The two points and the centre of the earth define a plane, and the intersection of this plane with the surface of the earth is a circle - the "Great Circle". The shortest distance between the two points is the smaller of the two arcs on this circle.
407,000 kmThe distance between the Moon and the Earth varies from around 356,400 km to 406,700 km at the extreme perigees (closest) and apogees (farthest).
The distance from Earth is about 6,500 light years (2000 parsecs).
Depending on where Mercury is relative to the Earth as the two planets orbit the sun, the distance from Mercury to Earth varies from 77.3x106km to 221.9x106km.
The earth's escape velocity is approx 25,000 miles per hour so at 70 mph you would ot be able to leave earth!Space rockets do not travel in a straight line. Instead, they first orbit the earth and then use a kind of sling-shot effect to travel across space. The distance travelled, therefore bears little relation to the distance between the earth and the moon.However, a journey as long as the earth-moon distance, at 70 mph, would take a little over 142 days.
A kilometre is quite a long unit of measurement. For this reason you would use it to measure large things on earth. For example:The distance between citiesThe length of a coastlineHow far a train journey is
the distance between the earth and sun is shortest in the month of...
... is called a Great Circle arc.
If they are in the same plane then it is the length of the straight line joining them. If they are not in a plane then things get complicated. On the surface of the earth (a sphere), the shortest distance is an arc along the great circle. The great circle is a circle whose centre is the centre of the earth and which passes through the two places. This is why New York to Tokyo flights go over the Arctic region. With polyhedra, one way to find the shortest distance is to mark the two points on a net the shape. If you can draw a straight line between the points such that all of it is on the net, then that is the shortest distance. You may need to play around with different nets.
The shortest route between two points on the surface of a planet, when routes are limited to the planet's surface, is the arc of the great circle that connects the two points. The shortest route between two points anywhere, without regard to intervening matter or energy preventing the route from being followed, is always the line connecting the two points.
Actually, this turns out to be more of a debate than you might think. Historically, most of us were taught the shortest distance between two points is a straight line; that is a principle of Euclid's geometry. But not everyone agrees with Euclid, and there are other types of geometry. For example, because the Earth is a sphere, and not flat as distance maps portray it, that is why some scientists say that the shortest distance is actually a sphere or a curve (in other words, the distance would be measured by following the Earth's contours).
There is not a converse, as such, but there are other metrics that may be applicable in different circumstances. One such is the Manhattan distance (deeloped by Minkovsky) which uses the grid pattern of roads as a way to measue distances. On the non-planar surface, such as that of the earth, the shortest distance between two points will be along the "Great Circle" passing through the two points. In some situations people may be interested in the fastest route between two points even if it is not the shortest straight line distance.
It is simply called the distance between the two points - simple as that. How that distance is measured will depend on the nature of the surface on which the two points are located as well as on the metric for measuring distance that is defined on that space.The common metric in Euclidean space is the Pythagorean distance while on the surface of a sphere (like the Earth, for example), distances are measured along the great arc.
Assuming the earth to be a perfect sphere, the shortest distance is an arc of the great circle. The two places and the centre of the earth define a plane. The great circle is the circle formed by the intersection of that plane and the surface of the earth. The shortest route between the two places is the smaller of the two arcs along that circle.
Every so-called "great circle" is (more or less) the longest circumference of the Earth that includes any two points. The great circle includes the shortest distance between the two points for travel along the Earth's surface.
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It is the shortest distance between two points on a sphere, where the sphere in question is the earth. Particularly long airline flights follow great circle routes.