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Consider a thought experiment (that I made when I was in high school) involving a universe with only two objects: a massive planet and a small asteroid. Initially, they are millions of light-years apart, with the asteroid slowly moving away from the planet at a velocity exceeding the escape velocity at that distance (1 cm/century). Assume Newtonian mechanics and gravity govern the system, with no relativity or universal expansion.

Suppose we have the ability to nudge the asteroid slightly towards the planet, giving it a minuscule velocity of 1 cm/millennium. Despite the minimal nudge, the asteroid will eventually be pulled back towards the planet due to their mutual gravity, ultimately colliding with significant kinetic energy. My question is: Where does this energy come from?

If we calculated the total mechanical energy (the sum of kinetic and potential energy) of the system in the initial state, when the asteroid and the planet are very far apart and the asteroid is moving away from the planet, we would get a very small positive value. But when we change the direction of the asteroid slightly towards the planet, we create a situation where the mechanical energy becomes very large and negative, because the potential energy becomes very large and negative as the asteroid approaches the planet. How is this possible? How can we create so much energy by just changing the direction of the asteroid a little bit?

I understand that there is still some gravitational potential energy between the asteroid and the planet even when they are very far apart, but it is very close to zero. As the asteroid moves closer to the planet, its speed increases because its potential energy becomes more negative and its kinetic energy becomes more positive. The total mechanical energy remains constant because gravity is a conservative force (it does not dissipate or create energy). When the asteroid reaches the surface of the planet, its speed reaches a maximum value because its potential energy reaches a minimum value .

But I still have some hard time believing that this is how it works, because it seems like we are creating energy out of nothing by just changing the direction of the asteroid, also that means that I have a potential energy from every galaxy or star in the universe and pretty much every object has also potential energy to something that they will never reach by gravity.

Following the logic above, wouldn't every object in the universe have potential energy with respect to every other object, even distant galaxies? Does this imply a vast amount of "unusable" potential energy throughout the universe, forever locked away and never convertible to other forms?

Consider a thought experiment (that I made when I was in high school) involving a universe with only two objects: a massive planet and a small asteroid. Initially, they are millions of light-years apart, with the asteroid slowly moving away from the planet at a velocity exceeding the escape velocity at that distance (1 cm/century). Assume only Newtonian mechanics , with no relativity or universal expansion.

Suppose we have the ability to nudge the asteroid slightly towards the planet, giving it a minuscule velocity of 1 cm/millennium. Despite the minimal nudge, the asteroid will eventually be pulled back towards the planet due to their mutual gravity, ultimately colliding with significant kinetic energy. My question is: Where does this energy come from?

If we calculated the total mechanical energy (the sum of kinetic and potential energy) of the system in the initial state, when the asteroid and the planet are very far apart and the asteroid is moving away from the planet, we would get a very small positive value. But when we change the direction of the asteroid slightly towards the planet, we create a situation where the mechanical energy becomes very large and negative, because the potential energy becomes very large and negative as the asteroid approaches the planet. How is this possible? How can we create so much energy by just changing the direction of the asteroid a little bit?

I understand that there is still some gravitational potential energy between the asteroid and the planet even when they are very far apart, but it is very close to zero. As the asteroid moves closer to the planet, its speed increases because its potential energy becomes more negative and its kinetic energy becomes more positive. The total mechanical energy remains constant because gravity is a conservative force (it does not dissipate or create energy). When the asteroid reaches the surface of the planet, its speed reaches a maximum value because its potential energy reaches a minimum value .

But I still have some hard time believing that this is how it works, because it seems like we are creating energy out of nothing by just changing the direction of the asteroid, also that means that I have a potential energy from every galaxy or star in the universe and pretty much every object has also potential energy to something that they will never reach by gravity.

Following the logic above, wouldn't every object in the universe have potential energy with respect to every other object, even distant galaxies? Does this imply a vast amount of "unusable" potential energy throughout the universe, forever locked away and never convertible to other forms? In this hypothetical scenario, there is no way for anyone on the planet to know that there is potential energy stored in some too-far-to-see asteroid. The existence of this potential energy doesn't affect the planet's current state or its ability to perform measurements.

I have a question that I made up when I was in high school in first year when we started physics and potential energy and something like that. The question goes like this:

Imagine the universe has only two objects, an asteroid and a planet. They are millions of light-years apart and the asteroid is moving very slowly away from the planet with a velocity of 1 centimeter per year. This velocity is greater than the escape velocity of the planet because the planet is too far away. Assume that Newton’s laws of motion and gravity are the only ones that apply, and ignore any effects of relativity or the expantion of the universe . Also assume that you have enough power to change the direction of the asteroid slightly towards the planet. It won’t take much energy, but even if you make it go towards the planet with a velocity of 1 centimeter per century, it will eventually reach the planet and crash into it. And as you know, the crash will release a lot of kinetic energy, which is equal to the change in potential energy. This kinetic energy seems to come out of nowhere. Here is my question: where does this energy come from?

If we calculated the total mechanical energy (the sum of kinetic and potential energy) of the system in the initial state, when the asteroid and the planet are very far apart and the asteroid is moving away from the planet, we would get a very small positive value. But when we change the direction of the asteroid slightly towards the planet, we create a situation where the mechanical energy becomes very large and negative, because the potential energy becomes very large and negative as the asteroid approaches the planet. How is this possible? How can we create so much energy by just changing the direction of the asteroid a little bit? I understand that there is still some gravitational potential energy between the asteroid and the planet even when they are very far apart, but it is very close to zero. As the asteroid moves closer to the planet, its speed increases because its potential energy becomes more negative and its kinetic energy becomes more positive. The total mechanical energy remains constant because gravity is a conservative force (it does not dissipate or create energy). When the asteroid reaches the surface of the planet, its speed reaches a maximum value because its potential energy reaches a minimum value (equal to minus infinity). The mechanical energy stays constant because the kinetic energy equals minus infinity plus a finite value.

But I still have some hard time believing that this is how it works, because it seems like we are creating energy out of nothing by just changing the direction of the asteroid. I mean, if we have some galactic calculators that can calculate all the amount of energy in the whole universe, and in my scenario there are only a planet and an asteroid, I don’t think they would count this potential energy as part of the total energy. And also that means that I have a potential energy from every galaxy or star in the universe and pretty much every object has also potential energy to something that they will never reach by gravity. Does that mean there are a lot of energy in the universe that is totally lost as it is in form of potential energy that will never turn to kinetic energy or any other form of energy?

Consider a thought experiment (that I made when I was in high school) involving a universe with only two objects: a massive planet and a small asteroid. Initially, they are millions of light-years apart, with the asteroid slowly moving away from the planet at a velocity exceeding the escape velocity at that distance (1 cm/century). Assume Newtonian mechanics and gravity govern the system, with no relativity or universal expansion.

Suppose we have the ability to nudge the asteroid slightly towards the planet, giving it a minuscule velocity of 1 cm/millennium. Despite the minimal nudge, the asteroid will eventually be pulled back towards the planet due to their mutual gravity, ultimately colliding with significant kinetic energy. My question is: Where does this energy come from?

If we calculated the total mechanical energy (the sum of kinetic and potential energy) of the system in the initial state, when the asteroid and the planet are very far apart and the asteroid is moving away from the planet, we would get a very small positive value. But when we change the direction of the asteroid slightly towards the planet, we create a situation where the mechanical energy becomes very large and negative, because the potential energy becomes very large and negative as the asteroid approaches the planet. How is this possible? How can we create so much energy by just changing the direction of the asteroid a little bit?

I understand that there is still some gravitational potential energy between the asteroid and the planet even when they are very far apart, but it is very close to zero. As the asteroid moves closer to the planet, its speed increases because its potential energy becomes more negative and its kinetic energy becomes more positive. The total mechanical energy remains constant because gravity is a conservative force (it does not dissipate or create energy). When the asteroid reaches the surface of the planet, its speed reaches a maximum value because its potential energy reaches a minimum value .

But I still have some hard time believing that this is how it works, because it seems like we are creating energy out of nothing by just changing the direction of the asteroid, also that means that I have a potential energy from every galaxy or star in the universe and pretty much every object has also potential energy to something that they will never reach by gravity.

Following the logic above, wouldn't every object in the universe have potential energy with respect to every other object, even distant galaxies? Does this imply a vast amount of "unusable" potential energy throughout the universe, forever locked away and never convertible to other forms?