What is the assumption while solving restricted three-body problem?

Orbits are circular

Mass of one of the bodies is negligible

Their positions don�t change over time t

The gravitational force exerted on each other cancels out

Correct Answer : Mass of one of the bodies is negligible

Explanation : In case of restricted three-body problem, it is a simplified version of three-body problem where it is assumed that one of the masses is almost negligible compared to the other two. This m1 and m2 move in Keplerian orbit which is unaffected by m3.

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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.