medical research and technology to environmental science and space exploration. 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. The nominal radius serves as a unit of length for astronomy. 1 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. [clarification needed]. 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. [1]:3 The nominal polar Earth radius is defined as Earth Radius by Latitude Calculator Calculates radius and diameter of the Earth for a given latitude. It is possible to combine the principal radii of curvature above in a non-directional manner. The total mass of all the asteroids combined is less than that of Earth's Moon. Thus, the surface of the earth at the equator moves at a speed of 460 meters per secondor roughly 1,000 miles per hour. This is roughly 6,371 kilometers (km) or 3,960 statute miles. 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. Also see the Table of Physical Units and Constants. 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. A: . The Earth's meridional radius of curvature at the equator equals the meridian's semi-latus rectum: The Earth's prime-vertical radius of curvature at the equator equals the equatorial radius, N = a. b) Calculate the surface free-fall acceleration. T he circumference of the Earth (around the equator) is approximately 24,887 miles. r What happens to the dry ice at room pressure and temperature? As an example, we will use Eratosthenes measurements. . , d Earth's polar radius is 3,950 miles (6,356 km) a difference of 13 miles (22 km). 6378 X 2 = 12 756 km. The value for the equatorial radius is defined to the nearest 0.1m in WGS-84. Could E.T. Well, the Moon is not always the same distance away from Earth. How do you find the acceleration of a system? Find the volume of Earth in cubic meters. in the second fundamental form for a surface (Equation (123) in[11]): e, f, and g are elements of the shape tensor: n , Area of sphere= 4pier 2. {\displaystyle r} {\displaystyle {\mathcal {R}}_{\mathrm {eE} }^{\mathrm {N} }} Here x is the circumference of the earth. By clicking Accept, you consent to the use of ALL the cookies. You can do this, too, by using his method. The magnitude of the gravitational force between earth and an object is given by the formula. 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. 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. J Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. George Jackson is the founder and lead contributor of Physics Network, a popular blog dedicated to exploring the fascinating world of physics. wikipedia article on the Juno spacecraft provides an a great overview of this type of process. A few definitions yield values outside the range between polar radius and equatorial radius because they include local or geoidal topography or because they depend on abstract geometrical considerations. [22] For both Aristotle and Eratosthenes, uncertainty in the accuracy of their estimates is due to modern uncertainty over which stadion length they meant. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". [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. Ocean Worlds Resources. Tack one end of a piece of string to the top of the stick. Your email address will not be published. r The mathematical expressions above apply over the top of ellipsoid. Point on the ellipsoid surface can be defined by the parametric curve equation. This value is between 6,378 km, particularly around the equator and about 6,357 km at the poles. How many miles is a meter in scientific notation? , and because (e) For that Earth 1/q 289, that is near to the measured inverse flattening 1/f 298. For information on the Earth, see the Earth Fact Sheet. Where K is the Gaussian curvature, Start your trial now! Her latest book, "A Travel for Taste: Germany," was published in 2015. The geoid height variation is under 110m (360ft) on Earth. [24] Claudius Ptolemy around 150AD gave empirical evidence supporting a spherical Earth,[25] but he accepted the lesser value attributed to Posidonius. A) 4.5 x 10-7 B) 4.5 x 107 C) 45 x 10-6 D) 45 x 106 As the parallels run east and west, places having the same latitude will be due east or due west of each other. The information were posted by senior high school classes all over the US, plus some in Canada and Mexico, employed in pairs. The radius of a chlorine atom is approximately meters. Radius refers to a line that connects to the centre point of a circle to any point on its outside layer. = Thus the curvature found this way is smaller than the curvature of a circle of constant latitude, except at the equator. This video explains how humans managed to measure the circumference of the earth long long ago using simple math, reasoning and assumptions. For the Earth, the authalic radius is 6,371.0072km (3,958.7603mi). Earth radius conversions Convert Earth radius to other length and distance measurement units using a free online calculator for length/distance unit conversions. e Definitions and Formulas. 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). 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. a) The diameter of the earth is approximately 1.276 1 0 7 1.276 \times 10^7 1.276107 m in scientific notation. Earths Equatorial Radius to Meter Conversion Table, How to Convert Earths Equatorial Radius to Meter, Convert Earths Equatorial Radius to Other Length Units. Do NOT follow this link or you will be banned from the site! The earth is made up of three different layers: the crust, the mantle and the core. 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. Since the estimate by Eratosthenes, many models have been created. The cookie is used to store the user consent for the cookies in the category "Analytics". r E Q. The first and second radii of curvature correspond, respectively, to the Earth's meridional and prime-vertical radii of curvature. High School Students Measure New Value for Earths Radius to Celebrate World Physics Year. 149597870700 meters nearly This is 10-sd (significant digits) approximation. The answer would be 695 500 000 m. Wiki User. Answer (1 of 3): First of all let us consider the shape of the earth to be a sphere. You have to find the circumference. It is with the values I gave you. Eratosthenes' methods result in a formula that would look like this: 39,350 = 2 x 3.14 x r, or 6,267 kilometers. A Of course, no one is claiming the size of Earth has actually changed. 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. Advertisement. 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. The planet's rotation causes it to bulge at the equator. 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 magnitude of the gravitational force between earth and an object is given by the formula. Testing, Testing: Space-Bound US-European Water Mission Passes Finals. Use scientific notation to show the above value of the radius. {\displaystyle R_{E}} [d] It is also common to refer to any mean radius of a spherical model as "the radius of the earth". state. The equatorial radius is most commonly used to calculate the volume of Earth, so as not to leave out any territory. Radius of sun is 695 500 km, so in meters you multiply by 1000. 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. 06. The winners are: Princetons Nima Arkani-Hamed, Juan Maldacena, Nathan Seiberg and Edward Witten. [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. 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. These cookies ensure basic functionalities and security features of the website, anonymously. also corresponds to the radius of (global) mean curvature, obtained by averaging the Gaussian curvature, Make sure both sticks are perpendicular to the Earth and that the same length of stick protrudes from the ground. Examples collapse all Earth Radius in Meters View the mean radius of the Earth using the default units, meters. for the nominal polar Jupiter radius. 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 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. for an oblate spheroid, the curvatures are. The equatorial radius of Earth is actually 6,378.1 kilometers. Required fields are marked *. Q4. In the modern age, satellites often provide the most accurate and current information through global imaging. Regarding this, what is the diameter of the Earth in scientific notation? For this calculation, the longitude isn't needed. r R Have Bugged an area Rock to pay attention In on Earthlings? N So, its circumference varies depending on how you calculate it. (8,849 meters), but it is not the highest point on Earth that is, the place most distant from the . B Convert the Earth-Sun distance of 93,000,000 miles into. => When Wi-Fi is available location accuracy is usually between 20 - 50 meters. At the equator, = 0 and this arc length = 111.32 km, nearly. The average light travel time to the earth is 8.3 minutes. Also a photographer, she records adventures by camera, combining photos with journals in her blogs. One reason that our program is so strong is that our . When we rearrange the equation and plug all the numbers in, we find that the mass of the Earth is 5.96 1024 kg. For integration limits of [0,/2], the integrals for rectifying radius and mean radius evaluate to the same result, which, for Earth, amounts to 6,367.4491km (3,956.5494mi). 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. So, radius of nth orbit is rn=rn2, as Z=1 for H atom. Earth's volume, or that of the reference ellipsoid, is V = 4/3a2b. Solution Verified Earth, the third planet from the sun, is one of the most unique celestial bodies in our solar system. And we divide that by Pi times 9.00 centimeters written as meters so centi is prefix meaning ten times minus two and we square that diameter. 1999. [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. 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. What is the radius of Earth in meters? This is the radius that Eratosthenes measured in his arc measurement. There are two principal radii of curvature: along the meridional and prime-vertical normal sections. [ 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. The circumference of the Earth is the length or distance measured around it. To determine the diameter of the earth in metres first multiply the original value by 2.