What is an Escape Velocity?

by Carson
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The escape velocity is the relative velocity that an object needs to reach relative to the celestial body so that the object can completely escape the gravitational field of the celestial object. While this might seem simple, there is more to how the escape velocity works and how to determine escape velocities. Find out about them in this article.

Getting to the Escape Velocity

When you adjust the relative velocity of an object launching out of a celestial object, things get interesting. We’re going to use Earth as an example in this section. At first, if you are only throwing it at a plodding speed like a few kilometers per hour, it quickly falls back to Earth. At that time, it’s at the orbit’s apoapsis, ready to fall towards the center of the Earth. However, if the object is thrown at a higher speed, like a few thousand kilometers an hour, the object will stay in the air for a significant amount of time but will eventually fall towards a periapsis below the surface of the Earth.

However, when the object is accelerated to be traveling at 8 kilometers per second relative to Earth, it is in a stable orbit around the Earth with almost no altitude change. The object is essentially falling around Earth. When you increase the velocity further, the object will get farther away from the planet. However, it will eventually stop increasing its altitude and fall back down. Finally, when the object reaches 11.2 kilometers per second, it simply escapes from Earth’s gravitational field instead of orbiting our planet. The orbit it takes is parabolic, meaning that it has an eccentricity of greater than 1.

However, this is only the escape velocity from the surface of our planet. This sentence is said because escape velocity also depends on distance. For instance, while the escape velocity from the surface of Earth exceeds 11 kilometers per second, if the distance from the surface of Earth is its radius, the escape velocity is only about 8 kilometers per second. Specifically, there is a formula for the escape velocity:

Where g is the gravitational constant, m is the object’s mass, and r is the radius of the object.

The First Cosmic Velocity

The first cosmic velocity is the relative speed at which an object can orbit a celestial object with an eccentricity of zero (i.e., the periapsis and the apoapsis are the same). Therefore, if the escape velocity of 11.2 kilometers per second, the first cosmic velocity at that place will be 11.2 km/s / √2, which is approximately 7.9 kilometers per second. It is precisely the velocity we mentioned at the beginning of the second paragraph of the last section.

A diagram showing the orbit a spacecraft will take if it has reached the first cosmic velocity relative to the celestial object
Image created using Canva

Black Holes

Black holes are at the extreme of the spectrum of escape velocities. They are theorized to contain an infinitely dense space called the singularity, and that density leads to the high escape velocity of black holes. In fact, the Schwarzschild radius, which is the distance between the event horizon and the singularity, is defined to be the point where the escape velocity from this black hole is precisely the speed of light. Any closer to the black hole, and the escape velocity will exceed the speed of light. Thus it would become physically impossible to escape from the singularity at that point, so we cannot see black holes directly.

Conclusion

In this article, we’ve mentioned the definition of an escape velocity, how the escape velocity is computed, the first cosmic velocity, and the special case for black holes. If you want to learn more about this fundamental concept, please visit the webpages in the references below.

References and Credits

  1. (n.d.). What is Escape Velocity? Retrieved March 2, 2022, from https://astrocampschool.org/escape-velocity/
  2. Mastyna, K. (n.d.). The cosmic velocities. Retrieved March 2, 2022, from https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.716.2417&rep=rep1&type=pdf
  3. (n.d.). Schwarzschild Radius. Retrieved March 2, 2022, from https://astronomy.swin.edu.au/cosmos/s/Schwarzschild+Radius

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