The three-body itself involves many situations: 1 is similar to the operation mode of the earth, the moon and the sun; 2. Two celestial bodies move around the same celestial body; 3. Three celestial bodies move around the same fixed point; 4. Three objects with equal mass move on the figure-eight orbit.
The main idea is to adopt the viewpoint of force balance.
For readers who have just come into contact with high school physics and college calculus, it is not difficult to deduce the mathematical equation of three bodies. In fact, according to Isaac Newton's law of universal gravitation and Newton's second law, we can get:
m 1(D2 q 1i/dt2)= k m 1 m2/(q2i-q 1i)(r 3 12)+km 1 m3/(q3i-q 1i)(r 3 13)
m2(D2 q2i/dt2)= k m2 m 1/(q 1i-q2i)(r 32 1)+km2 m3/(q3i-q2i)(r323)
m3(D2 q3i/dt2)= k m3 m 1/(q 1i-q3i)(r 33 1)+km3 m2/(q2i-q3i)(r332)
(i = 1，2，3)
Where m i is the mass of particles, k is the gravitational constant, r ij is the distance between two particles m i and m j, qi 1, qi2 and qi3 are the spatial coordinates of particles m i, so the three-body is mathematically a second-order ordinary differential equation of nine equations with corresponding initial conditions (in fact, according to the symmetry and inherent physical principles of the equation itself, the equation can be simplified and the number of variables can be reduced). The equation of N-body problem is also a set of second-order ordinary differential equations similar to N2 equation.
When N= 1, the monomer problem is a trivial equation. The trajectory of a single particle can only move in a straight line at a constant speed. When N=2 (binary problem), the problem is not so simple. But these equations can still be simplified to a less difficult equation, and any excellent science student may easily solve this problem.