Which of these problems helps us in analyzing motion of multiple celestial objects?

Euler problem

Kepler problem

Two-body problem

N-body problem

Correct Answer : N-body problem

Explanation : When we have o predict and analyze the motion of multiple celestial objects in the sky as a result of their gravitational forces acting on each other, we use N-body problem to solve the dynamics.

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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.