Kepler problem

This article is about a special case of the two-body problem in classical mechanics. For the problem of finding the densest packing of spheres in three-dimensional Euclidean space, see Kepler conjecture.

In classical mechanics, Kepler’s problem is a special case of the two-body problem, in which the two bodies interact by a central force F that varies in strength as the inverse square of the distance r between them. The force may be either attractive or repulsive. The "problem" to be solved is to find the position or speed of the two bodies over time given their masses and initial positions and velocities. Using classical mechanics, the solution can be expressed as a Kepler orbit using six orbital elements.

The Kepler problem is named after Johannes Kepler, who proposed Kepler's laws of planetary motion (which are part of classical mechanics and solve the problem for the orbits of the planets) and investigated the types of forces that would result in orbits obeying those laws (called Kepler's inverse problem).[1]

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The Yichang–Wanzhou Railway, or the Yiwan Railway (simplified Chinese: 宜万铁路; traditional Chinese: 宜萬鐵路; pinyin: Yíwàn Tiělù) connects cities of Yichang (Hubei Province) and Wanzhou (Chongqing Municipality) via Lichuan, in the central People's Republic of China. It was completed in 2010, and will be part of the future Huhanrong Passenger Dedicated Line from Shanghai to Wuhan to Chengdu. Out of the line's total 377 km (234 mi) length, 288 km (179 mi) runs on bridges or in tunnels. According to the chief engineer, Zhang Mei, the line was the most difficult ever constructed in China. Operation started on 22 December 2010.

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