Gravitational acceleration

(noun)

acceleration on an object caused by gravity; at different points on Earth, an acceleration between 9.78 and 9.82 m/s2, depending on altitude

Related Terms

Examples of Gravitational acceleration in the following topics:

  • Physics and Engineering: Fluid Pressure and Force

    • For fluids near the surface of the earth, the formula may be written as $p = \rho g h$, where $p$ is the pressure, $\rho$ is the density of the fluid, $g$ is the gravitational acceleration, and $h$ is the depth of the liquid in meters.

  • Planetary Motion According to Kepler and Newton

    • where $T$ is the period, $G$ is the gravitational constant, and $R$ is the distance between the center of mass of the two bodies.
    • Newton derived his theory of the acceleration of a planet from Kepler's first and second laws.
    • In addition, the magnitude of the acceleration is inversely proportional to the square of its distance from the Sun.
    • From this, Newton defined the force acting on a planet as the product of its mass and acceleration.

  • Vector Fields

    • Vector fields are often used to model the speed and direction of a moving fluid throughout space, for example, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from point to point.
    • A gravitational field generated by any massive object is a vector field.
    • For example, the gravitational field vectors for a spherically symmetric body would all point towards the sphere's center, with the magnitude of the vectors reducing as radial distance from the body increases.

  • Applications of Multiple Integrals

    • The gravitational potential associated with a mass distribution given by a mass measure $dm$ on three-dimensional Euclidean space $R^3$ is:
    • If there is a continuous function $\rho(x)$ representing the density of the distribution at $x$, so that $dm(x) = \rho (x)d^3x$, where $d^3x$ is the Euclidean volume element, then the gravitational potential is:

  • Higher Derivatives

    • The second derivative of $x$ is the derivative of $x'(t)$, the velocity, and by definition is the object's acceleration.
    • Acceleration is the time-rate of change of velocity, and the second-order rate of change of position.

  • Conic Sections

    • Conic sections are important in astronomy: the orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest.

  • Calculus of Vector-Valued Functions

    • Vector calculus is used extensively throughout physics and engineering, mostly with regard to electromagnetic fields, gravitational fields, and fluid flow.

  • Line Integrals

    • The line integral finds the work done on an object moving through an electric or gravitational field, for example.

  • Calculus with Parametric Curves

    • The acceleration can be written as follows with the double apostrophe signifying the second derivative:

  • Vectors in Three Dimensions

    • Vectors play an important role in physics: velocity and acceleration of a moving object and forces acting on it are all described by vectors.