An introduction to spherical distances, spherical distance formulas

We call this arc length the spherical distance of two points.

The method is as follows: as shown in the figure on the right, if the angle AOB (spherical center angle) is , the radius of the large sphere is r, the dimension and longitude of point A are , and the dimension and longitude of point B are , then the distance of the sphere is r

The formula for calculating the spherical distance is d(x1,y1,x2,y2)=r*arccos(sin(x1)*sin(x2)+cos(x1)*cos(x2)*cos(y1-y2)).

x1, y1 is the unit of radians of latitude and longitude, and r is the radius of the earth.

And when y1=y2, the formula becomes:

d=r*|x1-x2|

There are three points a, b, and b on the sphere, and the spherical distance between a and c is equal to 1 6 of the circumference of the great circle, and the spherical distance between b and c is equal to 1 4 of the circumference of the great circle. If the radius of the ball is r, then what is the distance from the center of the sphere to the section abc?

AB, AC spherical distance is 1 6*2 R = *R, then the angle between AC and the spherical center is =60°, the same way that the angle between BC and the spherical center is 90°, then BC=V2R, AB=AC=R, so ABC is RT, the small circle radius through ABC is half of the hypotenuse, the small circle radius, the large circle radius are known, and the spherical center distance is easy to calculate.

1) 30° at the same latitude.

2) Longitude difference: 83-(-97)=180°

3) Connect the center of the ball to the two cities and connect the two cities.

It can be seen that a fan and an isosceles triangle inside the fan, the central angle of the fan is also an isosceles triangle, and the apex angle of the isosceles triangle is 180-30-30=120°

The radius of the sector is also isosceles, and the triangle waist length is r

The distance between the two cities on the circle of latitude is the length of the base of the isosceles triangle, which is also the chord length of the fan: (root number 3)r

The spherical distance between the two cities on a spherical surface on the earth's surface is also a fan-shaped arc length:

120 360)*2*ttr=(2 3)ttrtt is pi}

The ratio of the two: [root number 3)r] [(2 3)ttr] = [3 * (root number 3)] (2tt).

The approximate value is (3*

The spherical distance formula is s=r·arcos[cos cos( 1-2)+sin ], and the length of the shortest line between two points on the sphere is the length of a bad acre arc between these two points of the great circle between these two points.

The shape of the earth is an irregular sphere with slightly flattened poles. The average radius of the Earth is 6,371 km, the equator is 6,378 km, and the polar radius is 6,357 km. Equatorial circumference.

It is about 40,000 kilometers. Zero warp.

It's called the prime meridian.

From the prime meridian to the east and west to the 180 degrees, the east of the 180 degrees belongs to the east longitude, with "e" as the code; The 180° to the west belongs to the west longitude and is coded with "w".

First, connect the two points with the center of the sphere respectively to obtain an angle, calculate the size of this angle without seepage, and then calculate the circumference according to the radius of the ball, multiply the circumference by the angle, and then divide by 360 is the spherical distance.

AB, AC spherical distance is 1 6*2 R = *R, then the angle between AC and the spherical center is =60°, the same way that the angle between BC and the spherical center is 90°, then BC=V2R, AB=AC=R, so ABC is RT, the small circle radius through ABC is half of the hypotenuse, the small circle radius, the large circle radius are known, and the spherical center distance is easy to calculate.

First, connect the two points with the center of the sphere respectively to obtain an angle, calculate the size of this angle, and then calculate the perimeter according to the radius of the ball, multiply the circumference by the angle, and then divide by 360 is the distance of the sphere.

AB, AC spherical distance is 1 6*2 R = *R, then the angle between AC and the spherical center is =60°, the same way that the angle between BC and the spherical center is 90°, then BC=V2R, AB=AC=R, so ABC is RT, the small circle radius through ABC is half of the hypotenuse, the small circle radius, the large circle radius are known, and the spherical center distance is easy to calculate.

1. Weft: The weft is all round, also known as the weft coil, and the length is unequal. The equator is the longest, and gradually shortens from the equator to the poles, and finally becomes a point. The parallels indicate the east-west direction.

2. Latitude: The equator is a zero-degree parallel. The latitude north of the equator is called the northern latitude, and the "n" is used as the code name; The latitude south of the equator is called southern latitude, and the "s" is used as the code name. There are 90° north latitude and 90° south latitude.

3. Warp: also called meridian. The warp threads are semicircular, and all the warp threads are equal in length. The meridian indicates the north-south direction.

The length of the shortest line between two points on a sphere is the length of a bad arc between these two points of the great circle passing through these two points. (A great circle is a circle obtained by passing through the plane of the sphere at the center of the sphere).

Yes, it can be deduced:

Let the radius of the earth be r, and the spherical coordinates of two points a and b on the sphere are a( 1, 1),b( 2, 2), 1,2 [-1, 2 [- 2, 2 ],ab =r 6 1arccos[cos 1cos 2cos( 1- 2)+sin 1sin 2].

Find the great circle that has passed the center of the ball and the two points, which is the inferior arc.

Of course, there are two points required for the "spherical distance", and there is a theorem "three points that are not on the same straight line determine a plane", so that these two points and the three points of the sphere center of the ball can form a plane, which is mathematically called a "great circle", and the arc length between the two points is the distance between the two points of the sphere.

1, 1= 2=, then the spherical distance formula is:

r·arcos[cos cos( 1- 2)+sin ] ii)2, 1- 2= , then the spherical distance formula is:

r·arcos（cosβ1cosβ2+sinβ1sinβ2）=r·arcoscos（β1-β2）

d(x1,y1,x2,y2)=r*arccos(sin(x1)*sin(x2)+cos(x1)*cos(x2)*cos(y1-y2))

x1, y1 is the unit of radians of latitude and longitude, r is the radius of the earth and when y1 = y2, the formula becomes:

d=r*|x1-x2|

d(x1,y1,x2,y2)=r*arccos(sin(x1)*sin(x2)+cos(x1)*cos(x2)*cos(y1-y2))

x1, y1 is the unit of radians of latitude and longitude, r is the radius of the earth and when y1 = y2, the formula becomes:

d=r*|x1-x2|

1.The two facets are on the same side of the heart of the ball mu.

r^2=（（r^2-12^2）^1/2+2）^2+8^22.Make a feast on both sides of the center of the ball.

r 2=(2-(r 2-12 2) 1 sterling silver 2) 2+8 2 solve r and you're good to go.