I have always thought of G.P.E as how much a constrained body wants to fall in the direction of Gravitational Force Feild.But a while back i came across the concept of Gravitational Binding Energy. The book said that it was the Modulus of G.P.E and it was the energy by which an object is bound to earth. So now do i have to think of G.P.E as the energy by which a object is bound to earth? And why should i supply this much energy to the body as Kinetic energy to separate the body from earth when the only reason its still bound is the Gravitational Force? I am sorry if the question is confusing as i spent few hours thinking of this and got confused.
Gravitational Binding energy is how much energy you would have to supply to remove an object from the Earth to "infinity". This only changes if you change the mass of the object you want to remove or you change the object you are removing it from. (IE the GBE changes for a 1kg block if you look at how much it takes to remove it from Mars instead of the Earth.) Gravitational Potential Energy is how much potential energy an object has based on its location in a gravitational field. IE a rock held up at 10 feet in the air has more GPE than a rock held at 5 feet in the air. Does that make sense?
Thanks. After some thinking i figured out about P.E. If a body has to escape the Gravitational Field of earth then it must be taken to a position where G.P.E is zero,right? if i supply a body with enough force( = Work done = Change in Energy??) it would probably move away from earth , But that is thinking the P.E. is constant. But doesnt G.P.E increase as we go up? SO can one say that G.B.E is constant?
interesting... I have come across the phrase "gravitational binding energy" to mean something different. When I have seen it, it means the total gravitational potential energy of a collection of objects. In other words, the energy required to move all those objects infinitely far away from every other one. I have seen this in questions about the gravitational binding energy of a planet. So in that case, it means the energy required to completely take apart all the matter which makes up the planet, and remove it all infinitely far away. (In that case, it is continuous matter, not a discrete set of objects, but the maths is pretty similar). Maybe your book was using "gravitational binding energy" in the sense I am talking about here. Or maybe not. It is difficult to tell, without knowing what the sentence was specifically..
No, it must be given enough energy so that the gravitational field of the Earth will never pull it back down. The potential energy will constantly increase, and the object will constantly decelerate, but since the strength of gravity falls off with distance, if we launch it with a high enough velocity the object will never fully stop. If you assume an object is "infinitely far away" from the Earth and you allow that object to come straight towards the Earth under the force of gravity, it will impact the Earth with X amount of energy. This energy, when the object was AT infinity, was gravitational potential energy. Right before it impacted the Earth it was all kinetic energy instead. Ignoring losses from air resistance and other factors, this same amount of energy must be given to an object in the form of kinetic energy to launch it back out "to infinity". Does that make sense?