An Etymological Dictionary of Astronomy and Astrophysics
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For an unbalanced force acting on a body, the acceleration produced is proportional to the force impressed; the constant of proportionality is the inertial mass of the body.

→ Newton; → second; → law; → motion.

In classical mechanics, an analytical method applied to a material sphere to determine the gravitational field at a point outside or inside the sphere. Newton's shell theorem states that: 1) The gravitational field outside a uniform spherical shell (i.e. a hollow ball) is the same as if the entire mass of the shell is concentrated at the center of the sphere. 2) The gravitational field inside the spherical shell is zero, regardless of the location within the shell. 3) Inside a solid sphere of constant density, the gravitational force varies linearly with distance from the center, being zero at the center of mass. For the relativistic generalization of this theorem, see → Birkhoff's theorem.

→ Newton; → shell; → theorem.

In a system where no external forces are present, every action force is always opposed by an equal and opposite reaction.

→ Newton; → third; → law; → motion.

The formula expressing the value of a → definite integral of a given function over an interval as the difference of the values at the end points of the interval of any → antiderivative of the function: ∫f(x)dx = F(b) - F(a), summed from x = a to x = b.

Named after Isaac → Newton and Gottfried Wilhelm Leibniz (1646-1716), who both knew the rule, although it was published later; → formula.

The incompatibility between → Galilean relativity and Mawxell's theory of → electromagnetism. Maxwell demonstrated that electrical and magnetic fields propagate as waves in space. The propagation speed of these waves in a vacuum is given by the expression c = (ε₀.μ₀)^-0.5, where ε₀ is the electric → permittivity and μ₀ is the magnetic → permeability, both → physical constants. Maxwell noticed that this value corresponds exactly to the → speed of light in vacuum. This implies, however, that the speed of light must also be a universal constant, just as are the electrical and the magnetic field constants! The problem is that → Maxwell's equations do not relate this velocity to an absolute background and specify no → reference frame against which it is measured. If we accept that the principle of relativity not only applies to mechanics, then it must also be true that Maxwell's equations apply in any → inertial frame, with the same values for the universal constants. Therefore, the speed of light should be independent of the movement of its source. This, however, contradicts the vector addition of velocities, which is a verified principle within → Newtonian mechanics. Einstein was bold enough to conclude that the principle of Newtonian relativity and Maxwell's theory of electromagnetism are incompatible! In other words, the → Galilean transformation and the → Newtonian relativity principle based on this transformation were wrong. There exists, therefore, a new relativity principle, → Einsteinian relativity, for both mechanics and electrodynamics that is based on the → Lorentz transformation.

→ Newton; → Maxwell; → incompatibility.

A method for finding roots of a → polynomial that makes explicit use of the → derivative of the function. It uses → iteration to continually improve the accuracy of the estimated root. If f(x) has a → simple root near x_n then a closer estimate to the root is x_n + 1 where x_n + 1 = x_n - f(x_n)/f'(x_n). The iteration begins with an initial estimate of the root, x₀, and continues to find x₁, x₂, . . . until a suitably accurate estimate of the position of the root is obtained. Also called → Newton's method.

→ Newton found the method in 1671, but it was not actually published until 1736; Joseph Raphson (1648-1715), English mathematician, independently published the method in 1690.

Of or pertaining to Sir Isaac Newton or to his theories or discoveries.

Newtonian, from → Newton + -ian a suffix forming adjectives.

A particular solution of the → general relativity when the → gravitational mass is small. The → space-time is then approximated to the → Minkowski's and this leads to → Newtonian mechanics.

→ Newtonian; → approximation.

Same as the → gravitational constant.

→ Newtonian; → constant; → gravitation.

The use of → Newtonian mechanics to derive homogeneous and isotropic solutions of → Einstein's field equations, which represent models of expanding Universe. The Newtonian cosmology deviates from the prediction of → general relativity in the general case of anisotropic and inhomogeneous models.

→ Newtonian; → cosmology.

Any → fluid with a constant → viscosity at a given temperature regardless of the rate of → shear.

→ Newtonian; → fluid.

The focus obtained by diverting the converging light beam of a reflecting telescope to the side of the tube.

→ Newtonian; → focus.

The limit attained by → general relativity when velocities are very smaller than the → speed of light or gravitational fields are weak. This limit corresponds to the transition between general relativity and the → Newtonian mechanics. See also → Newtonian approximation.

→ Newtonian; → limit.

A system of mechanics based on → Newton's law of gravitation and its derivatives. Same as → classical mechanics.

→ Newtonian; → mechanics.

A potential in a field of force obeying the inverse-square law such as → gravitational potential.

→ Newtonian; → potential.

The Newton's equations of motion, if they hold in any → reference frame, they are valid also in any other reference frame moving with uniform velocity relative to the first.

→ Newtonian; → principle; → relativity.

The laws of physics are unchanged under → Galilean transformation. This implies that no mechanical experiment can detect any intrinsic diff between two → inertial frames. Same as → Galilean relativity.

→ Newton; → relativity.

A telescope with a concave paraboloidal objective mirror and a small plane mirror that reflects rays from the primary mirror laterally outside the tube where the image is viewed with an eyepiece.

→ Newtonian; → telescope.

→ post-Newtonian formalism.

→ post-; → Newtonian; → expansion.

An approximate version of → general relativity that applies when the → gravitational field is → weak, and the matter → velocity is → small. Post-Newtonian formalism successfully describes the gravitational field of the solar system. It can also be applied to situations involving compact bodies with strong internal gravity, provided that the mutual gravity between bodies is weak. It also provides a foundation to calculate the → gravitational waves emitted by → compact binary star systems, as well as their orbital evolution under radiative losses. The formalism proceeds from the Newtonian description and then, step by step, adds correction terms that take into account the effects of general relativity. The correction terms are ordered in a systematic way (from the largest effects to the smallest ones), and the progression of ever smaller corrections is called the → post-Newtonian expansion.

→ post-; → Newtonian; → formalism.