The motion of a binary star rotates periodically around a fixed point? According to GM1m2/L2 = m1* 4π 2r1/t2gm1m2/L2 = m2 * 4π 2r 2/T2.

r 1=gm2t^2/4π^2l^2r2=gm 1t^2/4π^2l^2？ r 1+r2=L

m 1+m2=4π^2L^3/GT^2

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In the process of movement change, some features appear repeatedly, and the time required for two consecutive appearances is called "cycle".

1, mathematical cycle:

For a function f(x), if there is a positive number t, so that when x takes every value in the domain, there is f(x+T)=f(x), then this function f(x) is called a periodic function. A positive number t is called the period of this function.

For the function f(x)=Asin(ωx+φ), the minimum positive period of the function f(x) is T=2π/|ω|.

For the function f(x)=Atan(ωx+φ), the minimum positive period of the function f(x) is T=π/|ω|.

If f(x+2)=-f(x-2) is subtracted from parentheses to become a constant value, then the period t of this value f(x) is 4.

The essence of periodic function: when the difference between the two independent variables is equal to the multiple of the period, the function values of the two independent variables are equal. such as

F(x+6)=f(x-2) then the function period is T=8.

2, chemical cycle:

1. Classification of elements in the periodic table. A row in which a series of elements with the same number of electronic layers are arranged in order of increasing atomic number is a period. From left to right, the mineralization of elements gradually weakened and nonmetals gradually increased in the same period.

2. Refers to a series of elements with the same number of electronic layers, arranged in the order of increasing atomic number. The periodic table of elements has seven rows, that is, seven periods. The first, second and third periods are called short periods; The fourth, fifth, sixth and seventh periods are called long periods; Generally, each cycle begins with active metallic elements, gradually transitions to active nonmetallic elements, and finally ends with rare gas elements.

3. Physical cycle:

1. Uniform circular motion is a periodic motion. The so-called periodicity means that the moving object returns to its original position repeatedly after a certain period of time, and the instantaneous speed also returns to its original size and direction repeatedly. The time required for an object to make a uniform circular motion is called a period. The period is represented by symbol T, which is also a physical quantity describing the speed of uniform circular motion. A long period means that the object moves slowly, and a short period means that the object moves fast.

Periodic unit t: s? Angular velocity unit ω: radian/second

V (linear velocity) =2πr/Tω (angular velocity) = 2π/t.

2. When the object does reciprocating motion or the physical quantity changes repeatedly, the time required to repeat it once. The time required for an object or physical quantity (such as alternating current and voltage) to complete a vibration (or oscillation). In various periodic movements or periodic changes, an object or physical quantity changes from any state and always returns to its original state after a period or an integer multiple of a period.

Physics: The time required for an alternating current to complete a complete change is called a period, which is usually expressed by t. The unit of a period is seconds (s), and it is also commonly used in milliseconds (ms) or microseconds (us). 1s= 1000 ms, 1s = 100000 us.

4, biological cycle:

The spontaneous or passive activity of an object itself is called a cycle from the beginning to the end, such as the movement of celestial bodies, and the earth rotates around the sun for one year. Biological cell division, from cell preparation to division, goes through prophase, metaphase, anaphase and anaphase, and finally returns to interphase, which is a cycle.

5. Economic cycle:

Businesscycle: also known as business cycle and boom cycle, it refers to a phenomenon that economic expansion and economic contraction alternate in economic operation. It is the fluctuation of total national output, total income and total employment, and it is the alternating or periodic fluctuation of expansion and contraction of national income or overall economic activities. The past is divided into four stages: prosperity, recession, depression and recovery. Now it is generally called recession, trough, expansion and peak.