What is the degree of freedom of N-body problem?

Correct Answer : 3N

Explanation : The N-body problem has 3N degrees of freedom which makes use of 3N second order differential equations for finding the position of the particle.

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Why is it not possible to solve N-body problems analytically?

Result converge

It is time consuming

Lack of initial condition data

Closed form solution does not exist

Correct Answer : Option (D) : Closed form solution does not exist

Explanation : N-body problems are usually chaotic for initial conditions and require numerical method to compute the result. Analytical results cannot be obtained wince there no closed form solution existing. So far, two body problems and restricted 3-body problem can be solved.

Which of these is the simplest case of N-body problem?

One-body problem

Two-body problem

Three-body problem

Five-body problem

Correct Answer : Option (A) : One-body problem

Explanation : The simplest case of the N-body problem is a case which has only one body. In the entire space, there lies only one body with mass m. It experiences no force, acceleration and moves with a constant velocity.

What order of magnitude does the earth’s oblateness affect the gravitational forces?

10^-2 g’s

10^-3 g’s

10^-4 g’s

10^-5 g’s

Correct Answer : Option (B) : 10^-3 g’s

Explaination : There are certain variations introduced due to the earth’ oblateness effect. This force is of the order 10^-3 g’s. Newton’s law is only applicable for spherical objects.