# Explaining Escape Velocity: Zero KE and PE at r=infinite

• yasar1967
In summary, escape velocity is the minimum speed needed for an object to escape the gravitational pull of another object. At infinite distance, the potential energy is zero, leading to a total energy of zero. This means that the object will have zero kinetic energy as well. This is due to the object accelerating against gravity, causing the potential energy to decrease to zero. The escape velocity remains constant unless another force is applied.
yasar1967
Escape Velocity:
"An object given the escape speed will have zero kinetic energy at r=infinite, and the potential energy is defined to be zero at that point, so the total energy is 0"

I understand having zero potential energy at infinite distance but I do not correlate with having zero kinetic energy. Once you have given that escape velocity to the object it must have always that speed even even at the infinity unless another force is applied. So how could it be that it's kinetic energy will be zero?

The kinetic energy decreases to zero as the potential decreases to zero (because it is accelerating, against gravity). Gravity causes it to decrease (i.e. the escape velocity is the minimum needed to escape the field). Just a case of a limit.

That is a valid point. However, it is important to remember that escape velocity is the minimum velocity required for an object to escape the gravitational pull of a planet. Once the object reaches that velocity, it will continue to travel at a constant speed, without any additional force applied. At infinite distance, the object is no longer under the influence of the planet's gravitational pull and thus, has no kinetic energy. This does not mean that the object will come to a complete stop at infinite distance, but rather that its velocity will remain constant. It is also worth noting that in the real world, there will always be some external forces acting on the object, such as the gravitational pull of other celestial bodies, which may affect its velocity. However, for the purposes of understanding escape velocity, we assume a simplified scenario of a single planet with no external forces.

## 1. What is escape velocity?

Escape velocity is the minimum velocity required for an object to overcome the gravitational pull of a massive body, such as a planet or a star, and escape its gravitational field.

## 2. Why does an object have zero kinetic energy at r=infinite in the context of escape velocity?

At r=infinite, the object has escaped the gravitational pull of the massive body and is no longer under its influence. Therefore, it does not have any velocity and thus, zero kinetic energy.

## 3. How is escape velocity calculated?

The formula for calculating escape velocity is Ve = sqrt((2GM)/r), where Ve is the escape velocity, G is the gravitational constant, M is the mass of the massive body, and r is the distance between the object and the center of the massive body.

## 4. Can escape velocity be exceeded?

Yes, escape velocity can be exceeded if the object receives additional acceleration from other sources, such as a rocket boost. However, it is not necessary to exceed escape velocity in order to escape the gravitational pull of a massive body.

## 5. What factors affect escape velocity?

The factors that affect escape velocity are the mass of the massive body, the distance from the center of the massive body, and the object's mass. The greater the mass of the massive body or the closer the object is to the center of the massive body, the higher the escape velocity. Similarly, the higher the object's mass, the higher the escape velocity.

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