Conservative forces and systems

[Aniket1]

I read in a book that if the constraint forces do work, the system is conservative, else it's nonconservative. In that case, consider a system of two bodies moving in an elliptical path under gravitational attraction. Since the gravitational force is continuously doing work on the particles, by the above definition, gravitation is a nonconservative force and the system is nonconservative. However, the mechanical energy of the system remains constant and in Newtonian mechanics, gravitation is classifed under conservative force. Can someone explain where am I going wrong.

 

[russ_watters]

Are you counting the kinetic and potential energy of the orbiting object?

 

[Aniket1]

Yes.

 

[WannabeNewton]

What book did you read this in?

 

[mickybob]

I read in a book that if the constraint forces do work, the system is conservative, else it's nonconservative. In that case, consider a system of two bodies moving in an elliptical path under gravitational attraction. Since the gravitational force is continuously doing work on the particles, by the above definition, gravitation is a nonconservative force and the system is nonconservative. However, the mechanical energy of the system remains constant and in Newtonian mechanics, gravitation is classifed under conservative force. Can someone explain where am I going wrong.

Gravity is not a constraint force.

The term 'constraint force' is used to describe forces that essentially act to impose boundary conditions. An example is the reaction force of the ground on you, stopping you falling through it.

Generally these forces don't do work, since they don't act through any distance.

So the question of them being conservative or non-conservative is meaningless.