# How come escape velocity isn't imaginary?

• Jules Winnfield
In summary, escape velocity is equal to the potential energy and can be calculated using the formula $v=\sqrt{-2\frac{GM}{r}}$. It is the velocity that results in the sum of kinetic and potential energy being zero, with potential energy always being negative and kinetic energy always being positive.
Jules Winnfield
Going through several definitions, it appears that escape velocity is equal to the potential energy. That is:$$\frac{1}{2}m v^2=-\frac{G M m}{r}$$but if I solve for velocity, $v$, I get:$$v=\sqrt{-2\frac{G M}{r}}$$So how do I get an escape velocity that isn't imaginary?

It's the velocity such that the kinetic energy at launch is equal to the potential energy difference between infinity and the point of launch. So$$\frac 12mv^2=0-\left(-\frac{GMm}r\right)$$

Jules Winnfield said:
Going through several definitions, it appears that escape velocity is equal to the potential energy.

No, at escape velocity the sum of kinetic and potential energy is zero.

Ibix said:
It's the velocity such that the kinetic energy at launch is equal to the potential energy difference between infinity and the point of launch. So$$\frac 12mv^2=0-\left(-\frac{GMm}r\right)$$
That makes sense. Thank you for the clarification.

DrStupid said:
No, at escape velocity the sum of kinetic and potential energy is zero.
And in this sum PE is always negative so KE is always positive.

## 1. What is escape velocity?

Escape velocity is the minimum speed needed for an object to escape the gravitational pull of a celestial body, such as a planet or moon. It is usually measured in meters per second.

## 2. Why isn't escape velocity imaginary?

Escape velocity is a real and measurable value because it is based on the laws of physics and the strength of a celestial body's gravitational force. It is not a theoretical concept, but rather a practical calculation used in space exploration and other scientific fields.

## 3. How is escape velocity calculated?

The formula for calculating escape velocity is V = √(2GM/r), where V is the escape velocity, G is the universal gravitational constant, M is the mass of the celestial body, and r is the distance from the center of the celestial body to the object's starting point. This formula takes into account the mass and distance of the celestial body to determine the necessary speed for an object to escape its gravitational pull.

## 4. Can escape velocity be achieved?

Yes, escape velocity can be achieved with enough force and speed. It is commonly achieved by spacecraft during launch, as they need to reach a certain speed to break free from Earth's gravitational pull and enter orbit. However, achieving escape velocity in space travel is much more difficult and requires significantly more energy and speed.

## 5. Does escape velocity vary on different celestial bodies?

Yes, the escape velocity for an object will vary depending on the mass and size of the celestial body it is trying to escape from. For example, the escape velocity on the moon is much lower than on Earth because the moon has less mass and a weaker gravitational pull. Additionally, an object's shape and composition can also affect its escape velocity.

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