Name: escape velocity limits and black holes
Uploaded: 2025-05-22T09:05:41.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Pennsylvania State Academic Standards

9-12

Earth and Space Science

Space Systems

3.3.9-12.B

Schwarzschild Radius and Event Horizon

An imaginary projectile launched from the Sun&#39;s surface would require a velocity of 618 km/s to escape the Sun&#39;s gravitational field.
Now, suppose the Sun&#39;s radius is reduced by half, keeping its mass constant. Then its escape velocity would increase to 873 km/s. If the radius is decreased further, eventually to 2.9 km, the escape velocity will equal the speed of light.
Recall that the escape velocity of a projectile depends on the mass and radius of the object from which it is launched.
In general, the radius at which any mass has an escape velocity equal to the speed of light is called the Schwarzschild radius. Therefore, Schwarzschild radius equals twice the product of gravitational constant and the object&#39;s mass divided by the square of light&#39;s speed.
Any spherical non-rotating object having a radius smaller than its Schwarzschild radius is called a black hole.&#160;
The spherical surface surrounding the black hole, at Schwarzschild radius,&#160; is known as the event horizon, inside which the escape velocity is greater than the speed of light.

schwarzschild radius and event horizon

No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely high gravitational fields.
The minimum speed required to launch a projectile from the surface of an object to which it is gravitationally bound&#160;so that it eventually escapes the object&#8217;s gravitational field&#160;is called the escape velocity. The escape velocity is independent of the mass of the object. Merging the idea of escape velocity with the maximum speed with which matter can travel leads to the concepts of the Schwarzschild radius, black holes, and event horizons.
If an object is sufficiently dense, it collapses upon itself and is surrounded by an event horizon from which nothing can escape. The name for such an object, &#34;black hole,&#34;&#160;was coined by astronomer John Wheeler in 1969. It refers to the fact that even light cannot escape such an object. Karl Schwarzschild was the first person to note this phenomenon in 1916, but at that time, it was considered to be a mathematical curiosity.
Although a black hole cannot be directly observed because light does not escape its event horizon, there is overwhelming evidence that black holes exist in the universe. Their effects on nearby stars and infalling matter are typically interpreted by making astronomical observations.
This text is adapted from <a href="https://openstax.org/books/university-physics-volume-1/pages/13-7-einsteins-theory-of-gravity">Openstax, University Physics Volume 1, Section 13.7: Einstein&#39;s Theory of Gravity.</a>

No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely ...

Education

JoVE Core

Physics

Unit 1

Gravitation

KEY TERMS AND CONCEPTS

escape velocity limits and black holes

Escape velocity helps explain how black holes and event horizons form. It is the minimum speed a projectile needs to leave the surface of an object and eventually escape its gravitational field. In this context, escape velocity does not depend on the mass of the object being launched.

The key idea is that no object with finite mass can move faster than the speed of light in a vacuum. When escape velocity is compared with that speed limit, the Schwarzschild radius becomes important. If an object is dense enough, it can collapse under its own gravity and form an event horizon. Nothing can escape from inside that boundary.

An object like this is called a black hole. The name was coined by astronomer John Wheeler in 1969, and it describes the fact that even light cannot get out. Karl Schwarzschild first described this phenomenon in 1916, but it was then treated as a mathematical curiosity.

Black holes cannot be seen directly because light does not leave the event horizon. Even so, there is strong evidence that they exist in the universe. Astronomers study their effects on nearby stars and on matter falling toward them to infer their presence.

Escape Velocity Limits and Black Holes

gravitation

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Escape velocity helps explain how black holes and event horizons form. It is the minimum speed a projectile needs to leave the surface of an object and eventually escape its gravitational field. In this context, escape velocity does not depend on the mass of the object being launched. The key idea is that no object with finite mass can move faster than the speed of light in a vacuum. When escape velocity is compared with that speed limit, the Schwarzschild radius becomes important. If an...

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key terms and concepts

Learn how escape velocity, the Schwarzschild radius, and event horizons explain why black holes trap even light and how astronomers detect them.

Escape Velocity Limits and Black Holes | JoVE K12

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3.3.9-12.D

Louisiana Student Standards for Science

High School

Earth Science

Earth’s Place In The Universe

HS-ESS1-1

HS-ESS1-2

Virginia  Standards of Learning

HIgh School

ES.2

ES.2.a

ES.2.d

Alabama Course of Study Science

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Florida Department of Education

SC.912.E.5

SC.912.E.5.6

SC.912.E.5.10

Physical Science

SC.912.P.12

SC.912.P.12.7

Georgia Standards of Excellence

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SAST4

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Escape Velocity Limits and Black Holes

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