Kaarten: Ch 2: The dynamics of planetary systems | Quizlet

What is the underlying reason why the case N=2 is the only case of the N-body problem that can be solved analytically?

General: 6N unknowns (position and speed vectors) and 10 constants of motion so 6N-10 constants are required

Two-body problem= differential equation (one mass with respect to the other) can be formulated as two one-body problems

How does the period of a planet vary with its semi-major axis?

T~ a^3/2

What are the Lagrange points? Why are they important?

Lagrange points are specific locations in space where the gravitational forces of two large bodies, like the Earth and the Moon, balance the centripetal force felt by a smaller object. This creates areas where a small object can maintain a relatively stable position relative to the two larger bodies. There are five Lagrange points, named L1 through L5.

L1, L2 and L3 lie on the line of the two bodies and are unstable

L4 and L5 lie above and below the two bodies and are stable for m1/m2 > 27

How was the Martian catastrophe solved?

By adjusting the orbital speed of the earth in agreement with the law of Kepler