# What is negative and positive potential energy in Newtonian Mechanics?

In my latest post I became confused why potential energy would ever even be negative and what it even represents?

An individual who answered my question suggested that potential cannot be positive. Yet if you take a look at the picture from my past question, you see that the effective potential of an orbiting body should be positive beyond a point, can anyone clarify this for me? I am sorry if it is a stupid question but I've neglected a large part of Physics until now and focused more on Maths, now that I am starting to become more and more intrigued by this field, I am getting confused over these definitions. I've already had a post up for $$4$$ days and have become really fatigued over this question, can anyone please help me out?

(Side note: Can't find anything on this)

Long comment. You are confused because the two body problem can be analyzed in two different ways. The way in the picture you reference, analyzes the motion as if it were one dimensional, you discard information on angle and retain only r. You are in a reference frame that rotates with the mass, and the potential is not just the gravitational potential, but it also includes the centrifugal force. That is why it is labeled $$V_{eff}$$, effective potential. This one can become positive. The gravitational potential is an upside down hyperbola (V=-k/r), and can never be positive (if we define the potential to be zero when the particle is at infinity).

• Yes, a total positive energy implies that the object is not bounded.
– user65081
Jul 22, 2021 at 15:35
• Oh damn, that clarifies it for me. Is there any physical difference between positive and negative energy though? Jul 22, 2021 at 15:35
• Thank you man. That's all I needed, I am sorry for the stupid question, I really am. Jul 22, 2021 at 15:36
• It is not a stupid question! It can be shown that for the gravitational potentil E<0 implies an orbit,
– user65081
Jul 22, 2021 at 15:36
• The fact that energy can be negative really doesn't mean too much, because the definition of energy is always arbitrary. In this problem, it is convenient to define zero energy when the particle is infinitely far away and not moving, but you don't have to do that. All this does is shift your plot vertically.
– Garf
Jul 22, 2021 at 15:37