# If an object runs an infinite distance in universe....?

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• Noduagga
In summary: If an object falls from infinity, it will gain an amount of energy equal to \frac{GMm}{R0} which is a finite quantity.
Noduagga
...(after infinite distance) falls into earth, would exist infinite potential energy if E=mgh and h is infinite?

Since it would take an infinite amount of time, it would never happen.

If you are asking whether any object at an infinite distance from the Earth has infinite potential energy, the answer is no, absolutely not and it is easy to see why if you study "escape velocity".

Irrelevant, anything at infinity has no influence on the observable universe

Chronos said:
Irrelevant, anything at infinity has no influence on the observable universe
Everybody remember infinity is a "concept" (a very useful one) but not a physical "thing!"

Noduagga said:
...(after infinite distance) falls into earth, would exist infinite potential energy if E=mgh and h is infinite?

I think the real answer to your question is that E = mgh is just an approximation for small values of h near the Earth's surface. The full equation for the potential energy of an object of mass m at a distance R from the Earth's center is that E = -GMm/R, where M is the mass of the Earth, and G is Newton's constant of gravitation. Near the Earth's surface, R is approximately constant, so we can write
R = R0 + h where h <<R. Then the potential energy can be approximated by $$E=-\frac{GMm}{R0+h} \approx -\frac{GMm}{R0}(1-h/R0) = -\frac{GMm}{R0} +\frac{GM}{R0^2} mh$$ Then, for changes in the potential energy, we ignore the first term, since it doesn't change, and we call the quantity $$\frac{GM}{R0^2}$$ g, and then you have your formula E=mgh. So if you use the full formula, even an object falling from infinity only gains an amount of energy equal to $$\frac{GMm}{R0}$$, which is a finite quantity.

Drakkith
Noduagga said:
...(after infinite distance) falls into earth, would exist infinite potential energy if E=mgh and h is infinite?
E=mgh is only an approximation, valid for objects near the Earth's surface.

## 1. How is it possible for an object to run an infinite distance in the universe?

According to the theory of relativity, space is infinite and expanding. This means that an object can theoretically run forever without reaching an end point.

## 2. Is there a limit to how far an object can run in the universe?

Based on current scientific understanding, there is no limit to how far an object can run in the universe. However, factors such as the object's speed and the expansion of the universe may affect the distance it can cover.

## 3. What would happen if an object were to run an infinite distance in the universe?

If an object were to somehow run an infinite distance in the universe, it would continue moving at a constant speed without ever reaching an end point. This is because the universe is constantly expanding, so there would always be more space for the object to move into.

## 4. Can an object really run forever without stopping or slowing down?

In theory, yes, an object can run forever in the universe without stopping or slowing down. However, this would require the object to have an infinite source of energy, which is currently not possible according to the laws of physics.

## 5. How does the concept of infinity apply to an object running in the universe?

The concept of infinity in this context refers to the idea that the object can continue moving without reaching an end point, rather than an actual infinite distance. It is a theoretical concept that helps us understand the vastness and expansion of the universe.

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