Escape Velocity is a fundamental concept in astrophysics and space exploration. It refers to the minimum speed needed for an object to break free from the gravitational field of a celestial body, like a planet or moon, without further propulsion.
Imagine an object travelling at escape velocity, eventually reaching faraway enough to finally escape the effect of gravity. By Newton’s universal law of gravitation, this scenario can only occur at r = ∞ since:
g=GM/r²
K+U=0
½mv²=GMm/r
v²=2GM/r
vesc=√2GM/r
We can use this equation to determine the minimal velocity required to allow an object to escape the gravitational field it is in.
Like orbital velocity, escape velocity is independent of the mass of the object that tries to escape the gravitational field. Escape velocity is only dependent on the mass MM whose gravitational field the object is escaping from, and the distance of the object from the centre of this mass, r.
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Derivation of Escape Velocity Formula
To escape the gravitational field of a celestial body, an object must overcome the pull of gravity exerted by that body. This requires the object to have sufficient kinetic energy to counteract the gravitational potential energy holding it in place.Imagine an object travelling at escape velocity, eventually reaching faraway enough to finally escape the effect of gravity. By Newton’s universal law of gravitation, this scenario can only occur at r = ∞ since:
g=GM/r²
- As a mass travels away from the centre of a gravitational field, its kinetic energy is transformed to gravitational potential energy. Therefore, kinetic energy decreases while gravitational potential energy increases.
- At r = ∞ both gravitational potential and kinetic energy of the object both become zero. Therefore, the final total energy also becomes zero.
- By using law of conservation of energy, the initial total energy must be equal to the final total energy which is zero:
K+U=0
½mv²=GMm/r
v²=2GM/r
vesc=√2GM/r
We can use this equation to determine the minimal velocity required to allow an object to escape the gravitational field it is in.
Like orbital velocity, escape velocity is independent of the mass of the object that tries to escape the gravitational field. Escape velocity is only dependent on the mass MM whose gravitational field the object is escaping from, and the distance of the object from the centre of this mass, r.
HSC Physics: Escape Velocity Explained – Science Ready
This topic is part of the HSC Physics syllabus under the section Motion in Gravitational Fields. HSC Physics Syllabus Derive quantitatively and apply the concepts of gravitational force and gravitational potential energy in radial gravitational fields to a variety of situations, including but...
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