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

Julius Sumner Miller (May 17, 1909 – April 14, 1987) was an American physicist and television personality. He is best known for his work on children's television programs in North America and Australia.

Off-screen[link]

Julius Sumner Miller was born in Billerica, Massachusetts the youngest of nine children. His father was Latvian, his Lithuanian mother spoke 12 languages.^[1][2]

Miller graduated with a Philosophy degree and a Master's in Physics from Boston University in 1933 but due to the Depression worked as a butler for a wealthy Boston doctor for the next two years during which time he married the doctor's maid, Alice Brown; they were to have no children, but he was to go on to reach millions of children through his popular science programs.^[2]

After making over 700 applications for employment, in 1937 he was offered a place in the Physics Department of Dillard University, a private, black liberal arts college in New Orleans. During World War II he worked as a civilian physicist for the U.S. Army Signal Corps while holding fellowships in physics at the universities of Idaho and Oklahoma and was a Ford Foundation Fellow at UCLA. In 1950 he enrolled in the Institute for Advanced Studies in Princeton, N.J. where he was a student of Albert Einstein. He became a lifelong friend of Einstein and went on to amass a collection of Einstein memorabilia that included Einstein's birth certificate. Miller also taught at Princeton but disliked large institutions, leaving in 1952 to join the Physics Department at the then small El Camino College in Torrance, California (1952–1974), to maximum student enrollments due to his great popularity^[2] and where he was instantly recognizable by his casual hair and horn-rimmed spectacles.

Miller was intolerant of misspelled words and misplaced punctuation and often angered his colleagues because he charged that the students of most faculty were not learning enough. During an interview in the 1940s, he stated that intellectual life in America was in trouble, a belief he held for the rest of his life.

"We are approaching a darkness in the land. Boys and girls are emerging from every level of school with certificates and degrees, but they can't read, write or calculate. We don't have academic honesty or intellectual rigor. Schools have abandoned integrity and rigor."^[2]

From 1963 to 1986 he was the visiting lecturer for the Physics Department of the University of Sydney ^[3] and from 1965 to 1985, the US Air Force Academy.

Television[link]

Miller began hosting his educational program, "Why Is It So?" in 1959 on KNXT Channel 2 in Los Angeles. From 1962 to 1964, Miller was Disney's "Professor Wonderful" on new introductions, filmed at Disneyland, to the syndicated reruns of The Mickey Mouse Club. During the same period, he appeared on a semi-regular basis, performing physics experiments, on Steve Allen's late night TV show in Hollywood, syndicated by Group W.

Miller's first television appearance in Australia was on Bob Sanders People in 1963. In an improvised physics demonstration he attempted to drive a straw through a raw potato. A paper straw does not have the strength but if you pinch the end, the trapped air acts as a piston, easily piercing the potato. For the first time in his career he could not get it to work and loudly exclaimed "Australian straws ain't worth a damn". The next morning, Miller arrived at his Sydney University laboratory to find one million drinking straws on the floor with a telegram reading "You might find one of these fitting your requirements". He later stated "I sat amongst the straws with straws stuck in my hair and ears. But clearly I had made a mistake. I should have said: "Australian potatoes ain’t worth a damn," and I’d have cornered the potato market!"

Shortly after, he was offered a job presenting science for ABC Television. When asked how much money he wanted he replied he never asked, he listened to an offer then "multiplied it by a factor between two and ten". Due to budget constraints the offer was withdrawn but an agreement was reached for Miller to host his own science based TV series which was filmed at the University of Sydney where he taught. Why Is It So? (his eventual stock phrase), was broadcast from 1963 to 1986 and became an instant hit known for its "cool experiments, interesting science, and fantastic hair." The 1960s program became Demonstrations in Physics (also called Science Demonstrations when it was aired on American Public television). He introduced each episode with the line: "How do you do, ladies and gentlemen, and boys and girls [sometimes adding "and teachers"]. I am Julius Sumner Miller, and physics is my business."

"My first TV series on demonstrations in physics - titled Why Is It So were now seen and heard over the land. The mail was massive. The academics were a special triumph for me. They charged me with being superficial and trivial. If I had done what they wanted my programs would be as dull as their classes! I knew my purpose well and clear: to show how Nature behaves without cluttering its beauty with abtruse mathematics. Why cloud the charm of a Chladni plate with a Bessel function?"^[4]

Miller's on-air popularity was due to an enthusiasm not normally associated with serious science. Shows would be liberally sprinkled with phrases such as "He who is not stirred by the beauty of it is already dead!" and he also liked to trick the audience. A common ploy would be to hold up an empty glass and ask guests to confirm it was empty....then chide them for not noticing it was full of air. Before each demonstration he would usually ask for a show of hands to indicate which of several results they expected. Often he would then add "hands up those who don’t care".

In 1964 Miller suffered a near fatal heart attack. Scheduled to give a lecture in Australia, he sent Sydney University a telegram saying; "I've dropped dead here." He would suffer a second heart attack in 1986.^[2]

In 1966 questions from his show with an answer to the previous day’s question were published as "Millergrams" for The Australian newspaper. 112 of these questions were published as a book "Millergrams; Some Enchanting Questions for Enquiring Minds". Further books were published in 1967: "The Second Book of Millergrams: Some More Enchanting Questions for Enquiring Minds" and 1988: "Why is it So?: The Very Best Millergrams of Professor Julius Sumner Miller".

Sample Millergram:
Q32: A juggler comes to a foot-bridge of rather flimsy design. He has in hand four balls. The maximum load is no more than the juggler himself and one ball. Can he get across the bridge by juggling the balls, always having at most one ball in the hand (and three in the air)?
A: No. A falling ball exerts a force on the hand greater than its own weight.
Rather, a 'thrown' ball exerts greater force than a 'held' one. That is, the additional force equal and opposite to that imparted to a flung ball, in addition to the juggler's mass, would exceed the bridge's tolerance (the bridge can tolerate a juggler and held ball, but not the additional downward force associated with forcing a ball 'up').

Miller appeared as "The Professor" in the Canadian series The Hilarious House of Frightenstein (1971), in a 2- to 3-minute segment each episode where he demonstrated physics experiments and explained the principles involved.

Miller was also an occasional guest in the 1970s on The Tonight Show Starring Johnny Carson in the United States.

Commercials[link]

During the 1980s Miller appeared in a famous series of Australian television commercials for Cadbury chocolate, using his stock phrase "Why is it so?", demonstrating a simple scientific principle, and describing how each block of chocolate "embraces substantial nourishment and enjoyment," and contained "a glass and a half of full-cream dairy milk."

While in Australia, Miller also appeared in ads for non-stick saucepans and Ampol Petroleum which included demonstrations of real principles of physics, albeit briefly. The ads were sufficiently popular to be played for some years after his death.

Foundations[link]

In February 1987 Miller became ill while visiting Australia and returned to the United States where he was diagnosed with leukemia. Miller died six weeks later on April 14, 1987, in San Jose, California. Miller willed his body to the University of Southern California's School of Dentistry, no services were held at his request.^[2] Professor Miller's wife, Alice Brown Miller, wanted to perpetuate the memory and achievements of her husband, and so conceived the idea of the Julius Sumner Miller Foundation, which was established in 1998.^[1]

Through an offer by Cadbury-Schweppes Pty Ltd, the Cadbury-Julius Sumner Miller Scholarship for Academic Excellence was set up to provide undergraduate scholarships in the School of Physics at the University of Sydney.

In 1993 the Australian Science Foundation for Physics established the Julius Sumner Miller Fellowship in his memory. The fellowship is currently held by Karl Kruszelnicki, best known as "Doctor Karl" for his appearances on Australian radio and television as a science commentator and author.

Popular culture[link]

In 1966 Miller devised a word game "Milleranagrams" which was published in Australia by John Sands Limited. The game, whose only materials were 200 Scrabble-like letter tiles, required players in their turn to draw an unseen tile from the "pool" then either make a word from their stock of tiles or add a tile to a word already on the table (rearrangement of the letters being permitted, hence the name) to form another word.

Miller remains popular in Australia, where he is still quoted. As Professor Julius Sumner Miller often asked, "Why is it so?" and its variations are still often used in newspaper articles that pose questions unrelated to science.^[5]

Bibliography[link]

• Millergrams; Some Enchanting Questions for Enquiring Minds, Ure Smith, 1966
• The Second Book of Millergrams: Some More Enchanting Questions for Enquiring Minds, Ure Smith, 1967
• Quiz Questions in Physics, Horwitz-Martin, Australia 1967
• Why It Is So, ABC books, 1971 ISBN 0-642-97296-6
• The Kitchen Professor, ABC books, 1972 ISBN 0-642-97352-0
• Why It Is So: Heat and Temperature, ABC books, 1973 ISBN 0-642-97496-9
• Why It Is So: Sound and Electricity & Magnetism, ABC books, 1973 ISBN 0-642-97584-1
• Why It Is So: Mechanics, Heat & Temperature, Sound and Electricity, ABC books, 1978 ISBN 0-642-97523-X
• Enchanting Questions for Enquiring Minds, Currey/O'Neil, 1982 ISBN 0-85902-280-3
• Why is it so?: the very best Millergrams of Professor Julius Sumner Miller, Australian Red Cross Society, Ringwood, Vic; Penguin Books, 1988
• The Days of My Life: an autobiography, Macmillan, 1989. ISBN 0-333-50337-6

References[link]

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (April 2008)

External links[link]

Wikiquote has a collection of quotations related to: Julius Sumner Miller

• Julius Sumner Miller Foundation
• Australian Julius Sumner Miller tribute page
• Julius Sumner Miller page at a Hilarious House of Frightenstein tribute site
• Julius Sumner Miller at TV.com
• Julius Sumner Miller at the Internet Movie Database
• Why is it so? site at Australia's ABC.net.au featuring original episodes
• http://www.physics.usyd.edu.au/foundation/Outreach/DRK/jsm.pdf Julius Sumner Miller 1909 - 1987, Physics Department, University of Sydney.

Ashley Fiolek (born October 22, 1990) is a deaf motocross racer in the Women's Motocross Association.^[1] Racing with numberplate 67, she was the 2008 WMA Pro National champion after her first professional win at the WMA Pro National Hangtown.^[2] She also won many races in the 2009 season, including Moto 1 at Hangtown and both motos at Glen Helen.^[3] She repeated as 2009 WMA Pro National Champion by finishing 7th at Steel City Raceway in Delmont, Pennsylvania on September 5, 2009. She finished this race in pain with a collarbone fracture due to a spill during the race.

Early life[link]

Fiolek was born on October 22, 1990 in Dearborn, Michigan and has been deaf since birth. Fiolek's family moved to St. Augustine, Florida so she could attend the Florida School for the Deaf and Blind, the largest school of this type in the United States. At the school, she studied ballet, ran track, and played basketball. When Fiolek finished eighth grade, her parents decided to begin homeschooling her.^[4]

As a child, she used to ride on the front of her mother's 4-wheeler or her father's bike. Her family often went to her Grandfather's house in Northern Michigan and rode through the woods for hours. Around the age of three, Fiolek's parents gave her a Yamaha PW50, a bike suitable for very young riders. She did not use the bike very often; she had trouble with the training wheels and preferred to ride with her parents.^[5]

Career[link]

Fiolek began racing at age seven.^[3][6] In April 2010 Fiolek published her first book, Kicking Up Dirt,^[7] with It Books, co-written with journalist Caroline Ryder (HarperCollins Publishers). In May 2011, Fiolek and her motocross riding were featured in a commercial for Red Bull. She is the sixth athlete sponsored by Red Bull to appear in a commercial for the energy drink.^[8]

X Games[link]

In 2009, Fiolek won her first X-Games gold medal in Women's Moto X Super X at X-Games 15.^[9] Fiolek won her second consecutive X-Games Gold Medal in Super X Women's on July 31, 2010 at X-Games 16.

In 2011, at X-Games 17, Fiolek crashed during practice and was knocked unconscious. Doctors determined she would be unable to compete.

References[link]

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]