Question:

How east is the earth traveling?

The earth moves round the sun in an oval track that has an average radius of 93 million miles, at a speed of 18.5 miles a second.

510,072,000 km2
5.972191024 kg
0.367 (geometric)
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In classical geometry, the radius of a circle or sphere is the length of a line segment from its center to its perimeter. The name comes from Latin radius, meaning "ray" but also the spoke of a chariot wheel. The plural of radius can be either radii (from the Latin plural) or the conventional English plural radiuses. The typical abbreviation and mathematic variable name for "radius" is r. By extension, the diameter d is defined as twice the radius: If the object does not have an obvious center, the term may refer to its circumradius, the radius of its circumscribed circle or circumscribed sphere. In either case, the radius may be more than half the diameter, which is usually defined as the maximum distance between any two points of the figure. The inradius of a geometric figure is usually the radius of the largest circle or sphere contained in it. The inner radius of a ring, tube or other hollow object is the radius of its cavity. For regular polygons, the radius is the same as its circumradius. The inradius of a regular polygon is also called apothem. In graph theory, the radius of a graph is the minimum over all vertices u of the maximum distance from u to any other vertex of the graph. The radius of the circle with perimeter (circumference) C is The radius of a circle with area A is The radius is half the diameter. To compute the radius of a circle going through three points P1, P2, P3, the following formula can be used: where θ is the angle $\angle P_1 P_2 P_3.$ This formula uses the Sine Rule. If the three points are given by their coordinates $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$, one can also use the following formula : These formulas assume a regular polygon with n sides. The radius can be computed from the side s by: The radius of a d-dimensional hypercube with side s is
In 1991, Charlotte Motor Speedway created the first notable "Legends" oval course. The existing quad oval start/finish straight was connected to the pit lane by two 180 degree turns, resulting in a 1/4-mile short track oval. A special exhibition race featuring former NASCAR legends headlined one time on the course. A year later, the same 1/4-mile layout became a popular venue for Legends car racing. The name "Legends oval" was derived from this use. They have also seen use with go-karts, short track stock cars, and other disciplines. The Legends oval concept allows minor league levels of racing to compete in the stadium-style atmosphere of large speedways, when they would normally be confined to small, stand-alone 1/4-mile venues. It also allows them to serve as support races at tracks where they would not normally be able to compete (due to the track lengths and speeds) without track or car modification. Tracks with Legends ovals Oval tracks usually have slope in both straight and in curves, but the slope on the straights is usually smaller, circuits without any slope are rare to find, low-slope are usually old or small tracks, high gradient are more common in new circuits. Circuits like Milwaukee Mile and Indianapolis Motor Speedway are approximately 9° tilt in curves are considered low slope, superspeedways like Talladega has up to 33° tilt in curves, Daytona has up to 32°, both are considered high inclination. Charlotte and Dover are the intermediate with the highest bank, 24° tilt. Bristol is the short oval with up to 30°. Pack racing is a phenomenon found on fast, high-banked superspeedways. It occurs when the vehicles racing are cornering at their limit of aerodynamic drag, but within their limit of traction. This allows drivers to race around the track constantly at wide open throttle. Since the vehicles are within their limit of traction, drafting through corners will not hinder a vehicle's performance. As cars running together are faster than cars running individually, all cars in the field will draft each other simultaneously in one large pack. In stock car racing this is often referred to as "restrictor plate racing" because NASCAR mandates that each car on its two longest high-banked ovals, Talladega and Daytona, use an air restrictor to reduce horsepower. The results of pack racing may vary. As drivers are forced to race in a confined space, overtaking is very common as vehicles may travel two and three abreast. This forces drivers to use strong mental discipline in negotiating traffic. There are drawbacks, however. Should an accident occur at the front of the pack, the results could block the track in a short amount of time. This leaves drivers at the back of the pack with little time to react and little room to maneuver. The results are often catastrophic as several cars may be destroyed in a single accident. This type of accident is often called "The Big One". Oval track racing requires different tactics than road racing. While the driver doesn't have to shift gears nearly as frequently, brake as heavily or as often, or deal with turns of various radii in both directions as in road racing, drivers are still challenged by negotiating the track. Both types of racing place physical demands on the driver. A driver in an IndyCar race at Richmond International Raceway may be subject to as many lateral g-forces (albeit in only one direction) as a Formula One driver at Istanbul Park. Weather also plays a different role in each discipline. Road racing offers a variety of fast and slow corners that allow the use of rain tires. Paved ovals cannot support rain tires because the turns are all very fast and the soft rubber compound used in the tread would not survive long against the forces inflicted upon it. Dirt ovals will sometimes support a light rain. Some tracks (e.g., Evergreen Speedway in Monroe, WA) have "rain or shine" rules requiring races to be run in rain. Safety has also been a point of difference between the two. While a road course usually has abundant run-off areas, gravel traps, and tire barriers, ovals usually have a concrete retaining wall separating the track from the fans. Innovations have been made to change this, however. The SAFER barrier was created to provide a less dangerous alternative to a traditional concrete wall. The barrier can be retrofit onto an existing wall or may take the place of a concrete wall completely.
In astronomy, a lunar distance (LD) is a measurement of the distance from the Earth to the Moon. The average distance from Earth to the Moon is 384,400 km (238,900 mi). The actual distance varies over the course of the orbit of the moon, from 356,700 km (221,600 mi) at the perigee and 406,300 km (252,500 mi) at apogee. High-precision measurements of the lunar distance are made by measuring the time taken for light to travel between LIDAR stations on Earth and retroreflectors placed on the Moon. The Moon is spiraling away from Earth at an average rate of 3.8 cm (1.5 in) per year, as detected by the Lunar Laser Ranging Experiment. The recession rate is considered anomalously high. By coincidence, the diameter of corner cubes in retroreflectors on the Moon is also 3.8 cm (1.5 in). The tidal dissipation rate varied in the Earth geological history. The first person to measure the distance to the Moon was the 2nd-century-BC astronomer and geographer Hipparchus, who exploited the lunar parallax using simple trigonometry. He was approximately 26,000 km (16,000 mi) off the actual distance, an error of about 6.8%. The NASA Near Earth Object Catalog includes the distances of asteroids and comets measured in Lunar Distances.

Earth radius is the distance from Earth's center to its surface, about 6,371 kilometers (3,959 mi). This length is also used as a unit of distance, especially in astronomy and geology, where it is usually denoted by $R_\oplus$. This article deals primarily with spherical and ellipsoidal models of the Earth. See Figure of the Earth for a more complete discussion of models. The Earth is only approximately spherical, so no single value serves as its natural radius. Distances from points on the surface to the center range from 6,353 km to 6,384 km (3,947–3,968 mi). Several different ways of modeling the Earth as a sphere each yield a mean radius of 6,371 kilometers (3,959 mi). While "radius" normally is a characteristic of perfect spheres, the term as used in this article more generally means the distance from some "center" of the Earth to a point on the surface or on an idealized surface that models the Earth. It can also mean some kind of average of such distances, or of the radius of a sphere whose curvature matches the curvature of the ellipsoidal model of the Earth at a given point. The first scientific estimation of the radius of the earth was given by Eratosthenes about 240 BC. Estimates of the accuracy of Eratosthenes’s measurement range from within 2% to within 15%. Earth's rotation, internal density variations, and external tidal forces cause it to deviate systematically from a perfect sphere. Local topography increases the variance, resulting in a surface of unlimited complexity. Our descriptions of the Earth's surface must be simpler than reality in order to be tractable. Hence we create models to approximate the Earth's surface, generally relying on the simplest model that suits the need. Each of the models in common use come with some notion of "radius". Strictly speaking, spheres are the only solids to have radii, but looser uses of the term "radius" are common in many fields, including those dealing with models of the Earth. Viewing models of the Earth from less 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". It is also common to refer to any mean radius of a spherical model as "the radius of the earth". On the Earth's real surface, on other hand, it is uncommon to refer to a "radius", since there is no practical need. Rather, elevation above or below sea level is useful. Regardless of model, any radius falls between the polar minimum of about 6,357 km and the equatorial maximum of about 6,378 km (≈3,950 – 3,963 mi). Hence the Earth deviates from a perfect sphere by only a third of a percent, sufficiently close to treat it as a sphere in many contexts and justifying the term "the radius of the Earth". While specific values differ, the concepts in this article generalize to any major planet. 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 $a q$ where the oblateness constant $q$ is where $\omega$ is the angular frequency, $G$ is the gravitational constant, and $M$ is the mass of the planet. For the Earth , which is close to the measured inverse flattening . Additionally, the bulge at the equator shows slow variations. The bulge had been declining, but since 1998 the bulge has increased, possibly due to redistribution of ocean mass via currents. The variation in density and crustal thickness causes gravity to vary on the surface, so that the mean sea level will differ from the ellipsoid. This difference is the geoid height, positive above or outside the ellipsoid, negative below or inside. The geoid height variation is under 110 m on Earth. The geoid height can change abruptly due to earthquakes (such as the Sumatra-Andaman earthquake) or reduction in ice masses (such as Greenland). Not all deformations originate within the Earth. The gravity of the Moon and Sun cause the Earth's surface at a given point to undulate by tenths of meters over a nearly 12 hour period (see Earth tide). Given local and transient influences on surface height, the values defined below are based on a "general purpose" model, refined as globally precisely as possible within 5 m of reference ellipsoid height, and to within 100 m of mean sea level (neglecting geoid height). Additionally, the radius can be estimated from the curvature of the Earth at a point. Like a torus the curvature at a point will be largest (tightest) in one direction (North-South on Earth) and smallest (flattest) perpendicularly (East-West). The corresponding radius of curvature depends on location and direction of measurement from that point. A consequence is that a distance to the true horizon at the equator is slightly shorter in the north/south direction than in the east-west direction. In summary, local variations in terrain prevent the definition of a single absolutely "precise" radius. One can only adopt an idealized model. Since the estimate by Eratosthenes, many models have been created. Historically these models were based on regional topography, giving the best reference ellipsoid for the area under survey. As satellite remote sensing and especially the Global Positioning System rose in importance, true global models were developed which, while not as accurate for regional work, best approximate the earth as a whole. The following radii are fixed and do not include a variable location dependence. They are derived from the WGS-84 ellipsoid. The value for the equatorial radius is defined to the nearest 0.1 meter in WGS-84. The value for the polar radius in this section has been rounded to the nearest 0.1 meter, which is expected to be adequate for most uses. Please refer to the WGS-84 ellipsoid if a more precise value for its polar radius is needed. The radii in this section are for an idealized surface. Even the idealized radii have an uncertainty of ± 2 meters. The discrepancy between the ellipsoid radius and the radius to a physical location may be significant. 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. The symbol given for the named radius is used in the formulae found in this article. The Earth's equatorial radius $a$, or semi-major axis, is the distance from its center to the equator and equals 6,378.1370 kilometers (3,963.1906 mi). The equatorial radius is often used to compare Earth with other planets. The Earth's polar radius $b$, or semi-minor axis, is the distance from its center to the North and South Poles, and equals 6,356.7523 kilometers (3,949.9028 mi). The distance from the Earth's center to a point on the spheroid surface at geodetic latitude $\varphi\,\!$ is: where $a$ and $b$ are the equatorial radius and the polar radius, respectively. These are based on an oblate ellipsoid. Eratosthenes used two points, one almost exactly north of the other. The points are separated by distance $D$, and the vertical directions at the two points are known to differ by angle of $\theta$, in radians. A formula used in Eratosthenes' method is which gives an estimate of radius based on the north-south curvature of the Earth. Note that N=R at the equator: At geodetic latitude 48.46791 degrees (e.g., Lèves, Alsace, France), the radius R is 20000/π ≈ 6,366.197, namely the radius of a perfect sphere for which the meridian arc length from the equator to the North Pole is exactly 10000 km, the originally proposed definition of the meter. The Earth's mean radius of curvature (averaging over all directions) at latitude $\varphi\,\!$ is: The Earth's radius of curvature along a course at geodetic bearing (measured clockwise from north) $\alpha\,\!$, at $\varphi\,\!$ is derived from Euler's curvature formula as follows: The Earth's meridional radius of curvature at the equator equals the meridian's semi-latus rectum: The Earth's polar radius of curvature is: The Earth can be modeled as a sphere in many ways. This section describes the common ways. The various radii derived here use the notation and dimensions noted above for the Earth as derived from the WGS-84 ellipsoid; namely, 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. The International Union of Geodesy and Geophysics (IUGG) defines the mean radius (denoted $R_1$) to be For Earth, the mean radius is 6,371.009 kilometers (3,958.761 mi). Earth's authalic ("equal area") radius is the radius of a hypothetical perfect sphere which has the same surface area as the reference ellipsoid. The IUGG denotes the authalic radius as $R_2$. A closed-form solution exists for a spheroid: where $e^2=(a^2-b^2)/a^2$ and $A$ is the surface area of the spheroid. For Earth, the authalic radius is 6,371.0072 kilometers (3,958.7603 mi). Another spherical model is defined by the volumetric radius, which is the radius of a sphere of volume equal to the ellipsoid. The IUGG denotes the volumetric radius as $R_3$. For Earth, the volumetric radius equals 6,371.0008 kilometers (3,958.7564 mi). Another mean radius is the rectifying radius, giving a sphere with circumference equal to the perimeter of the ellipse described by any polar cross section of the ellipsoid. 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: For integration limits of [0…π/2], the integrals for rectifying radius and mean radius evaluate to the same result, which, for Earth, amounts to 6,367.4491 kilometers (3,956.5494 mi). The meridional mean is well approximated by the semicubic mean of the two axes: yielding, again, 6,367.4491 km; or less accurately by the quadratic mean of the two axes: about 6,367.454 km; or even just the mean of the two axes: about 6,367.445 kilometers (3,956.547 mi).
The orbital speed of a body, generally a planet, a natural satellite, an artificial satellite, or a multiple star, is the speed at which it orbits around the barycenter of a system, usually around a more massive body. It can be used to refer to either the mean orbital speed, i.e., the average speed as it completes an orbit, or the speed at a particular point in its orbit.][ The orbital speed at any position in the orbit can be computed from the distance to the central body at that position, and the specific orbital energy, which is independent of position: the kinetic energy is the total energy minus the potential energy. In the case of radial motion:][ The transverse orbital speed is inversely proportional to the distance to the central body because of the law of conservation of angular momentum, or equivalently, Kepler's second law. This states that as a body moves around its orbit during a fixed amount of time, the line from the barycenter to the body sweeps a constant area of the orbital plane, regardless of which part of its orbit the body traces during that period of time. This law is usually stated as "equal areas in equal time."][ This law implies that the body moves faster near its periapsis than near its apoapsis, because at the smaller distance it needs to trace a greater arc to cover the same area. For orbits with small eccentricity, the length of the orbit is close to that of a circular one, and the mean orbital speed can be approximated either from observations of the orbital period and the semimajor axis of its orbit, or from knowledge of the masses of the two bodies and the semimajor axis.][ where $v_o\,\!$ is the orbital velocity, $a\,\!$ is the length of the semimajor axis, $T\,\!$ is the orbital period, and $\mu\,\!$ is the standard gravitational parameter. Note that this is only an approximation that holds true when the orbiting body is of considerably lesser mass than the central one, and eccentricity is close to zero. Taking into account the mass of the orbiting body, where $m_1\,\!$ is now the mass of the body under consideration, $m_2\,\!$ is the mass of the body being orbited, $r\,\!$ is specifically the distance between the two bodies (which is the sum of the distances from each to the center of mass), and $G\,\!$ is the gravitational constant. This is still a simplified version; it doesn't allow for elliptical orbits, but it does at least allow for bodies of similar masses. When one of the masses is almost negligible compared to the other mass as the case for Earth and Sun, one can approximate the previous formula to get: or Where M is the (greater) mass around which this negligible mass or body is orbiting, and ve is the escape velocity. For an object in an eccentric orbit orbiting a much larger body, the length of the orbit decreases with eccentricity $e\,\!$, and is given at ellipse. This can be used to obtain a more accurate estimate of the average orbital speed: The mean orbital speed decreases with eccentricity.