Name: launching a satellite beyond gravity
Uploaded: 2025-05-22T09:05:41.000Z
Duration: 1 min 26 s
Channel: JoVE

K12 Standards

Pennsylvania State Academic Standards

9-12

Earth and Space Science

Space Systems

3.3.9-12.A

Escape Velocity

Consider an object of mass m at a distance r1 from the Earth&#39;s center. Since this object is in the Earth&#39;s gravitational field, it possesses gravitational potential energy U1.
Suppose the object moves farther away at a distance r2 such that its potential energy changes to U2.
Following the energy conservation law, the sum of kinetic energy and potential energy at r1 equals the sum of kinetic energy and potential energy at r2.
Considering distance r2 as infinity, where Earth&#39;s gravitational field is negligible, the potential energy U2 is zero.
Theoretically,&#160;K2 is equal to zero, since the object becomes stationary at infinity. Substituting for kinetic energy and potential energy at r1, the object&#39;s velocity at r1 is equal to the square root of two times the product of the gravitational constant and Earth&#39;s mass, divided by r1.
Approximating r1 equal to the radius of the Earth, an expression for the object&#39;s escape velocity is obtained. It is the minimum initial velocity which an object requires to escape the Earth&#39;s gravitational field.

escape velocity

The escape velocity of an object is defined as the minimum initial velocity that it requires to escape the surface of another object to which it is gravitationally bound and never to return. For example, what would be the minimum velocity at which a satellite should be launched from the Earth&#39;s surface such that it just escapes the Earth&#39;s gravitational field?
To calculate the escape velocity, it is assumed that no energy is lost to any frictional forces. In practice, a satellite launched from the Earth&#39;s surface not only has to escape the Earth&#39;s gravitational field, but the Earth&#39;s atmosphere slows it down as well. Thus, the escape velocity calculated purely from gravitational energy considerations is smaller than the actual escape velocity.
It is also assumed that the satellite has zero velocity at infinity, where the Earth&#39;s gravitational force is zero. Since the escape velocity does not depend on the satellite&#39;s mass, it would be the same for any object, whether a satellite or a ball.
If an object is at a larger distance from the Earth&#39;s surface, for example, the Moon, it would need a smaller velocity to escape the Earth&#39;s gravitational field. This is unless the mass is directly heading towards the Earth and collides with it, giving rise to forces that are not just gravitational.
Alternatively, the escape velocity can be calculated by equating the total energy of a system, say the Earth and a satellite, to zero. The gravitational potential energy at large distances is conventionally assumed to be zero. Since the escape velocity is defined as the minimum velocity with which a satellite should be launched from the surface, its kinetic energy at infinity can also be assumed to be zero. Of course, if it is positive, it would go further away and never return. Thus, the velocity of interest is when the kinetic energy at infinity is zero; that is, the body just escapes the gravitational field.
Calculations reveal that the escape velocity from the Earth&#39;s surface, assuming no atmosphere, is about 11 km/s. In comparison, the escape velocity from the Sun&#39;s gravitational field is about 42 km/s at the Earth&#39;s distance. Spacecraft being launched from the Earth to escape the solar system would need to consider both factors.
This text is adapted from <a href="https://openstax.org/books/university-physics-volume-1/pages/13-3-gravitational-potential-energy-and-total-energy">Openstax, University Physics Volume 1, Section 13.3: Gravitational Potential Energy and Total Energy.</a>

The escape velocity of an object is defined as the minimum initial velocity that it requires to escape the surface of another object to which it is ...

Education

JoVE Core

Physics

Unit 1

Gravitation

KEY TERMS AND CONCEPTS

launching a satellite beyond gravity

Launching a satellite beyond gravity requires enough escape velocity to leave a planet or other body and never return. Escape velocity is the minimum initial speed needed to break free from the gravitational pull of an object that is holding the satellite in orbit or near its surface.

For Earth, the idea is often shown with a satellite launched from the ground. The calculation assumes that no energy is lost to friction. In real life, Earth’s atmosphere also slows the satellite down, so the true launch speed must be higher than the value found from gravity alone.

The escape speed depends on gravity, not on the mass of the object being launched. That means a satellite and a ball would need the same escape velocity if they started from the same place. An object that starts farther from Earth’s surface, such as the Moon, needs a smaller speed to escape Earth’s gravitational field, unless it is moving directly toward Earth and collides with it.

Escape velocity can also be found by using energy. In this method, the total energy of the Earth-satellite system is set to zero. Gravitational potential energy is taken as zero at very large distances, and the satellite is treated as having zero speed at infinity, where Earth’s gravity is zero. The escape condition is the point where the object just makes it out, so its kinetic energy at infinity is also zero.

For Earth, the escape velocity is about 11 km/s if the atmosphere is ignored. For the Sun’s gravitational field at Earth’s distance, the escape velocity is about 42 km/s. Spacecraft leaving Earth to travel out of the solar system must take both Earth’s gravity and the Sun’s gravity into account.

Launching a Satellite Beyond Gravity

gravitation

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Launching a satellite beyond gravity requires enough escape velocity to leave a planet or other body and never return. Escape velocity is the minimum initial speed needed to break free from the gravitational pull of an object that is holding the satellite in orbit or near its surface. For Earth, the idea is often shown with a satellite launched from the ground. The calculation assumes that no energy is lost to friction. In real life, Earth’s atmosphere also slows the satellite down, so the...

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key terms and concepts

Explore escape velocity, the minimum speed needed for a satellite to leave Earth or the Sun’s gravity. Learn why mass, atmosphere, and starting distance matter.

Launching a Satellite Beyond Gravity | JoVE K12

physics

JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

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

HS-ESS1-3

Tennessee Academic Standards

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

PHYS.PS2.9

Virginia  Standards of Learning

HIgh School

ES.2

ES.2.b

ES.2.c

PH.3

PH.3.b

new-jersey-student-learning-standards-for-science

New Jersey Student Learning Standards for Science

Earth's Place in the Universe

HS-ESS1-4

Florida Department of Education

SC.912.E.5

SC.912.E.5.6

SC.912.E.5.10

Physical Science

SC.912.P.10

SC.912.P.10.6

Texas Essential Knowledge and Skills

PHYS.5

PHYS.5.H

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

Earth and Space Science (ESS)

Earth’s Place in the Universe

E-ESS1-6.

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3.3.9-12.C

Launching a Satellite Beyond Gravity

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