Title page of the 1st edition of Isaac Newton's Principia defining the laws of motion.

In classical mechanics, linear momentum or translational momentum (pl. momenta; SI unit kg•m/s, or, equivalently, N•s) is the product of the mass and velocity of an object:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{p} \equiv m\mathbf{v}.

Like velocity, linear momentum is a vector quantity, possessing a direction as well as a magnitude. Linear momentum is also a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum cannot change. Although originally expressed in Newton's second law, the conservation of linear momentum also holds in special relativity and, with appropriate definitions, a (generalized) linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, and general relativity. In relativistic mechanics, non-relativistic linear momentum is further multiplied by the Lorentz factor.

History of the concept[link]

Mōmentum was not merely the motion, which was mōtus, but was the power residing in a moving object, captured by today's mathematical definitions. A mōtus, "movement", was a stage in any sort of change,^[1] while velocitas, "swiftness", captured only speed. The concept of momentum in classical mechanics was originated by a number of great thinkers and experimentalists. The first of these was Byzantine philosopher John Philoponus, in his commentary to Aristotle´s Physics. As regards the natural motion of bodies falling through a medium, Aristotle's verdict that the speed is proportional to the weight of the moving bodies and indirectly proportional to the density of the medium is disproved by Philoponus through appeal to the same kind of experiment that Galileo was to carry out centuries later.^[2] This idea was refined by the European philosophers Peter Olivi and Jean Buridan. Buridan referred to impetus being proportional to the weight times the speed.^[3][4] Moreover, Buridan's theory was different to his predecessor's in that he did not consider impetus to be self dissipating, asserting that a body would be arrested by the forces of air resistance and gravity which might be opposing its impetus.^[5]

René Descartes believed that the total "quantity of motion" in the universe is conserved, where the quantity of motion is understood as the product of size and speed. This should not be read as a statement of the modern law of momentum, since he had no concept of mass as distinct from weight and size, and more importantly he believed that it is speed rather than velocity that is conserved. So for Descartes if a moving object were to bounce off a surface, changing its direction but not its speed, there would be no change in its quantity of motion.^[6] Galileo, later, in his Two New Sciences, used the Italian word "impeto".

The extent to which Isaac Newton contributed to the concept has been much debated. The answer is apparently nothing, except to state more fully and with better mathematics what was already known. Yet for scientists, this was the death knell for Aristotelian physics and supported other progressive scientific theories (i.e., Kepler's laws of planetary motion). Conceptually, the first and second of Newton's Laws of Motion had already been stated by John Wallis in his 1670 work, Mechanica sive De Motu, Tractatus Geometricus: "the initial state of the body, either of rest or of motion, will persist" and "If the force is greater than the resistance, motion will result".^[7] Wallis uses momentum and vis for force. Newton's Philosophiæ Naturalis Principia Mathematica, when it was first published in 1687, showed a similar casting around for words to use for the mathematical momentum. His Definition II^[8] defines quantitas motus, "quantity of motion", as "arising from the velocity and quantity of matter conjointly", which identifies it as momentum.^[9] Thus when in Law II he refers to mutatio motus, "change of motion", being proportional to the force impressed, he is generally taken to mean momentum and not motion.^[10] It remained only to assign a standard term to the quantity of motion. The first use of "momentum" in its proper mathematical sense is not clear but by the time of Jenning's Miscellanea in 1721, four years before the final edition of Newton's Principia Mathematica, momentum M or "quantity of motion" was being defined for students as "a rectangle", the product of Q and V, where Q is "quantity of material" and V is "velocity", s/t.^[11]

The Oxford English Dictionary dates the first print use of the word to 1699: John Keill, Reflections upon the Theory of the earth [written by himself] occasion'd by a late Examination of it, a letter (London).^[12]

Some languages, such as French and Italian still lack a single term for momentum, and use a phrase such as the literal translation of "quantity of motion". In Bulgarian and in Dutch the linear momentum is typically referred to as impulse, while the angular momentum is called momentum and the impulse has no distinct name.

Linear momentum of a particle[link]

Newton's apple in Einstein's elevator. In person A's frame of reference, the apple has non-zero velocity and momentum. In the elevator's and person B's frames of reference, it has zero velocity and momentum.

If an object is moving in any reference frame, then it has momentum in that frame. It is important to note that momentum is frame dependent. That is, the same object may have a certain momentum in one frame of reference, but a different amount in another frame. For example, a moving object has momentum in a reference frame fixed to a spot on the ground, while at the same time having 0 momentum in a reference frame attached to the object's center of mass.

The amount of momentum that an object has depends on two physical quantities: the mass and the velocity of the moving object in the frame of reference. In physics, the usual symbol for momentum is a boldface p (bold because it is a vector); so this can be written

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{p}= m \mathbf{v}\,,

where p is the momentum, m is the mass and v is the velocity.

Example: a model airplane of 1 kg traveling due north at 1 m/s in straight and level flight has a momentum of 1 kg•m/s due north measured from the ground. To the dummy pilot in the cockpit it has a velocity and momentum of zero.

According to Newton's second law, the rate of change of the momentum of a particle is proportional to the resultant force acting on the particle and is in the direction of that force. The derivation of force from momentum is given below.

Failed to parse (Missing texvc executable; please see math/README to configure.): \sum{\mathbf{F}} = {d\mathbf{p} \over dt} = m{d\mathbf{v} \over dt} + \mathbf{v}{dm \over dt}

Given that mass is constant, the second term of the derivative is zero (Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle \mathbf{v}{dm \over dt} = 0 ). We can therefore write the following:

Failed to parse (Missing texvc executable; please see math/README to configure.): \sum{\mathbf{F}} = m\mathbf{a}\,

or just simply

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{F}= m \mathbf{a}\,,

where F is understood to be the net force (or resultant).

Example: a model airplane of 1 kg accelerates from rest to a velocity of 1 m/s due north in 1 s. The thrust required to produce this acceleration is 1 newton. The change in momentum is 1 kg•m/s. To the dummy pilot in the cockpit there is no change of momentum. Its pressing backward in the seat is a reaction to the unbalanced thrust, shortly to be balanced by the drag.

Linear momentum of a system of particles[link]

Relating to mass and velocity[link]

The linear momentum of a system of particles is the vector sum of the momenta of all the individual objects in the system:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{p}= \sum_{i = 1}^n m_i \mathbf{v}_i = m_1 \mathbf{v}_1 + m_2 \mathbf{v}_2 + m_3 \mathbf{v}_3 + \cdots + m_n \mathbf{v}_n\,,

where p is the total momentum of the particle system, m_i and v_i are the respective mass and velocity of the i-th object, and n is the number of objects in the system.

It can be shown that, in the center of mass frame the momentum of a system is zero. Additionally, the momentum in a frame of reference that is moving at a velocity v_cm with respect to that frame is simply:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{p}= m\mathbf{v}_\text{cm}\,,

where:

Failed to parse (Missing texvc executable; please see math/README to configure.): m=\sum_{i = 1}^n m_i\,.

This is known as Euler's first law.^[13][14]

Relating to force – general equations of motion[link]

Motion of a material body

The linear momentum of a system of particles can also be defined as the product of the total mass, m, of the system times the velocity, v_cm, of the center of mass.

Failed to parse (Missing texvc executable; please see math/README to configure.): \sum{\mathbf{F}} = {d\mathbf{p} \over dt}= m \frac{d\mathbf{v}_{cm}}{dt}=m\mathbf{a}_{cm}\,

This is a special case of Newton's second law (if mass is constant).

For a more general derivation using tensors, we consider a moving body (see Figure), assumed as a continuum, occupying a volume V, at a time t, having a surface area S, with defined traction or surface forces per unit area represented by the stress vector Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle T_i^{(n)}\,

acting on every point of every body surface (external and internal), body forces Fi per unit of volume on every point within the volume V, and a velocity field vi, prescribed throughout the body. Following the previous equation, the linear momentum of the system is:

Failed to parse (Missing texvc executable; please see math/README to configure.): \int_S T_i^{(n)}dS + \int_V F_i dV = \frac{d}{dt}\int_V \rho\, v_i\, dV\,.

By definition the stress vector is defined as Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle T_i^{(n)} \equiv \sigma_{ij}n_j\, , then

Failed to parse (Missing texvc executable; please see math/README to configure.): \int_S \sigma_{ij}n_j\, dS + \int_V F_i\, dV = \frac{d}{dt}\int_V \rho\, v_i\, dV\,.

Using the Gauss's divergence theorem to convert a surface integral to a volume integral gives (we denote Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle \partial_j \equiv \frac{\partial}{\partial x_j}\,

as the differential operator):

Failed to parse (Missing texvc executable; please see math/README to configure.): \int_V \partial_j\sigma_{ij}\, dV + \int_V F_i\, dV = \frac{d}{dt}\int_V \rho\,v_i\, dV\,.

Now we only need to take care of the right side of the equation. We have to be careful, since we cannot just take the differential operator under the integral. This is because while the motion of the continuum body is taking place (the body is not necessarily solid), the volume we are integrating on can change with time too. So the above integral will be:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{d}{dt}\int \rho\,v_i\, dV=\int \frac{\partial (\rho v_i)}{\partial t}\, dV +\oint \rho v_i v_k n_k dA\,.

Performing the differentiation in the first part, and applying the divergence theorem on the second part we obtain:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{d}{dt}\int \rho\,v_i\, dV =\int \left[ \left(\rho\frac{\partial v_i}{\partial t}+v_i\frac{\partial \rho}{\partial t}\right)+\partial_k (\rho v_i v_k)\right]\, dV\,.

Now the second term inside the integral is: Failed to parse (Missing texvc executable; please see math/README to configure.): \partial_k (\rho v_i v_k)=\rho v_k \cdot \partial_k v_i +v_i\partial_k(\rho v_k)\,.

Plugging this into the previous equation, and rearranging the terms, we get:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{d}{dt}\int \rho\,v_i\, dV=\int\rho\left[\frac{\partial}{\partial t}+v_k\partial_k\right]v_i\,dV +\int\left[\frac{\partial\rho}{\partial t}+\partial_k(\rho v_k)\right]v_i\,dV\,.

We can easily recognize the two integral terms in the above equation. The first integral contains the convective derivative of the velocity vector, and the second integral contains the change and flow of mass in time. Now lets assume that there are no sinks and sources in the system, that is mass is conserved, so this term is zero. Hence we obtain:

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{d}{dt}\int \rho\,v_i\, dV=\int \rho\,\frac{Dv_i}{Dt}\, dV\,

putting this back into the original equation:

Failed to parse (Missing texvc executable; please see math/README to configure.): \int_V \left[ \partial_j\sigma_{ij} + F_i - \rho \frac{D v_i}{Dt}\right]\, dV = 0\,.

For an arbitrary volume the integrand itself must be zero, and we have the Cauchy's equation of motion

Failed to parse (Missing texvc executable; please see math/README to configure.): \partial_j\sigma_{ij} + F_i = \rho \frac{D v_i}{Dt}\,.

As we see the only extra assumption we made is that the system doesn't contain any mass sources or sinks, which means that mass is conserved. So this equation is valid for the motion of any continuum, even for that of fluids. If we are examining elastic continua only then the second term of the convective derivative operator can be neglected, and we are left with the usual time derivative, of the velocity field.

If a system is in equilibrium, the change in momentum with respect to time is equal to 0, as there is no acceleration

Failed to parse (Missing texvc executable; please see math/README to configure.): \sum{\mathbf{F}} = {d\mathbf{p} \over dt}=\ m\mathbf{a}_{cm}= 0\,

or using tensors,

Failed to parse (Missing texvc executable; please see math/README to configure.): \partial_j\sigma_{ij} + F_i = 0\,.

These are the equilibrium equations which are used in solid mechanics for solving problems of linear elasticity. In engineering notation, the equilibrium equations are expressed in Cartesian coordinates as

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\partial \sigma_x}{\partial x} + \frac{\partial \tau_{yx}}{\partial y} + \frac{\partial \tau_{zx}}{\partial z} + F_x = 0\,

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\partial \tau_{xy}}{\partial x} + \frac{\partial \sigma_y}{\partial y} + \frac{\partial \tau_{zy}}{\partial z} + F_y = 0\,

Failed to parse (Missing texvc executable; please see math/README to configure.): \frac{\partial \tau_{xz}}{\partial x} + \frac{\partial \tau_{yz}}{\partial y} + \frac{\partial \sigma_z}{\partial z} + F_z = 0\,.

Conservation of linear momentum[link]

This example (m1 = 4kg, u1 = 5m/s, m2 = 4kg, u2=0m/s) of collision shows carts in a perfectly inelastic collision—notice the center of mass of the masses m1 and m2 moves at a constant 2.5m/s throughout the motion.

The law of conservation of linear momentum is a fundamental law of nature, and it states that if no external force acts on a closed system of objects, the momentum of the closed system remains constant. One of the consequences of this is that the center of mass of any system of objects will always continue with the same velocity unless acted on by a force from outside the system.

Conservation of momentum is a mathematical consequence of the homogeneity (shift symmetry) of space (position in space is the canonical conjugate quantity to momentum). That is, conservation of momentum is equivalent to the fact that the physical laws do not depend on position.

In analytical mechanics the conservation of momentum is a consequence of translational invariance of Lagrangian in the absence of external forces. It can be proven that the total momentum is a constant of motion by making an infinitesimal translation of Lagrangian and then equating it with non translated Lagrangian. This is a special case of Noether's theorem .^[15]

In an isolated system (one where external forces are absent) the total momentum will be constant: this is implied by Newton's first law of motion. Newton's third law of motion, the law of reciprocal actions, which dictates that the forces acting between systems are equal in magnitude, but opposite in sign, is due to the conservation of momentum.

Since position in space is a vector quantity, momentum (being the canonical conjugate of position) is a vector quantity as well—it has direction. Thus, when a gun is fired, the final total momentum of the system (the gun and the bullet) is the vector sum of the momenta of these two objects. Assuming that the gun and bullet were at rest prior to firing (meaning the initial momentum of the system was zero), the final total momentum must also equal 0.

In an isolated system with only two objects, the change in momentum of one object must be equal and opposite to the change in momentum of the other object. Mathematically,

Failed to parse (Missing texvc executable; please see math/README to configure.): \Delta \mathbf{p}_1 = -\Delta \mathbf{p}_2\,.

Momentum has the special property that, in a closed system, it is always conserved, even in collisions and separations caused by explosive forces. Kinetic energy, on the other hand, is not conserved in collisions if they are inelastic. Since momentum is conserved it can be used to calculate an unknown velocity following a collision or a separation if all the other masses and velocities are known.

A common problem in physics that requires the use of this fact is the collision of two particles. Since momentum is always conserved, the sum of the momenta before the collision must equal the sum of the momenta after the collision:

Failed to parse (Missing texvc executable; please see math/README to configure.): m_1 \mathbf u_{1} + m_2 \mathbf u_{2} = m_1 \mathbf v_{1} + m_2 \mathbf v_{2}\,,

where u₁ and u₂ are the velocities before collision, and v₁ and v₂ are the velocities after collision.

Determining the final velocities from the initial velocities (and vice versa) depend on the type of collision. There are two types of collisions that conserve momentum: elastic collisions, which also conserve kinetic energy, and inelastic collisions, which do not.

Elastic collisions[link]

Example (m1 = 4kg, u1 = 5m/s, m2 = 4kg, u2=0m/s) of collision carts in perfectly elastic collision showing the equations of momentum and kinetic energy both conserved

A collision between two pool balls is a good example of an almost totally elastic collision, due to their high rigidity; a totally elastic collision exists only in theory, occurring between bodies with mathematically infinite rigidity. In addition to momentum being conserved when the two balls collide, the sum of kinetic energy before a collision must equal the sum of kinetic energy after:

Failed to parse (Missing texvc executable; please see math/README to configure.): \tfrac{1}{2} m_1 u_{1}^2 + \tfrac{1}{2} m_2 u_{2}^2 = \tfrac{1}{2} m_1 v_{1}^2 + \tfrac{1}{2} m_2 v_{2}^2\,.

In one dimension[link]

When the initial velocities are known, the final velocities for a head-on collision are given by

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{v}_{1} = \left( \frac{m_1 - m_2}{m_1 + m_2} \right) \mathbf{u}_{1} + \left( \frac{2 m_2}{m_1 + m_2} \right) \mathbf{u}_{2}\,

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{v}_{2} = \left( \frac{m_2 - m_1}{m_1 + m_2} \right) \mathbf{u}_{2} + \left( \frac{2 m_1}{m_1 + m_2} \right) \mathbf{u}_{1}\,.

This example m1=1000kg, u1=5m/s, m2=0.1kg, u2=0m/s, the final velocities are approximately given v1=4.999m/s, v2=9.999m/s

When the first body is much more massive than the other (that is, m₁ » m₂), the final velocities are approximately given by

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{v}_{1} = \mathbf{u}_{1}\,

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{v}_{2} = 2\mathbf{u}_{1} - \mathbf{u}_{2}\,.

Thus the more massive body does not change its velocity, and the less massive body travels at twice the velocity of the more massive body less its own original velocity. Assuming both masses were heading towards each other on impact, the less massive body is now therefore moving in the opposite direction at twice the speed of the more massive body plus its own original speed.

A Newton's cradle demonstrates conservation of momentum.

In a head-on collision between two bodies of equal mass (that is, m₁ = m₂), the final velocities are given by

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{v}_1 = \mathbf{u}_2\,

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{v}_2 = \mathbf{u}_1\,.

Thus the bodies simply exchange velocities. If the first body has nonzero initial velocity u₁ and the second body is at rest, then after collision the first body will be at rest and the second body will travel with velocity u₁. This phenomenon is demonstrated by Newton's cradle.

In multiple dimensions[link]

In the case of objects colliding in more than one dimension, as in oblique collisions, the velocity is resolved into orthogonal components with one component perpendicular to the plane of collision and the other component or components in the plane of collision. The velocity components in the plane of collision remain unchanged, while the velocity perpendicular to the plane of collision is calculated in the same way as the one-dimensional case.

For example, in a two-dimensional collision, the momenta can be resolved into x and y components. We can then calculate each component separately, and combine them to produce a vector result. The magnitude of this vector is the final momentum of the isolated system.

Perfectly inelastic collisions[link]

Example (m1 = 4kg, u1 = 5m/s, m2 = 4kg, u2=0m/s) of collision carts in perfectly inelastic collision showing the equations of momentum conserved and kinetic energy associated with some energy loss.

A common example of a perfectly inelastic collision is when two snowballs collide and then stick together afterwards. This equation describes the conservation of momentum:

Failed to parse (Missing texvc executable; please see math/README to configure.): m_1 \mathbf u_{1} + m_2 \mathbf u_{2} = \left( m_1 + m_2 \right) \mathbf v\,

It can be shown that a perfectly inelastic collision is one in which the maximum amount of kinetic energy is converted into other forms. For instance, if both objects stick together after the collision and move with a final common velocity, one can always find a reference frame in which the objects are brought to rest by the collision and 100% of the kinetic energy is converted. This is true even in the relativistic case and utilized in particle accelerators to efficiently convert kinetic energy into new forms of mass-energy (i.e. to create massive particles).

Coefficient of restitution[link]

The coefficient of restitution is defined as the ratio of relative velocity of separation to relative velocity of approach. It is a ratio hence it is a dimensionless quantity. The coefficient of restitution is given by:

Failed to parse (Missing texvc executable; please see math/README to configure.): C_R = \frac{v_2 - v_1}{u_1 - u_2}

for two colliding objects, where

v₁ is the scalar final velocity of the first object after impact,

v₂ is the scalar final velocity of the second object after impact,

u₁ is the scalar initial velocity of the first object before impact,

u₂ is the scalar initial velocity of the second object before impact.

A perfectly elastic collision implies that C_R is 1. So the relative velocity of approach is same as the relative velocity of separation of the colliding bodies.

Inelastic collisions have (C_R < 1). In case of a perfectly inelastic collision the relative velocity of separation of the centre of masses of the colliding bodies is 0. Hence the bodies stick together after collision.

Explosions[link]

An explosion occurs as a result of a chain reaction that transforms potential energy into kinetic energy displacing the surrounding material. Explosions do not conserve potential energy. Instead, potential energy stored in chemical, mechanical, or nuclear form, is transformed into kinetic energy, acoustic energy, and electromagnetic radiation.

See the inelastic collision page for more details.

Modern definitions of momentum[link]

Momentum in relativistic mechanics[link]

In relativistic mechanics, in order to be conserved, the momentum of an object must be defined as

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{p} = \gamma m_0\mathbf{v}\,,

where m₀ is the invariant mass of the object and γ is the Lorentz factor, given by

Failed to parse (Missing texvc executable; please see math/README to configure.): \gamma = \frac{1}{\sqrt{1 - (v/c)^2}}\,,

where v is the speed of the object and c is the speed of light. The inverse relation is given by:^[16]

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{v} = \frac{c^2 \mathbf{p}}{\sqrt{(pc)^2 + (m_0 c^2)^2}} = \frac{c^2 \mathbf{p}}{E} \,,

where Failed to parse (Missing texvc executable; please see math/README to configure.): p = \sqrt{p_x^2 + p_y^2 + p_z^2}

is the magnitude of the momentum.

Relativistic momentum can also be written as invariant mass times the object's proper velocity, defined as the rate of change of object position in the observer frame with respect to time elapsed on object clocks (i.e. object proper time). Within the domain of classical mechanics, relativistic momentum closely approximates Newtonian momentum: at low velocity, γm₀v is approximately equal to m₀v, the Newtonian expression for momentum.

A graphical representation of the interrelation of relativistic energy E, invariant mass m₀, relativistic momentum p, and relativistic mass m = γm₀.

The total energy E of a body is related to the relativistic momentum p by

Failed to parse (Missing texvc executable; please see math/README to configure.): E^2 = (pc)^2 + (m_0c^2)^2\,,

where p denotes the magnitude of p. This relativistic energy-momentum relationship holds even for massless particles such as photons; by setting m₀ = 0 it follows that

Failed to parse (Missing texvc executable; please see math/README to configure.): E = pc\,.

For both massive and massless objects, relativistic momentum is related to the de Broglie wavelength λ by

Failed to parse (Missing texvc executable; please see math/README to configure.): p = h/\lambda\,,

where h is the Planck constant.

Four-vector formulation[link]

Relativistic four-momentum as proposed by Albert Einstein arises from the invariance of four-vectors under Lorentzian translation. The four-momentum P is defined as:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{P} := (E/c, p_x , p_y ,p_z)\,,

where E = γm₀c² is the total relativistic energy of the system, and p_x, p_y, and p_z represent the x-, y-, and z-components of the relativistic momentum, respectively.

The magnitude ||P|| of the momentum four-vector is equal to m₀c, since

Failed to parse (Missing texvc executable; please see math/README to configure.): ||\mathbf{P}||^2 = (E/c)^2 - p^2 = (m_0c)^2\,.

which is invariant across all reference frames. For a closed system, the total four-momentum is conserved, which effectively combines the conservation of both momentum and energy into a single equation. For example, in the radiationless collision of two particles with rest masses Failed to parse (Missing texvc executable; please see math/README to configure.): m_1

and Failed to parse (Missing texvc executable; please see math/README to configure.): m_2
with initial velocities Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{v}_1
and Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{v}_2

, the respective final velocities Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{v}_3

and Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{v}_4
may be found from the conservation of four-momentum which states that:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{P}_1+\mathbf{P}_2=\mathbf{P}_3+\mathbf{P}_4\,,

where

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{P}_i=m_i\gamma_i(c,\mathbf{v}_i).

For elastic collisions, the rest masses remain the same (Failed to parse (Missing texvc executable; please see math/README to configure.): m_1=m_3

and Failed to parse (Missing texvc executable; please see math/README to configure.): m_2=m_4

), while for inelastic collisions, the rest masses will increase after collision due to an increase in their heat energy content. The conservation of four-momentum can be shown to be the result of the homogeneity of space–time.

Generalization of momentum[link]

Momentum is the Noether charge of translational invariance. As such, not just particles, but fields and other things can have momentum. However, where space–time is curved there is no Noether charge for translational invariance.

Momentum in quantum mechanics[link]

In quantum mechanics, momentum is defined as an operator on the wave function. The Heisenberg uncertainty principle defines limits on how accurately the momentum and position of a single observable system can be known at once. In quantum mechanics, position and momentum are conjugate variables.

For a single particle described in the position basis the momentum operator can be written as

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{p}={\hbar\over i}\nabla=-i\hbar\nabla\,,

where ∇ is the gradient operator, ħ is the reduced Planck constant, and i is the imaginary unit. This is a commonly encountered form of the momentum operator, though the momentum operator in other bases can take other forms. For example, in the momentum basis the momentum operator is represented as

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf{p}\psi(p) = p\psi(p)\,,

where the operator p acting on a wave function ψ(p) yields that wave function multiplied by the value p, in an analogous fashion to the way that the position operator acting on a wave function ψ(x) yields that wave function multiplied by the value x.

Momentum in electromagnetism[link]

Electric and magnetic fields possess momentum regardless of whether they are static or they change in time.^[17] The pressure, P, of an electrostatic (magnetostatic) field upon a metal sphere, cylindrical capacitor or ferromagnetic bar is:

Failed to parse (Missing texvc executable; please see math/README to configure.): P_{static} = {W}= \left[ {\epsilon_0 \epsilon}{\frac{{\mathbf E}^2 }{ {2}}} +{\frac{ 1 }{ {\mu_0 \mu} }} {\frac{{\mathbf B}^2}{{2}}} \right]\,,

where Failed to parse (Missing texvc executable; please see math/README to configure.): {W}\, , Failed to parse (Missing texvc executable; please see math/README to configure.): {\mathbf E}\, , Failed to parse (Missing texvc executable; please see math/README to configure.): {\mathbf B}\, , are the electromagnetic energy density, electric field, and magnetic field respectively. The electromagnetic pressure Failed to parse (Missing texvc executable; please see math/README to configure.): {P}={W}\,

may be sufficiently high to explode the capacitor.

Thus^{[clarification needed]} electric and magnetic fields do carry momentum.

Light (visible, UV, radio) is an electromagnetic wave and also has momentum. Even though photons (the particle aspect of light) have no mass, they still carry momentum. This leads to applications such as the solar sail. The calculation of the momentum of light within dielectric media is somewhat controversial (see Abraham–Minkowski controversy [2]).

Momentum is conserved in an electrodynamic system (it may change from momentum in the fields to mechanical momentum of moving parts). The treatment of the momentum of a field is usually accomplished by considering the so-called energy-momentum tensor and the change in time^{[citation needed]} of the Poynting vector integrated over some volume. This is a tensor field which has components related to the energy density and the momentum density.

The definition of canonical momentum corresponding to the momentum operator of quantum mechanics when it^{[clarification needed]} interacts with the electromagnetic field is, using the principle of least coupling^{[citation needed]}:

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf P = m\mathbf v + q\mathbf A\,

, instead of the customary

Failed to parse (Missing texvc executable; please see math/README to configure.): \mathbf p = m\mathbf v\,,

where:

A is the electromagnetic vector potential

m the charged particle's invariant mass

v its velocity

q its charge.

Non standard terminology is sometimes used for these momenta:^[18] P for canonical momentum, Π = mv for kinetic momentum, and q A for potential momentum.

Analogies between heat, mass, and momentum transfer[link]

There are some notable similarities in equations for momentum, heat, and mass transfer.^[19] The molecular transfer equations of Newton's law for fluid momentum, Fourier's law for heat, and Fick's law for mass are very similar. A great deal of effort has been devoted to developing analogies among these three transport processes so as to allow prediction of one from any of the others.

See also[link]

• Angular momentum
• Conservation law
• Force
• Impulse
• Kinetic energy
• Moment map
• Noether's theorem
• Planck momentum
• Velocity
• Galilean cannon
• Variable-mass system

Notes[link]

References[link]

• Halliday, David; Robert Resnick (1960-2007). Fundamentals of Physics. John Wiley & Sons. Chapter 9. 
• Serway, Raymond; Jewett, John (2003). Physics for Scientists and Engineers (6 ed.). Brooks Cole. ISBN 0-534-40842-7
• Stenger, Victor J. (2000). Timeless Reality: Symmetry, Simplicity, and Multiple Universes. Prometheus Books. Chpt. 12 in particular.
• Tipler, Paul (1998). Physics for Scientists and Engineers: Vol. 1: Mechanics, Oscillations and Waves, Thermodynamics (4th ed.). W. H. Freeman. ISBN 1-57259-492-6
• Hand, Louis N.; Finch, Janet D.. Analytical Mechanics. Cambridge University Press. Chapter 4. 

External links[link]

Look up momentum in Wiktionary, the free dictionary.

• Conservation of momentum – A chapter from an online textbook

Richard Garriott de Cayeux
Born	(1961-07-04) July 4, 1961 (age 50) Cambridge, England, UK
Nationality	British / American
Occupation	Video game developer
Known for	Video game development Space tourism

Richard Garriott de Cayeux (born Richard Allen Garriott on July 4, 1961) is a video game developer and entrepreneur. He is also known as his alter egos Lord British in Ultima and General British in Tabula Rasa. A well-known figure in the video game industry, Garriott was originally a game designer and programmer and now engages in various aspects of computer game development and business.

On October 12, 2008, Garriott launched aboard Soyuz TMA-13 to the International Space Station as a self-funded tourist,^[1][2] returning 12 days later aboard Soyuz TMA-12.

Garriott founded a new video game development and publishing company in 2009, called Portalarium.^[3]

In 2011 he was married and changed his name to Richard Garriott de Cayeux.^[4]

Biography[link]

Early life[link]

Garriott was born in Cambridge, England to American parents, ^[5] and was raised in Nassau Bay, Texas, United States. He is the son of scientist Owen K. Garriott, who became an astronaut and flew with Skylab 3 and Space Shuttle mission STS-9. At Clear Creek High School, he convinced the school to let him create a self-directed course in programming, in which he created fantasy computer games on the school's teletype machines^[6]. In the summer of 1977, Richard's parents sent him to the University of Oklahoma for a seven-week computer camp. Shortly after he arrived, some of the other boys attending the camp introduced themselves. When Garriott replied to their greeting of "Hi" with "Hello" they decided he sounded like he was from Britain, and gave him the nickname "British". Garriott uses the name to this day for his various gaming characters, including Ultima character Lord British and Tabula Rasa character General British,^[7] however, despite his nickname and birthplace, Garriott's parents moved to Texas when he was a baby and his accent is American rather than British.^[8]

Game Design Career[link]

In the summer of 1979 he went to work at a ComputerLand store where he had his first encounter with Apple computers. He created Akalabeth for fun, but the owner of the store convinced him it might sell. He spent $200 getting a manual and a cover sheet drawn by his mom printed out, and put them in Ziploc bags to sell around the store. Although he sold less than a dozen copies at the store, one of them made it to California Pacific, who signed a deal with him. He sold over 30,000 copies, receiving $5 for each game sold. ^[9]In the fall, he entered the University of Texas at Austin, joined the school's fencing team and later joined the Society for Creative Anachronism.

In the early 1980s, Garriott developed the Ultima computer game series. Originally programmed for the Apple II, the first was published by California Pacific Computers, and sold in Ziploc plastic bags to interested parties. The second part was published by Sierra On-Line, as they were the only company that agreed to publish it in a box. By the time he developed his third installment, the games had such a large following that Garriott (along with his brother, Robert, amongst others) established Origin Systems, their own video game publisher, to handle the publishing and distribution of his title, now available on several platforms.

Garriott sold Origin to Electronic Arts in September 1992. In 1997, he coined the term Massively Multiplayer Online Role-Playing Game, MMORPG, giving a new identity to the nascent genre previously known as graphical MUDs.^[10] In 1999 and 2000, EA canceled all of Origin's new development projects, including Privateer Online, and Harry Potter Online.^[11][12] In the midst of these events, Garriott resigned from the company and returned to the industry by forming Destination Games in April 2000 with his brother and Starr Long (the producer of Ultima Online). Once Garriott's non-compete agreement with EA expired a year later, Destination partnered with NCsoft where he acted as a producer and designer of MMORPGs. After that, he became the CEO of NCsoft Austin, also known as NC Interactive.

Tabula Rasa failed to be a commercial success despite its seven-year development period. In an open letter on the Tabula Rasa Web site that was posted on November 11, 2008, Garriott announced his plans to leave NCsoft to pursue new interests sparked by his spaceflight experiences. Later, however, Garriott claimed that the letter was forged as a means of forcing him out of his position and that he had had no intention of leaving.^[13] On November 24th, NCsoft announced that it planned to end the live service of Tabula Rasa. The servers shut down on February 28, 2009, after a period of free play from January 10 onward for existing account holders.^[14]

In July 2010, an Austin District Court awarded Garriott USD$28 million in his lawsuit against NCsoft, finding that the company did not appropriately handle his departure in 2008.^[15] In October 2011, the United States Court of Appeals for the Fifth Circuit affirmed the judgment.^[16]

Garriott founded the company Portalarium in 2009 with the intent of developing and publishing games for the emerging social network market. ^[17] The company will be launching a massively multiplayer spiritual successor to the Ultima series, though Garriott has remarked that if he were to secure the rights to the "Ultima" intellectual property from Electronic Arts, the game could literally become Ultima Online 2. ^[18]

Spaceflight[link]

Richard Garriott
Space Adventures Tourist
Nationality	British / American
Born	(1961-07-04) July 4, 1961 (age 50) Cambridge, England, UK
Other occupation	Game designer
Time in space	11d 20h 35m
Missions	Soyuz TMA-13/TMA-12
Mission insignia

The income from the success of Garriott's video game career allowed him to pursue his interest in spaceflight, and the sale of Origin Systems allowed him to invest in Space Adventures and purchase the ticket to become the first private citizen to fly into space. However, Garriott lost all of his wealth in 2001 after the dot-com bubble burst, and he was forced to sell his seat to Dennis Tito.^[19]

Screen capture from Windows on Earth, used by Garriott on ISS to identify targets for Earth photography. (Coast of Peru)

On September 28, 2007, Space Adventures announced that Garriott would fly to the International Space Station in October 2008 as the sixth space tourist, reportedly paying $30 million USD.^[1][20] On October 12, 2008, Garriott became the second second-generation space traveler (after Sergei Volkov)^[21][22] and the first offspring of an American astronaut to go into space,^[1][23][21] and the second person to wear the British Union flag in space.^[24] The Soyuz docked with the station on October 14. His father Owen K. Garriott was at the Baikonur Cosmodrome in Kazakhstan for the launch of his son Richard and was in attendance when a Soyuz capsule returned with his son twelve days later.^{[citation needed]}

During his spaceflight, Garriott took part in several education outreach efforts. He is an Amateur Radio Operator (callsign W5KWQ), and during his stay on the International Space Station (ISS), communicated with students and other Amateur Radio operators using Amateur Radio.^[25] Garriott also transmitted photographs using the Amateur Radio on the International Space Station (ARISS) slow-scan television system. Garriott also placed a geocache while aboard the ISS.^[26]

Garriott also worked with the Windows on Earth project, which provides an interactive, virtual view of Earth as seen from the ISS.^[27] Garriott used Windows on Earth software to assist in the selection of locations on Earth to photograph, and the public were able to use the same online tool to track the ISS and see the view Richard was experiencing out an ISS window. Richard's photographs, along with images taken by his astronaut father Owen Garriott in 1973, will be available to the public through Windows on Earth, adding a personal element to studies of Earth and how Earth has changed over time.^[27]

Tracy Hickman wrote a screenplay for Garriott, for the first science-fiction film shot in space, Apogee of Fear.^[28]

On October 24, Russian cosmonauts of ISS Expedition 17, Sergei Volkov and Oleg Kononenko, along with space tourist Richard Garriott, aboard Soyuz TMA-12 capsule, landed safely (ideal) at 9:37 a.m. (0336GMT, 07:36 Moscow time), 55 miles north of Arkalyk, Kazakhstan. They were lifted to the Kazakhstan Baikonur space center by helicopter, and then flew to Zvezdny Gorodok (Star City), Moscow Region.^{[29][30][31][32]}

On June 3, 2009, the New York Daily News announced that Garriott would officiate at the first wedding to be held in zero gravity.^[33] The wedding took place in a specially modified Boeing 727-200 aircraft, G-Force One, operated by Zero Gravity Corp, or ZERO-G, a company offering weightless flight experiences, of which he is the co-founder.^[34]

Other accomplishments and interests[link]

Garriott bought the Luna 21 lander and the Lunokhod 2 rover (both currently on lunar surface) from the Lavochkin Association for $68,500 in December 1993 at a Sotheby's auction in New York^[35] (although the catalog incorrectly lists lot 68A as Luna 17/Lunokhod 1).^[36]

Garriott acted as corner man for professional boxer and friend Jesús Chávez in his first title defense against Erik Morales in 2004.^[37]

He is also an avid magician and magic collector, and appeared on the cover of the January 2008 issue of MUM, the magazine of the Society of American Magicians.^[38]

Garriott built a haunted house/museum at his residence called Britannia Manor in Austin, Texas. He also promotes private space flight as vice-chairman of the board of directors for Space Adventures and as a trustee of the X PRIZE Foundation.^[39]

Awards[link]

Garriott became the ninth inductee into the Academy of Interactive Arts and Sciences' Hall of Fame in 2006.

Gameography[link]

References[link]

External links[link]

Wikiquote has a collection of quotations related to: Richard Garriott

Wikimedia Commons has media related to: Richard Garriott

• Portalarium
• Official website
• Richard Garriott on Twitter
• Richard Garriott at the Internet Movie Database
• Blog and details about Garriott's spaceflight
• Facebook page for Richard Garriott de Cayeux
• Spacefacts biography of Richard Garriott
• Richard Garriott interview with Next Generation
• Richard Garriott interview on UORadio
• Biography of Garriott from DragonCon.org^{[dead link]}
• Interview with Garriott in Austin Chronicle from 2000^{[dead link]}
• Munchkin Village mayor tries to go to space: Computer programmer touts commercial space tourism (The Daily Texan, 7/19/2005)
• Interview with Richard Garriott on space tourism (The Space Review, 8/8/2005)
• The Dot Eaters article featuring a history of Garriott/Lord British, his games, and Origin.
• Interview with Garriott on space and Operation Immortality featuring footage of Richard training.
• Windows on Earth
• MSNBC article entitled "Postcards From Space" about the amateur radio SSTV images sent from the ISS by Richard Garriott
• BBC Breakfast News video interview with Richard Garriott filmed about 10 weeks prior to his space mission.

Gwendolyn "Gwen" Stacy^[1][2] appears as a supporting character in Marvel Comics' Spider-Man series. Created by writer Stan Lee and artist Steve Ditko, she first appeared in The Amazing Spider-Man #31 (December 1965).

A blonde college student, Gwen was originally the first love of Peter Parker (Spider-Man) before the introduction of Mary Jane Watson. The Green Goblin (Norman Osborn) killed Gwen in The Amazing Spider-Man #121 (June 1973). Both the decision to kill Gwen and the method in which Marvel implemented it remain controversial among fans, but the death became a pivotal point in both Spider-Man’s history and in American comic books in general. Many point to Gwen's death as the end of the so-called Silver Age of comics.^[3] Spider-Man writers and fans disagree about who is the character’s "one true love;" Gwen or his subsequent love-interest Mary Jane. The character was ranked 89th in Comics Buyer's Guide's "100 Sexiest Women in Comics" list.^[4]

In the 2007 feature film Spider-Man 3, Gwen is portrayed by Bryce Dallas Howard. In the upcoming reboot The Amazing Spider-Man she will be played by Emma Stone.

Fictional character biography[link]

Background[link]

Gwen first appears in The Amazing Spider-Man #31 (December 1965). Peter Parker meets Gwen while both study as undergraduates at Empire State University.^[5] Initially, with Aunt May in the hospital, Peter feels troubled and ignores her advances; insulted, she dates both Flash Thompson and Harry Osborn. Gradually, however, a romance develops; Gwen, a science major, seems to appreciate Peter's intellectual personality. In the comic books, their relationship begins almost immediately after a relationship between Peter and Betty Brant ends.

Their relationship almost ends before it begins. A mind-controlled (police) Captain George Stacy, Gwen's father, gets into a fight with Peter, which Gwen observes. Thinking Peter attacked her father, she halts the relationship. Gwen eventually learns the truth and she and Peter reconcile. Their romance becomes more complicated when Gwen's father is killed by falling debris during a battle involving Spider-Man and Doctor Octopus (The Amazing Spider-Man #90). Gwen blames Spider-Man for his death, which sets their relationship back for a while. Gwen leaves for Europe to cope with her loss. She wants Peter to ask her to marry him and convince her to stay, but his guilt stops him from proposing.

Peter goes to London to see Gwen, but is forced into action as Spider-Man and leaves without seeing Gwen. Gwen eventually realizes her error in trying to pressure Peter into marriage, so she returns to New York and they get back together.

Death[link]

In The Amazing Spider-Man #121 (June 1973), by writer Gerry Conway and penciller Gil Kane, the Green Goblin (Norman Osborn, who has identified Peter Parker as Spider-Man) holds Gwen Stacy captive on a tower of the George Washington Bridge. Spider-Man arrives to fight the Green Goblin, and when the Goblin throws Gwen Stacy off the bridge, Spider-Man catches her by her leg with a string of web. He initially thinks he has saved her, but when he pulls her back onto the bridge, he realizes she has already died. In shock and anger, Spider-Man nearly kills the Green Goblin in retaliation, but in the end chooses not to do so. The Goblin still seemingly dies when he is impaled by his own goblin glider in an attempt to kill Spider-Man, and Norman Osborn would not return for nearly three hundred issues.

The death of Gwen Stacy had an enormous impact in the world of comic-book fandom.^[6] Before her, except possibly as part of an origin story, superheroes did not fail so catastrophically; nor did a loved-one of the superhero die so suddenly without warning. Because of this, some fans and historians take the death of Gwen Stacy as one marker of the end of the period they refer to as the Silver Age of Comic Books.

In the real world, physicist James Kakalios shows in his book The Physics of Superheroes that, consistent with Newton's laws of motion, the sudden stop would have killed Gwen Stacy.^[7] The comic book Civil War: Casualties of War: Captain America/Iron Man (2007) concurred that the proximate cause of death was the sudden stop during a high-speed fall. An issue of Peter Parker/Spider-Man revisits the issue, and further confirms that Gwen died of a broken neck due to the use of the webbing.

During a battle with the Sinister Twelve, the Green Goblin captures Mary Jane and takes her to another bridge, throwing her over the side just as he had Gwen; however, this time Peter succeeds in saving MJ by using multiple web-strands, providing her with enough support to avoid any fatal injuries.^[8]

After death[link]

Gwen Stacy's death has enormous repercussions. Mary Jane Watson feels the loss of Gwen deeply and becomes a more serious person. Gwen's death also draws Peter and Mary Jane into a closer friendship, and eventually to romance.

The Green Goblin's murder of Gwen Stacy greatly elevates his status in Spider-Man's rogues' gallery. Before her death, Doctor Octopus had seemed Spider-Man's primary nemesis, but Gwen's death pushed the Green Goblin into that role.

The Jackal, Miles Warren in disguise, a former professor of Gwen's, was secretly in love with her. Following her death, Warren had grown increasingly insane and adopted the persona of the Jackal.

In the fourth and final issue of the miniseries Marvels (April 1994), photographer Phil Sheldon befriends Gwen Stacy, who has absolved Spider-Man of any blame for her father's death. Gwen's simple faith in heroes convinces Sheldon of the purpose of the "Marvels" (superheroes) - to protect innocents such as Gwen. He resolves to write a book to praise the heroes and what they should mean to humanity. But the Green Goblin kidnaps Gwen and holds her hostage to ensure that Spider-Man will challenge him. Sheldon, frantically following the resulting chase in a taxi, arrives at the George Washington Bridge in time to see Spider-Man fight the Goblin and to see Gwen accidentally knocked off the bridge and killed, despite (and tragically because of) Spider-Man's desperate attempt to save her. Sheldon's faith in the Marvels is shattered and he retires, but not before passing on the body of his work to his assistant Marcie.

Clones[link]

Approximately two years after her death,^[9] Gwen Stacy reappears in Amazing Spider-Man 144 (May 1975), perfectly healthy but with no memory of the time since her death. The Jackal has managed to create a clone of Gwen, and uses her as part of a plot against Spider-Man in the original Clone Saga. At the end of that story, Gwen’s clone leaves to find a new life for herself.

In the 1988 crossover "The Evolutionary War", the High Evolutionary, who had once been Miles Warren's teacher, captures Gwen's clone. In the process, he discovers that Warren had not in fact cloned her, but had instead created a genetic virus (the "carrion virus") that transforms already living beings. Spider-Man investigates Warren's old laboratory and identifies Carrion as a genetic weapon developed by Warren. Another former student of Warren's, Malcolm McBride, is infected with the virus and becomes the second Carrion. The High Evolutionary identifies this Gwen Stacy to Spider-Man as in fact not a clone but a woman named Joyce Delaney whom Warren had altered.

During the second Clone Saga, Gwen Stacy's clone, now married to a clone of Professor Warren named Warren Miles, sees a copy of Peter Parker's book of Spider-Man photos, Webs, and remembers (to an extent) her real history, and returns to New York City. During this storyline, she again disappears from Spider-Man's life. It was recently revealed that the Gwen Stacy clone introduced in Amazing Spider-Man #144 was in fact the second Gwen clone that Miles Warren created and has been living in London under the name Joyce Delaney. This clone was murdered by the Gwen Stacy clone known as Abby-L.^[10]

Another Gwen clone appears in The Amazing Spider-Man #399 (March 1995). This clone believes she is the real Gwen. She dies from clone degeneration in Spider-Man vol. 1, #56 (March 1995), the next issue of the story arc.

Deadpool vol.3, #0 (December 1998) reveals that the evil geneticist Arnim Zola obtained samples of the DNA of various superhumans for cloning purposes. These experiments, discovered by the mercenary Deadpool, also involve four clones of Gwen Stacy. Zola allows Deadpool to take the four Gwens to his San Francisco base of operations, where they serve and entertain him. They later die in a plane crash.^[11]

Spider-Man: Blue[link]

Gwen and (to a lesser extent) Mary Jane become the focus of the critically acclaimed^{[citation needed]} Spider-Man: Blue, a 2002 limited series by Jeph Loeb and Tim Sale that retells the beginning of Peter's relationship with the two women.

The frame narrative has Peter, several years after her death, on Valentine's Day recording a voice "letter" to his dead love.

Dead Girl[link]

In the 2006 limited series X-Statix Presents: Dead Girl, Gwen, along with Moira MacTaggert and Mockingbird, appear in Heaven as members of the Dead Sisters' Book Club. They assist Doctor Strange, Dead Girl, and a small group of dead heroes on a mission to the lower depths of Hell.^[12]

[edit] Sins Past and Sins Remembered

The story arc "Sins Past" by J. Michael Straczynski in The Amazing Spider-Man #509-514 (August 2004 - January 2005) reveals that Norman Osborn, the Green Goblin's alter ego, fathered twins, a boy and a girl, with Gwen Stacy, to whom she gave birth while in France shortly before her death. She vowed she would raise them with Peter and refused to allow Norman access to them. Seeing her as a threat to his potential heirs, the Green Goblin killed Gwen Stacy. Norman Osborn then raised Gwen's two children, a boy and a girl named Gabriel and Sarah. Due to Norman's enhanced blood, the twins aged about 2 to 3 times faster than normal and became adults within the span of a few years. Osborn told them that Peter was really their father and was responsible for their mother's death.

The twins then attack Spider-Man, and he subsequently deduces their true identities. However, in seeking to confirm it, Peter goes to Gwen's grave and digs up a sample of her DNA to compare to the twins' DNA. Spider-Man tells Mary Jane about his initial encounter with Gabriel and Sarah, whereupon Mary Jane reveals that she knew about Norman's involvement with Gwen. By the story's end, Peter has told the twins the truth. Sarah believes Peter and concludes that he would never have dug up Gwen's grave to acquire a DNA sample if he thought there was even a chance that he was their father — but Gabriel does not. Gabriel takes the Green Goblin formula and briefly becomes the Grey Goblin. His glider explodes when it is shot by Sarah and he washes up on a beach with no memory of what happened.

"Sins Remembered," a follow-up story to "Sins Past" (published in The Spectacular Spider-Man (Vol. 2) issues #23-26, December 2004-March 2005 and written by Samm Barnes with art by Scot Eaton) spins directly out of the events of Amazing Spider-Man #509-514. Spider-Man locates Sarah in Paris, where Sarah has her brother (suffering from amnesia) restrained in her home. With the help of Spider-Man and Interpol, Sarah helps build a case against a criminal called Dupres in exchange for the government's help with her rapid-aging disease. However, during this time Gabriel escapes and has yet to be seen again. This story arc was later collected as a trade paperback in 2005 as The Spectacular Spider-Man Vol. 5: Sins Remembered (ISBN 0-7851-1628-1).

Straczynski later stated that he originally wanted to make Peter Parker the father of Gwen's kids but the editors vetoed the idea. They felt that it would age Peter Parker too much if he had two adult children. The whole creative and editorial team then decided that Norman Osborn would be the father.^[13] In an e-mail to popular comic book website Newsarama, Straczynski claimed that he regretted the version of Sins Past that went to press, and that he had hoped to "retcon" it out of continuity during the events of the recent One More Day storyline: "I wanted to retcon the Gwen twins out of continuity, which was something I always assumed I could do at the end of my run. I wasn't allowed to do this, and yes, it pissed me off."^[14] In the original plans for One More Day, the story would have ended with Gwen Stacy being resurrected by Mephisto's reality-warping spell along with Harry Osborn, but it was eventually decided to let her remain dead.

Other versions[link]

In the two-issue mini-series X-Universe which detailed what happened to the rest of the Marvel Universe during the Age of Apocalypse, the Green Goblin never killed Gwen Stacy; instead she became the bodyguard of Donald Blake, who, in this reality, had never become the Mighty Thor. Sometime later in the mainstream universe in X-Man #37, the Age of Apocalypse version of Gwen is pulled from her reality to the mainstream Earth's George Washington Bridge, much to Spider-Man's shock.

In the House of M storyline, in which the Scarlet Witch alters reality to make mutants the ruling class over humans, Gwen was never killed. Instead, she married Peter Parker, and the couple had a young son. She had become a scientist, a savvy businesswoman, and a peace activist – and had a decidedly hostile relationship with chemical weapon developer Norman Osborn. Mary Jane Watson, a popular actress in this reality, played Gwen Stacy in the film adaptation of Spider-Man's life story. Gwen and her father read textual accounts of their deaths in the main universe, though they believe this simply to be the morbid imaginings of Peter Parker, who is suffering from mental health issues.^[15]

Gwen Stacy first appeared in Marvel Adventures Spider-Man #53 as a new student of Midtown High. She had transferred from her previous school after the Torino Gang, a powerful New York mob, began harassing her in an attempt to keep her father, police captain George Stacy, from arresting members of their gang. However, the Torinos continued to harass Gwen at Midtown, prompting Spider-Man to help the police take down the gang.^[16] Like her father, Gwen believes Spider-Man is a hero. She subsequently began participating in a "Spider-Man Appreciation Society" designed to foster better public opinion of Spider-Man.^[17] Gwen is also attracted to Spider-Man's alter ego Peter Parker; although she openly flirted with him, Peter began dating a different girl, Sophia "Chat" Sanduval, which made Gwen very unhappy.^[18] Later, Gwen was brainwashed by Emma Frost into believing she was dating Peter. Gwen's brainwashing wore off (or was undone by Emma), but Gwen now believes her relationship with Peter ended when he chose Chat over her,^[19] causing her to treat Chat very coldly. She has since warmed to Chat, however.^[20] Recently, Gwen began a close friendship with Carter Torino who is the grandson of the head of the Torino Gang.^[17] Their relationship is complicated by the fact that Gwen's father is still trying to take down Carter's criminal family.^[21]

In the limited series, Marvel Zombies Return, Gwen of 'Earth Z' is still a college student out with her friends Mary Jane and Harry Osborn. The zombiefied Spider-Man travels to this earth and, despite his best intentions, turns the Sinister Six. They then slay and partly consume Gwen and her friends. To stop the spread of the virus, zombified Spider-Man obliterates the bodies.^[22]

Issue #1 of Spider-Man: Fairy Tales follows the fairy tale of Little Red Riding Hood. Gwen Stacy has been previously killed by the wolf. Issue #4 is an adaption of Cinderella with Gwen as Princess Gwendolyn. She falls in love with the masked "Prince of Arachne," who is revealed to be Peter Parker, servant to Sir Osborn, but is killed during a fight between Osborn and Parker.

Gwen Stacy first appears at the end of Spider-Man Loves Mary Jane #5.She is the new girl at school and quickly becomes close friends with Peter Parker. In Spider-Man Loves Mary Jane #9, Peter and Gwen take their relationship to the next level by sharing a tender kiss, much to the dismay of Mary Jane. They date for a time, though Gwen breaks up with Peter when she learns that Mary Jane is the girl he truly loves. MJ, attempting to fix this, breaks up with Peter and reunites with Harry, but Peter cannot commit to Gwen and she is unwilling to accept him as a friend and not a boyfriend.

In the fourth issue of the comic book based on the Spider-Man Unlimited animated series, Spidey encounters a Counter-Earth version of Gwen Stacy. She helps him escape a hidden paradise known as "The Haven".

In this mini-series, Gwen Stacy again appears as the girlfriend of Peter Parker. Norman Osborn again kidnaps and attempts to kill her as a part of a plan to intimidate Peter. In a twist, the powerless Peter (with a limb crippled from a spider bite) manages to save Gwen from falling to her death.

Ultimate Gwen Stacy[link]

In the Ultimate Marvel continuity, Gwen Stacy first appears in Ultimate Spider-Man #14 (December 2001) as a teenage girl at Peter's high school. In this continuity, she has amber eyes, wears punk-style clothing, and is rebellious.^[23] In her first appearance she gives a rousing speech on 'super powers'; in the next issue she pulls a knife on Kong, a classmate who was bullying Peter. She is suspended from school temporarily. Gwen becomes friends with Peter, which leads Mary Jane Watson to believe that Gwen is vying for his affections.

Gwen is later taken in by Aunt May after her father, police captain John Stacy, is killed by a burglar wearing a Spider-Man costume. Her estranged mother does not want to take her in. Her living in the Parker house creates more tension between Peter and Mary Jane, and leads to their temporary break-up. Peter's relationship with Gwen is further complicated by her hatred of Spider-Man, whom she blames for her father's death. When Peter finds his friend Eddie Brock, Gwen confides in him about her feelings of isolation. Eddie then tries to kiss her and Gwen is shocked.

When she eventually learns that Peter is Spider-Man, the angry Gwen pulls her father's gun on him. Fortunately, he manages to convince her that he is not to blame for her father's death. Gwen runs off but returns, explaining that she is just really mad at everything at the moment and that she wouldn't have really shot him, a fact Peter already knew because his spider sense didn't go off despite Gwen's wrath. Gwen then agrees to keep his secret.

Gwen Stacy dies in Ultimate Spider-Man #62. Before her death, she made peace with Mary Jane and assured her that she never had romantic feelings for Peter, and that she considered him just as a friend. She is killed by Carnage, a vampiric monster made by the splicing of genetic material from Peter Parker, his father, and Dr. Curt Connors. Although Peter is not in the area when she dies, he still feels some responsibility for her death, as he allowed Dr. Connors to use his genetic material for experimentation. His guilt makes him decide to retire as Spider-Man for a while, but eventually he takes up his hero identity when his responsibility for the innocent becomes too great to overlook.

At the end of the arc, there was an issue that dealt with Gwen's death. Flash makes an off-color remark about Gwen's passing, and it infuriates MJ to the point where she physically attacks Flash. It is revealed that Flash had a crush on Gwen all along.

A girl seeming to be Gwen Stacy appears in Ultimate Spider-Man #98. Says Ultimate artist Mark Bagley, "Gwen’s return is integral to the Clone storyline and is basically a way to rock Peter's world...again."^[24] In this issue "Gwen" appears to have no memory of her "death" and believes she was in a hospital, from which she has escaped. In issue #100, after a raft of revelations, the stress of the situation enrages "Gwen" and she transforms into what appears to be Ultimate Carnage before leaping out the window.

In the next issue, "Richard Parker" claims that "Gwen" should not have met Peter at all, and was merely an experiment in stem cell research. This Gwen/Carnage fights with the Fantastic Four, Nick Fury, and the Spider-Slayer drones, until she is knocked unconscious by a beam of light, and taken into custody. In issue #113, Norman Osborn as the Green Goblin causes a massive prison break from the Triskelion. An inmate appearing to be 'Gwen' walks out amidst the chaos, disappearing in the shadows. It has been revealed that the creature posing as Gwen Stacy is still the original Ultimate Carnage that Spider-man faced earlier in its run. After "devouring" Gwen, this incarnation of Carnage has gone on to mimic her "essence" and now believes itself to be Gwen Stacy.^[25]

During "War of the Symbiotes", Gwen/Carnage's back story in the Triskelion is revealed. It is shown that Gwen has been taking some form of therapy with Tony Stark. However, when the Green Goblin broke out of the Triskelion, Gwen escaped and went to Peter Parker's house in a confused and terrified state, with Carnage's face on her body. During an exchange between Peter and Gwen, Eddie Brock attempts to attack Aunt May and retake his symbiote. In a rage, Spider-Man engages Venom on a nearby rooftop. During the fight, Gwen is shown to be able to use her symbiote to fight off Eddie but Eddie reabsorbs his symbiote along with the Carnage symbiote rendering Gwen Stacy an average girl. After SHIELD intervenes, SHIELD Director Danvers states that Gwen will remain in SHIELD custody. Peter and May argue for her to come back to live with them, with Tony Stark supporting the Parkers. In Ultimate Spider-Man #129, the Parkers are now helping to rebuild Gwen's life. Six months after "Ultimatum", in Ultimate Comics Spider-Man #1, Gwen is living with the Parkers again and seems to be dating Peter. However, circumstances involving the Chameleon made Gwen realize she made a mistake dating Peter and she breaks up with him.

Early in the series, Ultimate Spider-Man #25 (October 2002) paid homage to Gwen Stacy's death in the Earth-616 continuity, although Gwen herself was not involved. The Green Goblin tossed Mary Jane off the Queensboro Bridge, and Spider-Man caught her leg with his webbing, just as with Gwen. The issue ended with a cliffhanger: when Spider-Man pulled Mary Jane up, she appeared to be either unconscious or dead. The cliffhanger was resolved in the next issue when Mary Jane awoke in #26, uninjured.

[edit] What If...?

In "What If" Volume 1 number 24, Peter manages to save Gwen by jumping after her rather than catching her with a web-line. In doing this, he was able to cushion her from the impact as they hit the water and subsequently give her CPR. In the aftermath of this rescue, Gwen sees him without his mask and after explaining himself to her, Peter proposes to Gwen. She accepts. In a subsequent confrontation with the Green Goblin in his apartment, Norman Osborn finally fights off his evil side for good upon seeing his son Harry move to protect him; realizing that he cannot kill his own son, Norman returns to normal.
During a battle in the warehouse, an escaping Goblin mails to "Spider-Man's second greatest enemy" (J. Jonah Jameson) proof of Spider-Man's real identity. On the day of Peter's wedding to Gwen, Jonah has published the expose and uses it to acquire a warrant for Peter's arrest, thus forcing Peter to escape from the police mere moments after his wedding to Gwen. The shock of her nephew "being that awful Spider-Man" causes Aunt May to have a heart attack as well. As the issue ends, Gwen departs with Joe 'Robbie' Robertson, who promises Gwen that they will do whatever they can to help Peter and quits the Bugle.

In "What If Spider-Man Had Kept His Six Arms?," Spider-Man (whose six-arms mutation was permanent here) was able to prevent Gwen Stacy's death.

At the very end of Peter David's "What If: The Other" one-shot, Peter Parker, now calling himself "Poison," uses part of the Venom symbiote attached to him in a resurrection of Gwen Stacy. She takes the appearance of Carnage.

In other media[link]

Television[link]

• Gwen was deliberately excluded from the 1990s animated series, as the creators felt they could neither allow her to live nor deliberately include a character who was going to die. As a result, a variant of the bridge scene occurs with Gwen replaced by Mary Jane. Both Mary Jane and Green Goblin are cast into a dimensional void in the forty-first episode of the series. Gwen Stacy did appear in the episode "Farewell Spider-Man" voiced by Mary Kay Bergman. She appears as the fiancée of the high-tech armored Spider-Man (resembling Iron Man) from another universe.

• Gwen Stacy appears in the animated television series, The Spectacular Spider-Man, voiced by Lacey Chabert. Gwen is portrayed as Peter's best friend, though she would like to be his girlfriend. Her appearance and personality appears to be partially influenced by Debra Whitman, though Debra also appears in a minor role. She gains an internship at Dr. Curt Connors's laboratory at Empire State University with Peter and Eddie Brock. After Peter seemingly runs out of the Connors's Lab, where Gwen, Eddie and Martha Connors are attempting a serum which will restore Curt's human side after he transformed into the lizard, Gwen becomes angry with him; she forgives Peter in the episode "Competition". In the episode "Reaction," Peter (as Spider-Man) ends up saving both MJ and Gwen. She then decides to talk to Peter about Harry's condition, as he is taking the Globulin Green formula. In the episode "Intervention," after a symbiote-controlled Peter blows her off, Mary Jane gets Gwen to admit to her true feelings for Peter. In "Nature vs. Nurture," the finale of the first season, Eddie Brock becomes Venom, ties up and gags Gwen, and then suspends her from a large balloon during the Thanksgiving Day parade, hoping that she will fall to her death. While Spider-Man battles Venom, the webs holding Gwen to the float eventually snap and she is sent hurtling to the street, but she is saved when her classmates use the now-deflated balloon to catch her. In the final moments of the episode, Gwen kisses Peter for the first time, making Peter realize his unknown deep feelings for her. In season 2 however, Liz Allan's own growing affections for Peter leads him to start going out with her instead, much to Gwen's dismay. Gwen is later kidnapped by Electro and Vulture and used as a hostage by the Master Planner, who forces her father to do as he says before she is saved by Spider-Man. She soon finds herself the center of the returned Harry Osborn's attention, and winds up his girlfriend. When Venom outs Peter's identity, she finds the entire concept hilarious. Peter and Gwen are soon mobbed by a gang of reporters, several of whom believe her to be "Spider-Man's Girl." When the Green Goblin takes control of New York, Peter and Gwen finally talk, and agree to end their respective relationships so they could be together. However, the series ended before the relationship began.

Film[link]

• Gwen Stacy is portrayed by Bryce Dallas Howard in Spider-Man 3. She is a potential new love interest for Peter Parker, serving as an unintended rival to Mary Jane Watson. Gwen is a classmate and lab partner of Peter, who (as Spider-Man) rescues her early in the film from a construction crane accident. She kisses an upside-down Spider-Man which causes MJ to become angry and hurt. As Peter is at the top of Dr. Connors's quantum mechanics class, he tutors her. She considers Peter a genius and is very fond of him. She is also friends with Eddie Brock, who took pictures of her so Gwen could be a model. his relationship is short-lived, as Peter Parker, under the influence of the symbiote, steals her from Eddie; he dances with her at the same jazz club where MJ works, but Gwen realizes that Peter is doing this to make MJ jealous, so she apologizes to Mary Jane, and leaves. Peter makes amends with Gwen since she is later present at Harry Osborn's funeral.

• Emma Stone will portray Gwen Stacy in The Amazing Spider-Man. Her character will be Peter Parker's main love interest in the film. She is first seen in the trailer working at Oscorp, where Peter gets bitten by the spider. She subsequently develops a crush on him. It is suggested in a trailer that Gwen might know that Peter is Spider-Man as she is seen to be appearing to patch up a wound.

Video games[link]

• Gwen Stacy, along with her dad is briefly mentioned in Spider-Man: Edge of Time. When the futuristic Peter Parker reveals his plans to Spider-Man 2099, he mentions he can save the lives of Uncle Ben, Gwen Stacy, George Stacy, and countless others.
• Gwen Stacy will appear in The Amazing Spider-Man based on the film.

See also[link]

• The Night Gwen Stacy Died
• Spider-Man supporting characters
• Portrayal of women in comics
• Women in Refrigerators

References[link]

External links[link]

• The Grand Comics Database
• The Unofficial Handbook of Marvel Comics Creators
• Physics of Superheroes 1 - Death of Gwen Stacy